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class="vector-toc-numb">2</span> <span>How a forward contract works</span> </div> </a> <ul id="toc-How_a_forward_contract_works-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Example_of_how_forward_prices_should_be_agreed_upon" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Example_of_how_forward_prices_should_be_agreed_upon"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Example of how forward prices should be agreed upon</span> </div> </a> <ul id="toc-Example_of_how_forward_prices_should_be_agreed_upon-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spot–forward_parity" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Spot–forward_parity"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Spot–forward parity</span> </div> </a> <button aria-controls="toc-Spot–forward_parity-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Spot–forward parity subsection</span> </button> <ul id="toc-Spot–forward_parity-sublist" class="vector-toc-list"> <li id="toc-Investment_assets" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Investment_assets"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Investment assets</span> </div> </a> <ul id="toc-Investment_assets-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Consumption_assets" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Consumption_assets"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Consumption assets</span> </div> </a> <ul id="toc-Consumption_assets-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cost_of_carry" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cost_of_carry"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Cost of carry</span> </div> </a> <ul id="toc-Cost_of_carry-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Relationship_between_the_forward_price_and_the_expected_future_spot_price" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Relationship_between_the_forward_price_and_the_expected_future_spot_price"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Relationship between the forward price and the expected future spot price</span> </div> </a> <ul id="toc-Relationship_between_the_forward_price_and_the_expected_future_spot_price-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Futures_versus_Forwards" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Futures_versus_Forwards"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Futures versus Forwards</span> </div> </a> <ul id="toc-Futures_versus_Forwards-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Outright_versus_Premium" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Outright_versus_Premium"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Outright versus Premium</span> </div> </a> <ul id="toc-Outright_versus_Premium-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rational_pricing" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Rational_pricing"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Rational pricing</span> </div> </a> <button aria-controls="toc-Rational_pricing-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Rational pricing subsection</span> </button> <ul id="toc-Rational_pricing-sublist" class="vector-toc-list"> <li id="toc-Extensions_to_the_forward_pricing_formula" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Extensions_to_the_forward_pricing_formula"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Extensions to the forward pricing formula</span> </div> </a> <ul id="toc-Extensions_to_the_forward_pricing_formula-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Theories_of_why_a_forward_contract_exists" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Theories_of_why_a_forward_contract_exists"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Theories of why a forward contract exists</span> </div> </a> <ul id="toc-Theories_of_why_a_forward_contract_exists-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Citations" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Citations"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Citations</span> </div> </a> <ul id="toc-Citations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-General_and_cited_references" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#General_and_cited_references"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>General and cited references</span> </div> </a> <ul id="toc-General_and_cited_references-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" 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Available in 33 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-33" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">33 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A4%D0%BE%D1%80%D1%83%D1%8A%D1%80%D0%B4%D0%B5%D0%BD_%D0%B4%D0%BE%D0%B3%D0%BE%D0%B2%D0%BE%D1%80" title="Форуърден договор – Bulgarian" lang="bg" hreflang="bg" data-title="Форуърден договор" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Forwardov%C3%BD_kontrakt" title="Forwardový kontrakt – Czech" lang="cs" hreflang="cs" data-title="Forwardový kontrakt" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Forward_(Wirtschaft)" title="Forward (Wirtschaft) – German" lang="de" hreflang="de" data-title="Forward (Wirtschaft)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Forvard" title="Forvard – Estonian" lang="et" hreflang="et" data-title="Forvard" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Contrato_forward" title="Contrato forward – Spanish" lang="es" hreflang="es" data-title="Contrato forward" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%BE%DB%8C%D9%85%D8%A7%D9%86_%D8%A2%D8%AA%DB%8C" title="پیمان آتی – Persian" lang="fa" hreflang="fa" data-title="پیمان آتی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Forward_(finance)" title="Forward (finance) – French" lang="fr" hreflang="fr" data-title="Forward (finance)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%84%A0%EB%8F%84_%EA%B3%84%EC%95%BD" title="선도 계약 – Korean" lang="ko" hreflang="ko" data-title="선도 계약" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%96%D5%B8%D6%80%D5%BE%D5%A1%D6%80%D5%A4%D5%A1%D5%B5%D5%AB%D5%B6_%D5%BA%D5%A1%D5%B5%D5%B4%D5%A1%D5%B6%D5%A1%D5%A3%D5%AB%D6%80" title="Ֆորվարդային պայմանագիր – Armenian" lang="hy" hreflang="hy" data-title="Ֆորվարդային պայմանագիր" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BE%E0%A4%AF%E0%A4%A6%E0%A4%BE_%E0%A4%AC%E0%A4%BE%E0%A4%9C%E0%A4%BE%E0%A4%B0" title="वायदा बाजार – Hindi" lang="hi" hreflang="hi" data-title="वायदा बाजार" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kontrak_serah" title="Kontrak serah – Indonesian" lang="id" hreflang="id" data-title="Kontrak serah" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Framvirkur_samningur" title="Framvirkur samningur – Icelandic" lang="is" hreflang="is" data-title="Framvirkur samningur" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Contratto_a_termine_(finanza)" title="Contratto a termine (finanza) – Italian" lang="it" hreflang="it" data-title="Contratto a termine (finanza)" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A4%D0%BE%D1%80%D0%B2%D0%B0%D1%80%D0%B4" title="Форвард – Kazakh" lang="kk" hreflang="kk" data-title="Форвард" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Regul%C4%93t%C4%81_tirg%C5%AB_netirgots_n%C4%81kotnes_l%C4%ABgums" title="Regulētā tirgū netirgots nākotnes līgums – Latvian" lang="lv" hreflang="lv" data-title="Regulētā tirgū netirgots nākotnes līgums" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/I%C5%A1ankstinis_sandoris" title="Išankstinis sandoris – Lithuanian" lang="lt" hreflang="lt" data-title="Išankstinis sandoris" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BE%E0%A4%AF%E0%A4%A6%E0%A5%87_%E0%A4%AC%E0%A4%BE%E0%A4%9C%E0%A4%BE%E0%A4%B0" title="वायदे बाजार – Marathi" lang="mr" hreflang="mr" data-title="वायदे बाजार" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A4%D0%BE%D1%80%D0%B2%D0%B0%D1%80%D0%B4_%D0%B3%D1%8D%D1%80%D1%8D%D1%8D" title="Форвард гэрээ – Mongolian" lang="mn" hreflang="mn" data-title="Форвард гэрээ" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%85%88%E6%B8%A1%E5%8F%96%E5%BC%95" title="先渡取引 – Japanese" lang="ja" hreflang="ja" data-title="先渡取引" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Forwardkontrakt" title="Forwardkontrakt – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Forwardkontrakt" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Forvard_(shartnoma)" title="Forvard (shartnoma) – Uzbek" lang="uz" hreflang="uz" data-title="Forvard (shartnoma)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Kontrakt_forward" title="Kontrakt forward – Polish" lang="pl" hreflang="pl" data-title="Kontrakt forward" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Contrato_a_termo" title="Contrato a termo – Portuguese" lang="pt" hreflang="pt" data-title="Contrato a termo" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Contract_forward" title="Contract forward – Romanian" lang="ro" hreflang="ro" data-title="Contract forward" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A4%D0%BE%D1%80%D0%B2%D0%B0%D1%80%D0%B4_(%D0%BA%D0%BE%D0%BD%D1%82%D1%80%D0%B0%D0%BA%D1%82)" title="Форвард (контракт) – Russian" lang="ru" hreflang="ru" data-title="Форвард (контракт)" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Forward" title="Forward – Slovak" lang="sk" hreflang="sk" data-title="Forward" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A4%D0%BE%D1%80%D0%B2%D0%B0%D1%80%D0%B4_%D1%83%D0%B3%D0%BE%D0%B2%D0%BE%D1%80" title="Форвард уговор – Serbian" lang="sr" hreflang="sr" data-title="Форвард уговор" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Termiini" title="Termiini – Finnish" lang="fi" hreflang="fi" data-title="Termiini" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/Forward_(iqtisad)" title="Forward (iqtisad) – Tatar" lang="tt" hreflang="tt" data-title="Forward (iqtisad)" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Alivre" title="Alivre – Turkish" lang="tr" hreflang="tr" data-title="Alivre" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A4%D0%BE%D1%80%D0%B2%D0%B0%D1%80%D0%B4%D0%BD%D0%B8%D0%B9_%D0%BA%D0%BE%D0%BD%D1%82%D1%80%D0%B0%D0%BA%D1%82" title="Форвардний контракт – Ukrainian" lang="uk" hreflang="uk" data-title="Форвардний контракт" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li 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href="/wiki/File:Philippine-stock-market-board.jpg" class="mw-file-description"><img alt="Looking up at a computerized stocks-value board at the Philippine Stock Exchange" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Philippine-stock-market-board.jpg/200px-Philippine-stock-market-board.jpg" decoding="async" width="200" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Philippine-stock-market-board.jpg/300px-Philippine-stock-market-board.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Philippine-stock-market-board.jpg/400px-Philippine-stock-market-board.jpg 2x" data-file-width="640" data-file-height="480" /></a></span></td></tr><tr><td class="sidebar-above" style="padding-bottom:0.7em;"> <ul><li><a href="/wiki/Market_(economics)" title="Market (economics)">Public market</a></li> <li><a href="/wiki/Exchange_(organized_market)" title="Exchange (organized market)">Exchange</a> <b>·</b> <a 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title="Stock market">Stock market</a></th></tr><tr><td class="sidebar-content hlist" style="padding:0.15em 0.5em 0.7em;"> <ul><li><a href="/wiki/Common_stock" title="Common stock">Common stock</a></li> <li><a href="/wiki/Growth_stock" title="Growth stock">Growth stock</a></li> <li><a href="/wiki/Preferred_stock" title="Preferred stock">Preferred stock</a></li> <li><a href="/wiki/Registered_share" title="Registered share">Registered share</a></li> <li><a href="/wiki/Shareholder" title="Shareholder">Shareholder</a></li> <li><a href="/wiki/Stock" title="Stock">Stock</a></li> <li><a href="/wiki/Stockbroker" title="Stockbroker">Stockbroker</a></li> <li><a href="/wiki/Stock_certificate" title="Stock certificate">Stock certificate</a></li> <li><a href="/wiki/Stock_exchange" title="Stock exchange">Stock exchange</a></li> <li><a href="/wiki/Watered_stock" title="Watered stock">Watered stock</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#ddddff;"> Other markets</th></tr><tr><td class="sidebar-content hlist" style="padding:0.15em 0.5em 0.7em;"> <div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em; line-height:1.25em;"><a href="/wiki/Derivatives_market" title="Derivatives market">Derivatives</a> <div class="hlist"><ul><li>(<a href="/wiki/Credit_derivative" title="Credit derivative">Credit derivative</a></li><li><a href="/wiki/Futures_exchange" title="Futures exchange">Futures exchange</a></li><li><a href="/wiki/Hybrid_security" title="Hybrid security">Hybrid security</a>)</li></ul></div> </div> <div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em; line-height:1.25em;padding-bottom:0.25em;"><a href="/wiki/Foreign_exchange_market" title="Foreign exchange market">Foreign exchange</a> <div class="hlist"><ul><li>(<a href="/wiki/Currency" title="Currency">Currency</a></li><li><a href="/wiki/Exchange_rate" title="Exchange rate">Exchange rate</a>)</li></ul></div> </div> <ul><li><a href="/wiki/Commodity_market" title="Commodity market">Commodity</a></li> <li><a href="/wiki/Exchange-traded_fund" title="Exchange-traded fund">ETF</a></li> <li><a href="/wiki/Money_market" title="Money market">Money</a></li> <li><a href="/wiki/Mutual_fund" title="Mutual fund">Mutual fund</a></li> <li><a href="/wiki/Option_(finance)" title="Option (finance)">Option</a></li> <li><a href="/wiki/Real_estate" title="Real estate">Real estate</a></li> <li><a href="/wiki/Reinsurance" title="Reinsurance">Reinsurance</a></li> <li><a href="/wiki/Structured_product" title="Structured product">Structured product</a></li> <li><a href="/wiki/Swap_(finance)" title="Swap (finance)">Swap (finance)</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#ddddff;"> <a href="/wiki/Over-the-counter_(finance)" title="Over-the-counter (finance)">Over-the-counter (off-exchange)</a></th></tr><tr><td class="sidebar-content hlist" style="padding:0.15em 0.5em 0.7em;"> <div class="hlist"><ul><li><a class="mw-selflink selflink">Forwards</a></li><li><a href="/wiki/Option_(finance)" title="Option (finance)">Options</a></li></ul></div> <div class="hlist"><ul><li><a href="/wiki/Spot_market" title="Spot market">Spot market</a></li><li><a href="/wiki/Swap_(finance)" title="Swap (finance)">Swaps</a></li></ul></div></td> </tr><tr><th class="sidebar-heading" style="background:#ddddff;"> <a href="/wiki/Trader_(finance)" title="Trader (finance)">Trading</a></th></tr><tr><td class="sidebar-content hlist" style="padding:0.15em 0.5em 0.7em;"> <ul><li><a href="/wiki/Financial_market_participants" title="Financial market participants">Participants</a></li> <li><a href="/wiki/Financial_regulation" title="Financial regulation">Regulation</a></li> <li><a href="/wiki/Clearing_(finance)" title="Clearing (finance)">Clearing</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#ddddff;"> Related areas</th></tr><tr><td class="sidebar-content hlist" style="padding:0.15em 0.5em 0.7em;"> <ul><li><a href="/wiki/Alternative_investment" title="Alternative investment">Alternative investment</a></li> <li><a href="/wiki/Angel_investor" title="Angel investor">Angel investor</a></li> <li><a href="/wiki/Asset_(economics)" title="Asset (economics)">Asset (economics)</a></li> <li><a href="/wiki/Asset_pricing" title="Asset pricing">Asset pricing</a></li> <li><a href="/wiki/Bank" title="Bank">Banks and banking</a></li> <li><a href="/wiki/Bull_(stock_market_speculator)" title="Bull (stock market speculator)">Bull</a></li> <li><a href="/wiki/Climate_finance" title="Climate finance">Climate finance</a></li> <li><a href="/wiki/Diversification_(finance)" title="Diversification (finance)">Diversification (finance)</a></li> <li><a href="/wiki/Eco-investing" title="Eco-investing">Eco-investing</a></li> <li><a href="/wiki/Environmental_finance" title="Environmental finance">Environmental finance</a></li> <li><a href="/wiki/Environmental,_social,_and_governance" title="Environmental, social, and governance">ESG</a></li> <li><a href="/wiki/Finance" title="Finance">Financial</a> <ul><li><a href="/wiki/Financial_analysis" title="Financial analysis">analysis</a></li> <li><a href="/wiki/Financial_analyst" title="Financial analyst">analyst</a></li> <li><a href="/wiki/Financial_asset" title="Financial asset">asset</a></li> <li><a href="/wiki/Financial_betting" title="Financial betting">betting</a></li> <li><a href="/wiki/Corporate_finance" title="Corporate finance">corporate</a></li> <li><a href="/wiki/Financial_crime" title="Financial crime">crime</a></li> <li><a href="/wiki/Financial_forecast" title="Financial forecast">forecast</a></li> <li><a href="/wiki/Personal_finance" title="Personal finance">personal</a></li> <li><a href="/wiki/Public_finance" title="Public finance">public</a></li> <li><a href="/wiki/Financial_services" title="Financial services">services</a></li></ul></li> <li><a href="/wiki/Fintech" title="Fintech">Fintech</a></li> <li><a href="/wiki/Greenwashing" title="Greenwashing">Greenwashing</a></li> <li><a href="/wiki/Growth_investing" title="Growth investing">Growth investing</a></li> <li><a href="/wiki/Impact_investing" title="Impact investing">Impact investing</a></li> <li><a href="/wiki/Investment_management" title="Investment management">Investment management</a></li> <li><a href="/wiki/Market_risk" title="Market risk">Market risk</a></li> <li><a href="/wiki/Market_trend" title="Market trend">Market trend</a></li> <li><a href="/wiki/Speculative_attack" title="Speculative attack">Speculative attack</a></li> <li><a href="/wiki/Sustainable_development_goals" class="mw-redirect" title="Sustainable development goals">Sustainable development goals</a></li> <li><a href="/wiki/Sustainable_finance" title="Sustainable finance">Sustainable finance</a></li></ul></td> </tr><tr><td class="sidebar-navbar" style="border-top:1px solid #aaa;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Financial_markets" title="Template:Financial markets"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Financial_markets" title="Template talk:Financial markets"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Financial_markets" title="Special:EditPage/Template:Financial markets"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>In <a href="/wiki/Finance" title="Finance">finance</a>, a <b>forward contract</b>, or simply a <b>forward</b>, is a non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed on in the contract, making it a type of <a href="/wiki/Derivative_(finance)" title="Derivative (finance)">derivative instrument</a>.<sup id="cite_ref-hull_1-0" class="reference"><a href="#cite_note-hull-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The party agreeing to buy the underlying asset in the future assumes a <a href="/wiki/Long_position" class="mw-redirect" title="Long position">long position</a>, and the party agreeing to sell the asset in the future assumes a <a href="/wiki/Short_position" class="mw-redirect" title="Short position">short position</a>. The price agreed upon is called the <i>delivery price</i>, which is equal to the <a href="/wiki/Forward_price" title="Forward price">forward price</a> at the time the contract is entered into. </p><p>The price of the underlying instrument, in whatever form, is paid before control of the instrument changes. This is one of the many forms of buy/sell orders where the time and date of trade is not the same as the <a href="/wiki/Value_date" title="Value date">value date</a> where the <a href="/wiki/Securities" class="mw-redirect" title="Securities">securities</a> themselves are exchanged. Forwards, like other derivative securities, can be used to <a href="/wiki/Hedge_(finance)" title="Hedge (finance)">hedge</a> risk (typically currency or exchange rate risk), as a means of <a href="/wiki/Speculation" title="Speculation">speculation</a>, or to allow a party to take advantage of a quality of the underlying instrument which is time-sensitive. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Payoffs">Payoffs</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=1" title="Edit section: Payoffs"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The value of a forward position <i>at maturity</i> depends on the relationship between the delivery price (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b76fce82a62ed5461908f0dc8f037de4e3686b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.066ex; height:2.176ex;" alt="{\displaystyle K}"></span>) and the underlying price (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f065368172f8e0d3167d59dbb03c41a3c8dd3ccc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.814ex; height:2.509ex;" alt="{\displaystyle S_{T}}"></span>) at that time. </p> <ul><li>For a long position this payoff is: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{T}=S_{T}-K}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>−</mo> <mi>K</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{T}=S_{T}-K}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12c0ec41f0206ec91212556e2c3e89df1a905443" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.347ex; height:2.509ex;" alt="{\displaystyle f_{T}=S_{T}-K}"></span></li> <li>For a short position, it is: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{T}=K-S_{T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mi>K</mi> <mo>−</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{T}=K-S_{T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/67e3a2043a598a6060ec9a29134909f22d01781c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.347ex; height:2.509ex;" alt="{\displaystyle f_{T}=K-S_{T}}"></span></li></ul> <p>Since the final value (at maturity) of a forward position depends on the spot price which will then be prevailing, this contract can be viewed, from a purely financial point of view, as <i>"a bet on the future spot price"</i><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Long_forward_payoff.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Long_forward_payoff.png/120px-Long_forward_payoff.png" decoding="async" width="120" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Long_forward_payoff.png/180px-Long_forward_payoff.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Long_forward_payoff.png/240px-Long_forward_payoff.png 2x" data-file-width="910" data-file-height="831" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Short_forward_payoff.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Short_forward_payoff.png/120px-Short_forward_payoff.png" decoding="async" width="120" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Short_forward_payoff.png/180px-Short_forward_payoff.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/05/Short_forward_payoff.png/240px-Short_forward_payoff.png 2x" data-file-width="910" data-file-height="831" /></a></span></div> <div class="gallerytext"></div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="How_a_forward_contract_works">How a forward contract works</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=2" title="Edit section: How a forward contract works"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Suppose that Bob wants to buy a house a year from now. At the same time, suppose that Alice currently owns a <span class="nowrap"><span data-sort-value="7005100000000000000♠"></span>$100,000</span> house that she wishes to sell a year from now. Both parties could enter into a forward contract with each other. Suppose that they both agree on the sale price in one year's time of <span class="nowrap"><span data-sort-value="7005104000000000000♠"></span>$104,000</span> (more below on why the sale price should be this amount). Alice and Bob have entered into a forward contract. Bob, because he is buying the underlying, is said to have entered a long forward contract. Conversely, Alice will have the short forward contract. </p><p>At the end of one year, suppose that the current market valuation of Alice's house is <span class="nowrap"><span data-sort-value="7005110000000000000♠"></span>$110,000</span>. Then, because Alice is obliged to sell to Bob for only <span class="nowrap"><span data-sort-value="7005104000000000000♠"></span>$104,000</span>, Bob will make a profit of <span class="nowrap"><span data-sort-value="7003600000000000000♠"></span>$6,000</span>. To see why this is so, one needs only to recognize that Bob can buy from Alice for <span class="nowrap"><span data-sort-value="7005104000000000000♠"></span>$104,000</span> and immediately sell to the market for <span class="nowrap"><span data-sort-value="7005110000000000000♠"></span>$110,000</span>. Bob has made the difference in profit. In contrast, Alice has made a potential loss of <span class="nowrap"><span data-sort-value="7003600000000000000♠"></span>$6,000</span>, and an actual profit of <span class="nowrap"><span data-sort-value="7003400000000000000♠"></span>$4,000</span>. </p><p>The similar situation works among currency forwards, in which one party opens a forward contract to buy or sell a currency (e.g. a contract to buy Canadian dollars) to expire/settle at a future date, as they do not wish to be exposed to exchange rate/currency risk over a period of time. As the exchange rate between U.S. dollars and Canadian dollars fluctuates between the trade date and the earlier of the date at which the contract is closed or the expiration date, one party gains and the counterparty loses as one currency strengthens against the other. Sometimes, the buy forward is opened because the investor will actually need Canadian dollars at a future date such as to pay a debt owed that is denominated in Canadian dollars. Other times, the party opening a forward does so, not because they need Canadian dollars nor because they are hedging currency risk, but because they are speculating on the currency, expecting the exchange rate to move favorably to generate a gain on closing the contract. </p><p>In a currency forward, the <a href="/wiki/Notional_amount" title="Notional amount">notional amounts</a> of currencies are specified (ex: a contract to buy <span class="nowrap"><span data-sort-value="7002100000000000000♠"></span>$100</span> million Canadian dollars equivalent to, say <span style="white-space: nowrap">US$75.2 million</span> at the current rate—these two amounts are called the notional amount(s)). While the notional amount or reference amount may be a large number, the cost or margin requirement to command or open such a contract is considerably less than that amount, which refers to the <a href="/wiki/Leverage_(finance)" title="Leverage (finance)">leverage</a> created, which is typical in <a href="/wiki/Derivative_(finance)" title="Derivative (finance)">derivative</a> contracts. </p> <div class="mw-heading mw-heading2"><h2 id="Example_of_how_forward_prices_should_be_agreed_upon">Example of how forward prices should be agreed upon</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=3" title="Edit section: Example of how forward prices should be agreed upon"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Continuing on the example above, suppose now that the initial price of Alice's house is <span class="nowrap"><span data-sort-value="7005100000000000000♠"></span>$100,000</span> and that Bob enters into a forward contract to buy the house one year from today. But since Alice knows that she can immediately sell for <span class="nowrap"><span data-sort-value="7005100000000000000♠"></span>$100,000</span> and place the proceeds in the bank, she wants to be compensated for the delayed sale. Suppose that the risk free rate of return R (the bank rate) for one year is 4%. Then the money in the bank would grow to <span class="nowrap"><span data-sort-value="7005104000000000000♠"></span>$104,000</span>, risk free. So Alice would want at least <span class="nowrap"><span data-sort-value="7005104000000000000♠"></span>$104,000</span> one year from now for the contract to be worthwhile for her – the <a href="/wiki/Opportunity_cost" title="Opportunity cost">opportunity cost</a> will be covered. </p> <div class="mw-heading mw-heading2"><h2 id="Spot–forward_parity"><span id="Spot.E2.80.93forward_parity"></span>Spot–forward parity</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=4" title="Edit section: Spot–forward parity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Forward_price" title="Forward price">Forward price</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Cost_of_carry" title="Cost of carry">Cost of carry</a> and <a href="/wiki/Convenience_yield" title="Convenience yield">convenience yield</a></div> <p>For <a href="/wiki/Market_liquidity" title="Market liquidity">liquid assets</a> ("tradeables"), spot–forward parity provides the link between the spot market and the forward market. It describes the relationship between the spot and forward price of the underlying asset in a forward contract. While the overall effect can be described as the <i>cost of carry</i>, this effect can be broken down into different components, specifically whether the asset: </p> <ul><li>pays income, and if so whether this is on a discrete or continuous basis</li> <li>incurs storage costs</li> <li>is regarded as <ul><li>an <i>investment asset</i>, i.e. an asset held primarily for investment purposes (e.g. gold, financial securities);</li> <li>or a <i>consumption asset</i>, i.e. an asset held primarily for consumption (e.g. oil, iron ore etc.)</li></ul></li></ul> <div class="mw-heading mw-heading3"><h3 id="Investment_assets">Investment assets</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=5" title="Edit section: Investment assets"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For an asset that provides <b>no income</b>, the relationship between the current forward (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f58df5f4307605e8fa07ae29d6262393b3b0c19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.549ex; height:2.509ex;" alt="{\displaystyle F_{0}}"></span>) and spot (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebe0ac45a38c4437bd2689a14ec434cd499e7e49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.479ex; height:2.509ex;" alt="{\displaystyle S_{0}}"></span>) prices is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{0}=S_{0}e^{rT}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mi>T</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{0}=S_{0}e^{rT}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e5981fedbab73dc903d42a12c9d84ef13e6daac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.341ex; height:3.009ex;" alt="{\displaystyle F_{0}=S_{0}e^{rT}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> is the continuously compounded risk free rate of return, and <i>T</i> is the time to maturity. The intuition behind this result is that given you want to own the asset at time <i>T</i>, there should be no difference in a perfect capital market between buying the asset today and holding it and buying the forward contract and taking delivery. Thus, both approaches must cost the same in present value terms. For an arbitrage proof of why this is the case, see <a class="mw-selflink-fragment" href="#Rational_pricing">Rational pricing</a> below. </p><p>For an asset that pays <b>known income</b>, the relationship becomes: </p> <ul><li>Discrete: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{0}=(S_{0}-I)e^{rT}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>I</mi> <mo stretchy="false">)</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mi>T</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{0}=(S_{0}-I)e^{rT}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d606dab1e84dfdf2faa58542cbb5a62bce4d920f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.162ex; height:3.176ex;" alt="{\displaystyle F_{0}=(S_{0}-I)e^{rT}}"></span></li> <li>Continuous: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{0}=S_{0}e^{(r-q)T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>r</mi> <mo>−</mo> <mi>q</mi> <mo stretchy="false">)</mo> <mi>T</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{0}=S_{0}e^{(r-q)T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd0253a96d829446f831b1ffbec28a602895f49f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.655ex; height:3.176ex;" alt="{\displaystyle F_{0}=S_{0}e^{(r-q)T}}"></span></li></ul> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/705a4b880769ca31b1b5e6692b7ec32de96ce88b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.625ex; height:2.176ex;" alt="{\displaystyle I=}"></span> the present value of the discrete income at time <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{0}<T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo><</mo> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{0}<T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3a2da029d2a02ab7ab8468aad13a97135b4470a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.629ex; height:2.509ex;" alt="{\displaystyle t_{0}<T}"></span>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q\%p.a.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> <mi mathvariant="normal">%</mi> <mi>p</mi> <mo>.</mo> <mi>a</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q\%p.a.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a07d0972f31a2a34f2b621c450fadce5dbfe237e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.085ex; height:2.676ex;" alt="{\displaystyle q\%p.a.}"></span> is the continuously compounded dividend yield over the life of the contract. The intuition is that when an asset pays income, there is a benefit to holding the asset rather than the forward because you get to receive this income. Hence the income (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> or <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06809d64fa7c817ffc7e323f85997f783dbdf71d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.07ex; height:2.009ex;" alt="{\displaystyle q}"></span>) must be subtracted to reflect this benefit. An example of an asset which pays discrete income might be a <a href="/wiki/Stock" title="Stock">stock</a>, and an example of an asset which pays a continuous yield might be a <a href="/wiki/Foreign_currency" class="mw-redirect" title="Foreign currency">foreign currency</a> or a <a href="/wiki/Stock_index" class="mw-redirect" title="Stock index">stock index</a>. </p><p>For investment assets which are <b>commodities</b>, such as <a href="/wiki/Gold" title="Gold">gold</a> and <a href="/wiki/Silver" title="Silver">silver</a>, storage costs must also be considered. Storage costs can be treated as 'negative income', and like income can be discrete or continuous. Hence with storage costs, the relationship becomes: </p> <ul><li>Discrete: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{0}=(S_{0}+U)e^{rT}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>U</mi> <mo stretchy="false">)</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mi>T</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{0}=(S_{0}+U)e^{rT}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3946c7a8a6b32c643c778ff912af3486f38aaeab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.773ex; height:3.176ex;" alt="{\displaystyle F_{0}=(S_{0}+U)e^{rT}}"></span></li> <li>Continuous: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{0}=S_{0}e^{(r+u)T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>r</mi> <mo>+</mo> <mi>u</mi> <mo stretchy="false">)</mo> <mi>T</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{0}=S_{0}e^{(r+u)T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c234447863668343f658a80ee181b007417287d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.839ex; height:3.176ex;" alt="{\displaystyle F_{0}=S_{0}e^{(r+u)T}}"></span></li></ul> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5efcc08ed1ab84adbcb09b36f723a93daef6660f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.236ex; height:2.176ex;" alt="{\displaystyle U=}"></span> the present value of the discrete storage cost at time <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{0}<T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo><</mo> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{0}<T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3a2da029d2a02ab7ab8468aad13a97135b4470a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.629ex; height:2.509ex;" alt="{\displaystyle t_{0}<T}"></span>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u\%p.a.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mi mathvariant="normal">%</mi> <mi>p</mi> <mo>.</mo> <mi>a</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u\%p.a.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/485201782015bcc915554303a4a401ee3dce069b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.346ex; height:2.676ex;" alt="{\displaystyle u\%p.a.}"></span> is the continuously compounded storage cost where it is proportional to the price of the commodity, and is hence a 'negative yield'. The intuition here is that because storage costs make the final price higher, we have to add them to the spot price. </p> <div class="mw-heading mw-heading3"><h3 id="Consumption_assets">Consumption assets</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=6" title="Edit section: Consumption assets"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Consumption assets are typically raw material commodities which are used as a source of energy or in a production process, for example <a href="/wiki/Crude_oil" class="mw-redirect" title="Crude oil">crude oil</a> or <a href="/wiki/Iron_ore" title="Iron ore">iron ore</a>. Users of these consumption commodities may feel that there is a benefit from physically holding the asset in inventory as opposed to holding a forward on the asset. These benefits include the ability to "profit from" (hedge against) temporary shortages and the ability to keep a production process running,<sup id="cite_ref-hull_1-1" class="reference"><a href="#cite_note-hull-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> and are referred to as the <i>convenience yield</i>. Thus, for consumption assets, the spot-forward relationship is: </p> <ul><li>Discrete storage costs: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{0}=(S_{0}+U)e^{(r-y)T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>U</mi> <mo stretchy="false">)</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>r</mi> <mo>−</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mi>T</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{0}=(S_{0}+U)e^{(r-y)T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/978c8ac9eff1c2f633107712a8f562a030964a58" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.148ex; height:3.343ex;" alt="{\displaystyle F_{0}=(S_{0}+U)e^{(r-y)T}}"></span></li> <li>Continuous storage costs: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{0}=S_{0}e^{(r+u-y)T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>r</mi> <mo>+</mo> <mi>u</mi> <mo>−</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mi>T</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{0}=S_{0}e^{(r+u-y)T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d01d4a9bbdf2e46f72c30e991316198c9ef03c9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.934ex; height:3.176ex;" alt="{\displaystyle F_{0}=S_{0}e^{(r+u-y)T}}"></span></li></ul> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y\%p.a.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mi mathvariant="normal">%</mi> <mi>p</mi> <mo>.</mo> <mi>a</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y\%p.a.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90d9ce46f879ee6f07d47a2f53c777b49b51236d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.171ex; height:2.676ex;" alt="{\displaystyle y\%p.a.}"></span> is the convenience yield over the life of the contract. Since the convenience yield provides a benefit to the holder of the asset but not the holder of the forward, it can be modelled as a type of 'dividend yield'. However, it is important to note that the convenience yield is a non cash item, but rather reflects the market's expectations concerning future availability of the commodity. If users have low inventories of the commodity, this implies a greater chance of shortage, which means a higher convenience yield. The opposite is true when high inventories exist.<sup id="cite_ref-hull_1-2" class="reference"><a href="#cite_note-hull-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Cost_of_carry">Cost of carry</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=7" title="Edit section: Cost of carry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The relationship between the spot and forward price of an asset reflects the net cost of holding (or carrying) that asset relative to holding the forward. Thus, all of the costs and benefits above can be summarised as the <i>cost of carry</i>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span>. Hence, </p> <ul><li>Discrete: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{0}=(S_{0}+U-I)e^{(r-y)T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>U</mi> <mo>−</mo> <mi>I</mi> <mo stretchy="false">)</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>r</mi> <mo>−</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mi>T</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{0}=(S_{0}+U-I)e^{(r-y)T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a233c53f9aa899459770f49e7a5a0a3240b239f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.16ex; height:3.343ex;" alt="{\displaystyle F_{0}=(S_{0}+U-I)e^{(r-y)T}}"></span></li> <li>Continuous: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{0}=S_{0}e^{cT},{\text{ where }}c=r-q+u-y.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>T</mi> </mrow> </msup> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> where </mtext> </mrow> <mi>c</mi> <mo>=</mo> <mi>r</mi> <mo>−</mo> <mi>q</mi> <mo>+</mo> <mi>u</mi> <mo>−</mo> <mi>y</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{0}=S_{0}e^{cT},{\text{ where }}c=r-q+u-y.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c6b2b4650aa1ca3a81116cb774794952c678f13" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:37.33ex; height:3.009ex;" alt="{\displaystyle F_{0}=S_{0}e^{cT},{\text{ where }}c=r-q+u-y.}"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Relationship_between_the_forward_price_and_the_expected_future_spot_price">Relationship between the forward price and the expected future spot price</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=8" title="Edit section: Relationship between the forward price and the expected future spot price"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Normal_backwardation" title="Normal backwardation">Normal backwardation</a> and <a href="/wiki/Contango" title="Contango">Contango</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Contangobackwardation.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Contangobackwardation.png/232px-Contangobackwardation.png" decoding="async" width="232" height="172" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Contangobackwardation.png/348px-Contangobackwardation.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Contangobackwardation.png/464px-Contangobackwardation.png 2x" data-file-width="1331" data-file-height="986" /></a><figcaption></figcaption></figure> <p>The market's opinion about what the spot price of an asset will be in the future is the <i>expected future spot price</i>.<sup id="cite_ref-hull_1-3" class="reference"><a href="#cite_note-hull-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Hence, a key question is whether or not the current forward price actually predicts the respective spot price in the future. There are a number of different hypotheses which try to explain the relationship between the current forward price, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f58df5f4307605e8fa07ae29d6262393b3b0c19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.549ex; height:2.509ex;" alt="{\displaystyle F_{0}}"></span> and the expected future spot price, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E(S_{T})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(S_{T})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/573abccc845f291b0396841a7300de6b73212477" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.399ex; height:2.843ex;" alt="{\displaystyle E(S_{T})}"></span>. </p><p>The economists <a href="/wiki/John_Maynard_Keynes" title="John Maynard Keynes">John Maynard Keynes</a> and <a href="/wiki/John_Hicks" title="John Hicks">John Hicks</a> argued that in general, the natural hedgers of a commodity are those who wish to sell the commodity at a future point in time.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Thus, hedgers will collectively hold a net short position in the forward market. The other side of these contracts are held by speculators, who must therefore hold a net long position. Hedgers are interested in reducing risk, and thus will accept losing money on their forward contracts. Speculators on the other hand, are interested in making a profit, and will hence only enter the contracts if they <i>expect</i> to make money. Thus, if speculators are holding a net long position, it must be the case that the expected future spot price is greater than the forward price. </p><p>In other words, the expected payoff to the speculator at maturity is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E(S_{T}-K)=E(S_{T})-K}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>−</mo> <mi>K</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>E</mi> <mo stretchy="false">(</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>−</mo> <mi>K</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(S_{T}-K)=E(S_{T})-K}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f08d908e8086320d6ce7867c33bb246e31361ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.709ex; height:2.843ex;" alt="{\displaystyle E(S_{T}-K)=E(S_{T})-K}"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b76fce82a62ed5461908f0dc8f037de4e3686b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.066ex; height:2.176ex;" alt="{\displaystyle K}"></span> is the delivery price at maturity</dd></dl> <p>Thus, if the speculators expect to profit, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E(S_{T})-K>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>−</mo> <mi>K</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(S_{T})-K>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f91d8d872923aee4096f6bb8392c6bcb3844e320" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.566ex; height:2.843ex;" alt="{\displaystyle E(S_{T})-K>0}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E(S_{T})>K}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>></mo> <mi>K</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(S_{T})>K}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a0fc67210927080f26e56a73ea1bcd2e775b057" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.564ex; height:2.843ex;" alt="{\displaystyle E(S_{T})>K}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E(S_{T})>F_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>></mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(S_{T})>F_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d711ab05ee301f8350e9139b3d90c3440b02656f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.046ex; height:2.843ex;" alt="{\displaystyle E(S_{T})>F_{0}}"></span>, as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K=F_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> <mo>=</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K=F_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a800d61ede5d20e4e89479700279d2212945001" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.713ex; height:2.509ex;" alt="{\displaystyle K=F_{0}}"></span> when they enter the contract</dd></dl> <p>This market situation, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E(S_{T})>F_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>></mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(S_{T})>F_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d711ab05ee301f8350e9139b3d90c3440b02656f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.046ex; height:2.843ex;" alt="{\displaystyle E(S_{T})>F_{0}}"></span>, is referred to as <a href="/wiki/Normal_backwardation" title="Normal backwardation">normal backwardation</a>. Forward/futures prices converge with the spot price at maturity, as can be seen from the previous relationships by letting T go to 0 (see also <a href="/wiki/Basis_(options)" class="mw-redirect" title="Basis (options)">basis</a>); then normal backwardation implies that futures prices for a certain maturity are increasing over time. The opposite situation, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E(S_{T})<F_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo><</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(S_{T})<F_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0717fe62d16b4c319cfaed6a367b4b0192aff75c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.046ex; height:2.843ex;" alt="{\displaystyle E(S_{T})<F_{0}}"></span>, is referred to as <a href="/wiki/Contango" title="Contango">contango</a>. Likewise, contango implies that futures prices for a certain maturity are falling over time.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Futures_versus_Forwards">Futures versus Forwards</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=9" title="Edit section: Futures versus Forwards"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Forward contracts are <a href="/wiki/Futures_contract#Futures_versus_forwards" title="Futures contract">very similar to futures contracts</a>, except they are not exchange-traded, or defined on standardized assets.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Forwards also typically have no interim partial settlements or "true-ups" in margin requirements like futures, that is the parties do not exchange additional property securing the party at gain and the entire unrealized gain or loss builds up while the contract is open. Therefore, forward contracts have a significant <a href="/wiki/Credit_risk" title="Credit risk">counterparty risk</a> which is also the reason why they are not readily available to retail investors.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> However, being traded <a href="/wiki/Over-the-counter_(finance)" title="Over-the-counter (finance)">over the counter (OTC)</a>, forward contracts specification can be customized and may include <a href="/wiki/Mark-to-market_accounting" title="Mark-to-market accounting">mark-to-market</a> and daily margin calls. </p><p>Having no upfront cashflows is one of the advantages of a forward contract compared to its futures counterpart. Especially when the forward contract is denominated in a foreign currency, not having to post (or receive) daily settlements simplifies cashflow management.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>Compared to the futures markets it is very difficult to close out one's position, that is to rescind the forward contract. For instance while being long in a forward contract, entering short into another forward contract might cancel out delivery obligations but adds to credit risk exposure as there are now three parties involved. Closing out a contract almost always involves reaching out to the counterparty.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>Compared to their futures counterparts, forwards (especially <a href="/wiki/Forward_rate_agreement" title="Forward rate agreement">Forward Rate Agreements</a>) need <a href="/wiki/Convexity_(finance)#Convexity_adjustments" title="Convexity (finance)">convexity adjustments</a>, that is a drift term that accounts for future rate changes. In futures contracts, this risk remains constant whereas a forward contract's risk changes when rates change.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Outright_versus_Premium">Outright versus Premium</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=10" title="Edit section: Outright versus Premium"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Outright prices, as opposed to premium points or forward points, are quoted in absolute price units. Outrights are used in markets where there is no (unitary) spot price or rate for reference, or where the spot price (rate) is not easily accessible.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>Conversely, in markets with easily accessible spot prices or basis rates, in particular the <a href="/wiki/Foreign_exchange_market" title="Foreign exchange market">Foreign exchange market</a> and <a href="/wiki/Overnight_indexed_swap" title="Overnight indexed swap">OIS market</a>, forwards are usually quoted using premium points or forward points. That is using the spot price or basis rate as reference forwards are quoted as the difference in <a href="/wiki/Percentage_in_point" title="Percentage in point">pips</a> between the outright price and the spot price for FX, or the difference in <a href="/wiki/Basis_point" title="Basis point">basis points</a> between the forward rate and the basis rate for interest rate swaps and forward rate agreements.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>Note: The term <i>outright</i> is used in the futures markets in a similar way but is contrasted with futures spreads instead of premium points, which is more than just a quoting convention, and in particular involves the simultaneous transaction in two outright futures.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Rational_pricing">Rational pricing</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=11" title="Edit section: Rational pricing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e2391e6e796fbf718be3828080775ac2ac3d3d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.251ex; height:2.509ex;" alt="{\displaystyle S_{t}}"></span> is the <a href="/wiki/Spot_price" class="mw-redirect" title="Spot price">spot price</a> of an asset at time <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> is the continuously compounded rate, then the forward price at a future time <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> must satisfy <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{t,T}=S_{t}e^{r(T-t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>−</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{t,T}=S_{t}e^{r(T-t)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0d4e64b4c720767d90cb090e61a192e033351d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.65ex; height:3.509ex;" alt="{\displaystyle F_{t,T}=S_{t}e^{r(T-t)}}"></span>. </p><p>To prove this, suppose not. Then we have two possible cases. </p><p><b>Case 1:</b> Suppose that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{t,T}>S_{t}e^{r(T-t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>></mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>−</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{t,T}>S_{t}e^{r(T-t)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b1628a3b57a542c4339dab6bc74a43dd4eeffb7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.65ex; height:3.509ex;" alt="{\displaystyle F_{t,T}>S_{t}e^{r(T-t)}}"></span>. Then an investor can execute the following trades at time <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span>: </p> <ol><li>go to the bank and get a loan with amount <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e2391e6e796fbf718be3828080775ac2ac3d3d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.251ex; height:2.509ex;" alt="{\displaystyle S_{t}}"></span> at the continuously compounded rate r;</li> <li>with this money from the bank, buy one unit of asset for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e2391e6e796fbf718be3828080775ac2ac3d3d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.251ex; height:2.509ex;" alt="{\displaystyle S_{t}}"></span>;</li> <li>enter into one short forward contract costing 0. A short forward contract means that the investor owes the <a href="/wiki/Counterparty" title="Counterparty">counterparty</a> the asset at time <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span>.</li></ol> <p>The initial cost of the trades at the initial time sum to zero. </p><p>At time <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> the investor can reverse the trades that were executed at time <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span>. Specifically, and mirroring the trades 1., 2. and 3. the investor </p> <ol><li>' repays the loan to the bank. The inflow to the investor is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -S_{t}e^{r(T-t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>−</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -S_{t}e^{r(T-t)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23b2025cd316b4b02aebe8d36a1cf338db5fefcc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.425ex; height:3.176ex;" alt="{\displaystyle -S_{t}e^{r(T-t)}}"></span>;</li> <li>' settles the short forward contract by selling the asset for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{t,T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{t,T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4958c202767368cecdf6406b3c6aa3bb8686113b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.935ex; height:2.843ex;" alt="{\displaystyle F_{t,T}}"></span>. The cash inflow to the investor is now <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{t,T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{t,T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4958c202767368cecdf6406b3c6aa3bb8686113b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.935ex; height:2.843ex;" alt="{\displaystyle F_{t,T}}"></span> because the buyer receives <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f065368172f8e0d3167d59dbb03c41a3c8dd3ccc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.814ex; height:2.509ex;" alt="{\displaystyle S_{T}}"></span> from the investor.</li></ol> <p>The sum of the inflows in 1.' and 2.' equals <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{t,T}-S_{t}e^{r(T-t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>−</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{t,T}-S_{t}e^{r(T-t)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ccd17430ef83a30fc4036212354ce8dd6bede40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.392ex; height:3.509ex;" alt="{\displaystyle F_{t,T}-S_{t}e^{r(T-t)}}"></span>, which by hypothesis, is positive. This is an arbitrage profit. Consequently, and assuming that the non-arbitrage condition holds, we have a contradiction. This is called a cash and carry arbitrage because you "carry" the asset until maturity. </p><p><b>Case 2:</b> Suppose that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{t,T}<S_{t}e^{r(T-t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo><</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>−</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{t,T}<S_{t}e^{r(T-t)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e47f45165b6b09a2dfc61d38103751e736cd4837" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.65ex; height:3.509ex;" alt="{\displaystyle F_{t,T}<S_{t}e^{r(T-t)}}"></span>. Then an investor can do the reverse of what he has done above in case 1. This means selling one unit of the asset, investing this money into a bank account and entering a long forward contract costing 0. </p><p>Note: if you look at the <a href="/wiki/Convenience_yield" title="Convenience yield">convenience yield</a> page, you will see that if there are finite assets/inventory, the reverse cash and carry arbitrage is not always possible. It would depend on the elasticity of demand for forward contracts and such like. </p> <div class="mw-heading mw-heading3"><h3 id="Extensions_to_the_forward_pricing_formula">Extensions to the forward pricing formula</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=12" title="Edit section: Extensions to the forward pricing formula"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Suppose that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle FV_{T}(X)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle FV_{T}(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97f34d241ea6e6c84e06bf99859e7a3b3170203a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.275ex; height:2.843ex;" alt="{\displaystyle FV_{T}(X)}"></span> is the time value of cash flows <i>X</i> at the contract expiration time <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span>. The <a href="/wiki/Forward_price" title="Forward price">forward price</a> is then given by the formula: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{t,T}=S_{t}e^{r(T-t)}-FV_{T}({\text{all cash flows over the life of the contract}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>−</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mo>−</mo> <mi>F</mi> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>all cash flows over the life of the contract</mtext> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{t,T}=S_{t}e^{r(T-t)}-FV_{T}({\text{all cash flows over the life of the contract}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f76d3719d3cfe13bb5adaf234254ddc1fdbf4ae6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:65.514ex; height:3.509ex;" alt="{\displaystyle F_{t,T}=S_{t}e^{r(T-t)}-FV_{T}({\text{all cash flows over the life of the contract}})}"></span></dd></dl> <p>The cash flows can be in the form of <a href="/wiki/Dividend" title="Dividend">dividends</a> from the asset, or costs of maintaining the asset. </p><p>If these price relationships do not hold, there is an <a href="/wiki/Arbitrage" title="Arbitrage">arbitrage</a> opportunity for a riskless profit similar to that discussed above. One implication of this is that the presence of a forward market will force spot prices to reflect current expectations of future prices. As a result, the forward price for nonperishable commodities, securities or currency is no more a predictor of future price than the spot price is - the relationship between forward and spot prices is driven by interest rates. For perishable commodities, arbitrage does not have this </p><p>The above forward pricing formula can also be written as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{t,T}=(S_{t}-I_{t})e^{r(T-t)}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>−</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{t,T}=(S_{t}-I_{t})e^{r(T-t)}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4edf55d7e577e7e0ee686bf30c3512cc271637a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:22.536ex; height:3.509ex;" alt="{\displaystyle F_{t,T}=(S_{t}-I_{t})e^{r(T-t)}\,}"></span></dd></dl> <p>Where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc386d951e8ffae76357542f14e160621e6668b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.849ex; height:2.509ex;" alt="{\displaystyle I_{t}}"></span> is the time <i>t</i> value of all cash flows over the life of the contract. </p><p>For more details about pricing, see <a href="/wiki/Forward_price" title="Forward price">forward price</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Theories_of_why_a_forward_contract_exists">Theories of why a forward contract exists</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=13" title="Edit section: Theories of why a forward contract exists"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Allaz and Vila (1993) suggest that there is also a strategic reason (in an imperfect competitive environment) for the existence of forward trading, that is, forward trading can be used even in a world without uncertainty. This is due to firms having <a href="/wiki/Stackelberg_competition" title="Stackelberg competition">Stackelberg</a> incentives to anticipate their production through forward contracts.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=14" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/988_transaction" title="988 transaction">988 transaction</a></li> <li><a href="/wiki/Derivative_(finance)" title="Derivative (finance)">Derivative (finance)</a></li> <li><a href="/wiki/Forward_exchange_market" class="mw-redirect" title="Forward exchange market">Forward exchange market</a></li> <li><a href="/wiki/Forward_market" title="Forward market">Forward market</a></li> <li><a href="/wiki/Forward_price" title="Forward price">Forward price</a></li> <li><a href="/wiki/Futures_contract" title="Futures contract">Futures contract</a></li> <li><a href="/wiki/Hedge_(finance)" title="Hedge (finance)">Hedging</a></li> <li><a href="/wiki/Non-deliverable_forward" title="Non-deliverable forward">Non-deliverable forward</a></li> <li><a href="/wiki/Option_(finance)" title="Option (finance)">Option</a></li> <li><a href="/wiki/Swap_(finance)" title="Swap (finance)">Swap (finance)</a></li></ul> <p><b>Other types of trade contracts:</b> </p> <ul><li><a href="/wiki/Spot_price" class="mw-redirect" title="Spot price">Spot price</a></li> <li><a href="/wiki/Spot_market" title="Spot market">Spot market</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Citations">Citations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=15" title="Edit section: Citations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-hull-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-hull_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-hull_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-hull_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-hull_1-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text">John C Hull<i>, Options, Futures and Other Derivatives (6th edition)</i>, Prentice Hall: New Jersey, USA, 2006, 3</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://chicagofed.org/webpages/publications/understanding_derivatives/index.cfm">Understanding Derivatives: Markets and Infrastructure</a>, <i>Federal Reserve Bank of Chicago</i></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output 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Geert (2006). <a rel="nofollow" class="external text" href="http://www.nber.org/papers/w10595.pdf">"Facts and Fantasies about Commodity Futures"</a> <span class="cs1-format">(PDF)</span>. <i>Financial Analysts Journal</i>. <b>62</b> (2): 47–68. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2469%2Ffaj.v62.n2.4083">10.2469/faj.v62.n2.4083</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Financial+Analysts+Journal&rft.atitle=Facts+and+Fantasies+about+Commodity+Futures&rft.volume=62&rft.issue=2&rft.pages=47-68&rft.date=2006&rft_id=info%3Adoi%2F10.2469%2Ffaj.v62.n2.4083&rft.aulast=Gorton&rft.aufirst=Gary&rft.au=Rouwenhorst%2C+K.+Geert&rft_id=http%3A%2F%2Fwww.nber.org%2Fpapers%2Fw10595.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AForward+contract" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">J.M. Keynes, <i>A Treatise on Money</i>, London: Macmillan, 1930</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">J.R. Hicks, <i>Value and Capital</i>, Oxford: Clarendon Press, 1939</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.investopedia.com/articles/07/contango_backwardation.asp">Contango Vs. Normal Backwardation</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140726183442/http://www.investopedia.com/articles/07/contango_backwardation.asp">Archived</a> 2014-07-26 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, <i>Investopedia</i></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><a href="https://meta.wikimedia.org/wiki/Interwiki_map/discontinued#Wikinvest" class="extiw" title="wikinvest:Forward Contract">Forward Contract on Wikinvest</a></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.investopedia.com/ask/answers/06/forwardsandfutures.asp">"Understanding Forward Contracts vs. Futures Contracts"</a>. <i>Investopedia</i><span class="reference-accessdate">. Retrieved <span class="nowrap">28 June</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Investopedia&rft.atitle=Understanding+Forward+Contracts+vs.+Futures+Contracts&rft_id=https%3A%2F%2Fwww.investopedia.com%2Fask%2Fanswers%2F06%2Fforwardsandfutures.asp&rfr_id=info%3Asid%2Fen.wikipedia.org%3AForward+contract" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20211124111724/http://www.microrate.com/media/docs/investment/V-Guide-to-FX-Fowards.pdf">"Understanding FX Forwards"</a> <span class="cs1-format">(PDF)</span>. Archived from <a rel="nofollow" class="external text" href="http://www.microrate.com/media/docs/investment/V-Guide-to-FX-Fowards.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 24 November 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">28 June</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Understanding+FX+Forwards&rft_id=http%3A%2F%2Fwww.microrate.com%2Fmedia%2Fdocs%2Finvestment%2FV-Guide-to-FX-Fowards.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AForward+contract" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.diffen.com/difference/Forward_Contract_vs_Futures_Contract">"Forward Contract vs Futures Contract"</a>. <i>Diffen</i><span class="reference-accessdate">. Retrieved <span class="nowrap">28 June</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Diffen&rft.atitle=Forward+Contract+vs+Futures+Contract&rft_id=https%3A%2F%2Fwww.diffen.com%2Fdifference%2FForward_Contract_vs_Futures_Contract&rfr_id=info%3Asid%2Fen.wikipedia.org%3AForward+contract" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.investopedia.com/terms/c/convexity-adjustment.asp">"Convexity Adjustment Definition"</a>. <i>Investopedia</i><span class="reference-accessdate">. Retrieved <span class="nowrap">28 June</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Investopedia&rft.atitle=Convexity+Adjustment+Definition&rft_id=https%3A%2F%2Fwww.investopedia.com%2Fterms%2Fc%2Fconvexity-adjustment.asp&rfr_id=info%3Asid%2Fen.wikipedia.org%3AForward+contract" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSteiner2012" class="citation book cs1">Steiner, Bob (September 2012). <i>Key Financial Market Concepts</i> (2nd ed.). Financial Times/Prentice Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780273750284" title="Special:BookSources/9780273750284"><bdi>9780273750284</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Key+Financial+Market+Concepts&rft.edition=2nd&rft.pub=Financial+Times%2FPrentice+Hall&rft.date=2012-09&rft.isbn=9780273750284&rft.aulast=Steiner&rft.aufirst=Bob&rfr_id=info%3Asid%2Fen.wikipedia.org%3AForward+contract" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.investopedia.com/terms/f/forwardpoints.asp">"Forward Points"</a>. <i>Investopedia</i><span class="reference-accessdate">. Retrieved <span class="nowrap">29 June</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Investopedia&rft.atitle=Forward+Points&rft_id=https%3A%2F%2Fwww.investopedia.com%2Fterms%2Ff%2Fforwardpoints.asp&rfr_id=info%3Asid%2Fen.wikipedia.org%3AForward+contract" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.cmegroup.com/confluence/display/EPICSANDBOX/Instrument+Types+Available+on+CME+Globex">"Instrument Types Available on CME Globex"</a>. <i>CME Globex</i><span class="reference-accessdate">. Retrieved <span class="nowrap">29 June</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=CME+Globex&rft.atitle=Instrument+Types+Available+on+CME+Globex&rft_id=https%3A%2F%2Fwww.cmegroup.com%2Fconfluence%2Fdisplay%2FEPICSANDBOX%2FInstrument%2BTypes%2BAvailable%2Bon%2BCME%2BGlobex&rfr_id=info%3Asid%2Fen.wikipedia.org%3AForward+contract" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAllazVila1993" class="citation journal cs1">Allaz, Blaise; Vila, Jean-Luc (1993). "Cournot Competition, Forward Markets and Efficiency". <i>Journal of Economic Theory</i>. <b>59</b> (1): 1–16. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1006%2Fjeth.1993.1001">10.1006/jeth.1993.1001</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Economic+Theory&rft.atitle=Cournot+Competition%2C+Forward+Markets+and+Efficiency&rft.volume=59&rft.issue=1&rft.pages=1-16&rft.date=1993&rft_id=info%3Adoi%2F10.1006%2Fjeth.1993.1001&rft.aulast=Allaz&rft.aufirst=Blaise&rft.au=Vila%2C+Jean-Luc&rfr_id=info%3Asid%2Fen.wikipedia.org%3AForward+contract" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="General_and_cited_references">General and cited references</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=16" title="Edit section: General and cited references"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>John C. Hull (2000), <i>Options, Futures and Other Derivatives</i>, Prentice-Hall.</li> <li>Abraham Lioui & Patrice Poncet (March 30, 2005), <i>Dynamic Asset Allocation with Forwards and Futures</i>, Springer</li> <li>Keith Redhead (31 October 1996), <i>Financial Derivatives: An Introduction to Futures, Forwards, Options and Swaps</i>, Prentice-Hall</li> <li><a href="https://meta.wikimedia.org/wiki/Interwiki_map/discontinued#Wikinvest" class="extiw" title="wikinvest:Forward Contract">Forward Contract on Wikinvest</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Forward_contract&action=edit&section=17" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Allaz, B. and Vila, J.-L., Cournot competition, futures markets and efficiency, Journal of Economic Theory 59,297-308.</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20130812135118/http://www.chicagofed.org/webpages/publications/understanding_derivatives/index.cfm">Understanding Derivatives: Markets and Infrastructure</a> Federal Reserve Bank of Chicago, Financial Markets Group</li> <li><a rel="nofollow" class="external text" href="https://www.investopedia.com/terms/f/forwardcontract.asp">Forward Contract Definition - Investopedia</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output 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style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Derivatives_market" title="Template:Derivatives market"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Derivatives_market" title="Template talk:Derivatives market"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Derivatives_market" title="Special:EditPage/Template:Derivatives market"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Derivatives_market" style="font-size:114%;margin:0 4em"><a href="/wiki/Derivatives_market" title="Derivatives market">Derivatives market</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div><a href="/wiki/Derivative_(finance)" title="Derivative (finance)">Derivative (finance)</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Option_(finance)" title="Option (finance)">Options</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Terms</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Delta_neutral" title="Delta neutral">Delta neutral</a></li> <li><a href="/wiki/Exercise_(options)" title="Exercise (options)">Exercise</a></li> <li><a href="/wiki/Expiration_(options)" title="Expiration (options)">Expiration</a></li> <li><a href="/wiki/Moneyness" title="Moneyness">Moneyness</a></li> <li><a href="/wiki/Open_interest" title="Open interest">Open interest</a></li> <li><a href="/wiki/Pin_risk" title="Pin risk">Pin risk</a></li> <li><a href="/wiki/Risk-free_interest_rate" class="mw-redirect" title="Risk-free interest rate">Risk-free interest rate</a></li> <li><a href="/wiki/Strike_price" title="Strike price">Strike price</a></li> <li><a href="/wiki/Synthetic_position" title="Synthetic position">Synthetic position</a></li> <li><a href="/wiki/Greeks_(finance)" title="Greeks (finance)">the Greeks</a></li> <li><a href="/wiki/Volatility_(finance)" title="Volatility (finance)">Volatility</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Vanilla_option" class="mw-redirect" title="Vanilla option">Vanillas</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/American_option" class="mw-redirect" title="American option">American</a></li> <li><a href="/wiki/Bond_option" title="Bond option">Bond option</a></li> <li><a href="/wiki/Call_option" title="Call option">Call</a></li> <li><a href="/wiki/Employee_stock_option" title="Employee stock option">Employee stock option</a></li> <li><a href="/wiki/European_option" class="mw-redirect" title="European option">European</a></li> <li><a href="/wiki/Fixed_income" title="Fixed income">Fixed income</a></li> <li><a href="/wiki/Foreign_exchange_option" title="Foreign exchange option">FX</a></li> <li><a href="/wiki/Option_style" title="Option style">Option styles</a></li> <li><a href="/wiki/Put_option" title="Put option">Put</a></li> <li><a href="/wiki/Warrant_(finance)" title="Warrant (finance)">Warrants</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Exotic_option" title="Exotic option">Exotics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Asian_option" title="Asian option">Asian</a></li> <li><a href="/wiki/Barrier_option" title="Barrier option">Barrier</a></li> <li><a href="/wiki/Basket_option" title="Basket option">Basket</a></li> <li><a href="/wiki/Binary_option" title="Binary option">Binary</a></li> <li><a href="/wiki/Callable_bull/bear_contract" title="Callable bull/bear contract">Callable bull/bear contract</a></li> <li><a href="/wiki/Chooser_option" title="Chooser option">Chooser</a></li> <li><a href="/wiki/Cliquet_option" title="Cliquet option">Cliquet</a></li> <li><a href="/wiki/Commodore_option" title="Commodore option">Commodore</a></li> <li><a href="/wiki/Compound_option" title="Compound option">Compound</a></li> <li><a href="/wiki/Forward_start_option" title="Forward start option">Forward start</a></li> <li><a href="/wiki/Interest_rate_option" title="Interest rate option">Interest rate</a></li> <li><a href="/wiki/Lookback_option" title="Lookback option">Lookback</a></li> <li>Mountain range</li> <li><a href="/wiki/Rainbow_option" title="Rainbow option">Rainbow</a></li> <li><a href="/wiki/Spread_option" title="Spread option">Spread</a></li> <li><a href="/wiki/Swaption" title="Swaption">Swaption</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Options_strategy" title="Options strategy">Strategies</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Backspread" title="Backspread">Backspread</a></li> <li><a href="/wiki/Box_spread_(options)" class="mw-redirect" title="Box spread (options)">Box spread</a></li> <li><a href="/wiki/Butterfly_(options)" title="Butterfly (options)">Butterfly</a></li> <li><a href="/wiki/Calendar_spread" title="Calendar spread">Calendar spread</a></li> <li><a href="/wiki/Collar_(finance)" title="Collar (finance)">Collar</a></li> <li><a href="/wiki/Condor_(options)" title="Condor (options)">Condor</a></li> <li><a href="/wiki/Covered_option" title="Covered option">Covered option</a></li> <li><a href="/wiki/Credit_spread_(options)" title="Credit spread (options)">Credit spread</a></li> <li><a href="/wiki/Debit_spread" title="Debit spread">Debit spread</a></li> <li><a href="/wiki/Diagonal_spread" title="Diagonal spread">Diagonal spread</a></li> <li><a href="/wiki/Fence_(finance)" title="Fence (finance)">Fence</a></li> <li><a href="/wiki/Intermarket_spread" title="Intermarket spread">Intermarket spread</a></li> <li><a href="/wiki/Iron_butterfly_(options_strategy)" title="Iron butterfly (options strategy)">Iron butterfly</a></li> <li><a href="/wiki/Iron_condor" title="Iron condor">Iron condor</a></li> <li><a href="/wiki/Jelly_roll_(options)" title="Jelly roll (options)">Jelly roll</a></li> <li><a href="/wiki/Ladder_(option_combination)" title="Ladder (option combination)">Ladder</a></li> <li><a href="/wiki/Naked_option" title="Naked option">Naked option</a></li> <li><a href="/wiki/Straddle" title="Straddle">Straddle</a></li> <li><a href="/wiki/Strangle_(options)" title="Strangle (options)">Strangle</a></li> <li><a href="/wiki/Protective_option" title="Protective option">Protective option</a></li> <li><a href="/wiki/Ratio_spread" title="Ratio spread">Ratio spread</a></li> <li><a href="/wiki/Risk_reversal" title="Risk reversal">Risk reversal</a></li> <li><a href="/wiki/Vertical_spread" title="Vertical spread">Vertical spread</a> (<a href="/wiki/Bear_spread" title="Bear spread">Bear</a>, <a href="/wiki/Bull_spread" title="Bull spread">Bull</a>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Valuation_of_options" title="Valuation of options">Valuation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bachelier_model" title="Bachelier model">Bachelier</a></li> <li><a href="/wiki/Binomial_options_pricing_model" title="Binomial options pricing model">Binomial</a></li> <li><a href="/wiki/Black_model" title="Black model">Black</a></li> <li><a href="/wiki/Black%E2%80%93Scholes_model" title="Black–Scholes model">Black–Scholes</a> (<a href="/wiki/Black%E2%80%93Scholes_equation" title="Black–Scholes equation">equation</a>)</li> <li><a href="/wiki/Finite_difference_methods_for_option_pricing" title="Finite difference methods for option pricing">Finite difference</a></li> <li><a href="/wiki/Foreign_exchange_option#Valuation:_the_Garman–Kohlhagen_model" title="Foreign exchange option">Garman–Kohlhagen</a></li> <li><a href="/wiki/Heston_model" title="Heston model">Heston</a></li> <li><a href="/wiki/Lattice_model_(finance)" title="Lattice model (finance)">Lattices</a></li> <li><a href="/wiki/Margrabe%27s_formula" title="Margrabe's formula">Margrabe</a></li> <li><a href="/wiki/Put%E2%80%93call_parity" title="Put–call parity">Put–call parity</a></li> <li><a href="/wiki/Monte_Carlo_methods_for_option_pricing" title="Monte Carlo methods for option pricing">MC Simulation</a></li> <li><a href="/wiki/Real_options_valuation" title="Real options valuation">Real options</a></li> <li><a href="/wiki/Trinomial_tree" title="Trinomial tree">Trinomial</a></li> <li><a href="/wiki/Vanna%E2%80%93Volga_pricing" title="Vanna–Volga pricing">Vanna–Volga</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Swap_(finance)" title="Swap (finance)">Swaps</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Amortising_swap" title="Amortising swap">Amortising</a></li> <li><a href="/wiki/Asset_swap" title="Asset swap">Asset</a></li> <li><a href="/wiki/Basis_swap" title="Basis swap">Basis</a></li> <li><a href="/wiki/Commodity_swap" title="Commodity swap">Commodity</a></li> <li><a href="/wiki/Conditional_variance_swap" title="Conditional variance swap">Conditional variance</a></li> <li><a href="/wiki/Constant_maturity_swap" title="Constant maturity swap">Constant maturity</a></li> <li><a href="/wiki/Correlation_swap" title="Correlation swap">Correlation</a></li> <li><a href="/wiki/Credit_default_swap" title="Credit default swap">Credit default</a></li> <li><a href="/wiki/Currency_swap" title="Currency swap">Currency</a></li> <li><a href="/wiki/Dividend_swap" title="Dividend swap">Dividend</a></li> <li><a href="/wiki/Equity_swap" title="Equity swap">Equity</a></li> <li><a href="/wiki/Foreign_exchange_swap" title="Foreign exchange swap">Forex</a></li> <li><a href="/wiki/Forward_rate_agreement" title="Forward rate agreement">Forward Rate Agreement</a></li> <li><a href="/wiki/Inflation_swap" title="Inflation swap">Inflation</a></li> <li><a href="/wiki/Interest_rate_swap" title="Interest rate swap">Interest rate</a></li> <li><a href="/wiki/Overnight_indexed_swap" title="Overnight indexed swap">Overnight indexed</a></li> <li><a href="/wiki/Total_return_swap" title="Total return swap">Total return</a></li> <li><a href="/wiki/Variance_swap" title="Variance swap">Variance</a></li> <li><a href="/wiki/Volatility_swap" title="Volatility swap">Volatility</a></li> <li><a href="/wiki/Year-on-year_inflation-indexed_swap" title="Year-on-year inflation-indexed swap">Year-on-year inflation-indexed</a></li> <li><a href="/wiki/Zero_coupon_swap" title="Zero coupon swap">Zero Coupon</a></li> <li><a href="/wiki/Zero-coupon_inflation_swap" title="Zero-coupon inflation swap">Zero-coupon inflation-indexed</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div class="hlist"><ul><li><a class="mw-selflink selflink">Forwards</a></li><li><a href="/wiki/Futures_contract" title="Futures contract">Futures</a></li></ul></div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Contango" title="Contango">Contango</a></li> <li><a href="/w/index.php?title=Commodities_future&action=edit&redlink=1" class="new" title="Commodities future (page does not exist)">Commodities future</a></li> <li><a href="/wiki/Currency_future" title="Currency future">Currency future</a></li> <li><a href="/wiki/Dividend_future" title="Dividend future">Dividend future</a></li> <li><a href="/wiki/Forward_market" title="Forward market">Forward market</a></li> <li><a href="/wiki/Forward_price" title="Forward price">Forward price</a></li> <li><a class="mw-selflink-fragment" href="#Spot–forward_parity">Forwards pricing</a></li> <li><a href="/wiki/Forward_rate" title="Forward rate">Forward rate</a></li> <li><a href="/wiki/Futures_contract#Pricing" title="Futures contract">Futures pricing</a></li> <li><a href="/wiki/Interest_rate_future" title="Interest rate future">Interest rate future</a></li> <li><a href="/wiki/Margin_(finance)" title="Margin (finance)">Margin</a></li> <li><a href="/wiki/Normal_backwardation" title="Normal backwardation">Normal backwardation</a></li> <li><a href="/wiki/Perpetual_futures" title="Perpetual futures">Perpetual futures</a></li> <li><a href="/wiki/Single-stock_futures" title="Single-stock futures">Single-stock futures</a></li> <li><a href="/wiki/Slippage_(finance)" title="Slippage (finance)">Slippage</a></li> <li><a href="/wiki/Stock_market_index_future" title="Stock market index future">Stock market index future</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Exotic_derivative" title="Exotic derivative">Exotic derivatives</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Commodity_derivative&action=edit&redlink=1" class="new" title="Commodity derivative (page does not exist)">Commodity derivative</a></li> <li><a href="/wiki/Energy_derivative" title="Energy derivative">Energy derivative</a></li> <li><a href="/wiki/Freight_derivative" class="mw-redirect" title="Freight derivative">Freight derivative</a></li> <li><a href="/wiki/Inflation_derivative" title="Inflation derivative">Inflation derivative</a></li> <li><a href="/wiki/Property_derivative" title="Property derivative">Property derivative</a></li> <li><a href="/wiki/Weather_derivative" title="Weather derivative">Weather derivative</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other derivatives</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Collateralized_debt_obligation" title="Collateralized debt obligation">Collateralized debt obligation (CDO)</a></li> <li><a href="/wiki/Constant_proportion_portfolio_insurance" title="Constant proportion portfolio 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