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class="vector-toc-numb">2</span> <span>VIX Formula</span> </div> </a> <ul id="toc-VIX_Formula-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Interpretation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Interpretation"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Interpretation</span> </div> </a> <ul id="toc-Interpretation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Volatility_of_volatility" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Volatility_of_volatility"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Volatility of volatility</span> </div> </a> <ul id="toc-Volatility_of_volatility-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_Volatility_indexes_in_the_world" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Other_Volatility_indexes_in_the_world"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Other Volatility indexes in the world</span> </div> </a> <ul id="toc-Other_Volatility_indexes_in_the_world-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">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-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">9</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div 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Volatility Index – German" lang="de" hreflang="de" data-title="CBOE Volatility Index" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/VIX" title="VIX – Spanish" lang="es" hreflang="es" data-title="VIX" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/VIX_(finance)" title="VIX (finance) – French" lang="fr" hreflang="fr" data-title="VIX (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/%EB%B3%80%EB%8F%99%EC%84%B1%EC%A7%80%EC%88%98" title="변동성지수 – Korean" lang="ko" hreflang="ko" data-title="변동성지수" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/VIX" title="VIX – Hebrew" lang="he" hreflang="he" data-title="VIX" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/VIX_rodiklis" title="VIX rodiklis – Lithuanian" lang="lt" hreflang="lt" data-title="VIX rodiklis" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/VIX_(%C3%ACndes)" title="VIX (ìndes) – Lombard" lang="lmo" hreflang="lmo" data-title="VIX (ìndes)" 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href="https://www.google.com/search?tbs=bks:1&q=%22VIX%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22VIX%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22VIX%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">February 2020</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Lead_too_long plainlinks metadata ambox ambox-style ambox-lead_too_long" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article's <b><a href="/wiki/Wikipedia:Manual_of_Style/Lead_section" title="Wikipedia:Manual of Style/Lead section">lead section</a> may be too long</b>.<span class="hide-when-compact"> Please read the <a href="/wiki/Wikipedia:Manual_of_Style/Lead_section#Length" title="Wikipedia:Manual of Style/Lead section">length guidelines</a> and help <a class="external text" href="https://en.wikipedia.org/w/index.php?title=VIX&action=edit">move details into the article's body</a>.</span> <span class="date-container"><i>(<span class="date">August 2024</span>)</i></span></div></td></tr></tbody></table> </div> </div><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:CBOE_Volatlity_Index,_VIX.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/CBOE_Volatlity_Index%2C_VIX.png/440px-CBOE_Volatlity_Index%2C_VIX.png" decoding="async" width="440" height="317" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/CBOE_Volatlity_Index%2C_VIX.png/660px-CBOE_Volatlity_Index%2C_VIX.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/CBOE_Volatlity_Index%2C_VIX.png/880px-CBOE_Volatlity_Index%2C_VIX.png 2x" data-file-width="2025" data-file-height="1458" /></a><figcaption>CBOE Volatility Index (VIX) 2004–2020.</figcaption></figure> <p><b>VIX</b> is the <a href="/wiki/Ticker_symbol" title="Ticker symbol">ticker symbol</a> and the popular name for the <a href="/wiki/Chicago_Board_Options_Exchange" class="mw-redirect" title="Chicago Board Options Exchange">Chicago Board Options Exchange</a>'s <b>CBOE Volatility Index</b>, a popular measure of the <a href="/wiki/Stock_market" title="Stock market">stock market</a>'s expectation of <a href="/wiki/Volatility_(finance)" title="Volatility (finance)">volatility</a> based on <a href="/wiki/S%26P_500" title="S&P 500">S&P 500</a> index <a href="/wiki/Option_(finance)" title="Option (finance)">options</a>. It is calculated and disseminated on a real-time basis by the <a href="/wiki/Chicago_Board_Options_Exchange" class="mw-redirect" title="Chicago Board Options Exchange">CBOE</a>, and is often referred to as the <i>fear index</i> or <i>fear gauge.</i> </p><p>The VIX traces its origin to the financial economics research of <a href="/wiki/Menachem_Brenner" title="Menachem Brenner">Menachem Brenner</a> and Dan Galai. In a series of papers beginning in 1989, Brenner and Galai proposed the creation of a series of volatility indices, beginning with an index on stock market volatility, and moving to interest rate and foreign exchange rate volatility.<sup id="cite_ref-1" class="reference"><a href="#cite_note-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> </p><p>In their papers, Brenner and Galai proposed, "[the] volatility index, to be named 'Sigma Index', would be updated frequently and used as the underlying asset for futures and options. ... A volatility index would play the same role as the market index plays for options and futures on the index."<sup id="cite_ref-:3_3-0" class="reference"><a href="#cite_note-:3-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> In 1992, the CBOE hired consultant <a href="/wiki/Robert_E._Whaley" title="Robert E. Whaley">Bob Whaley</a> to calculate values for stock market volatility based on this theoretical work.<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> </p><p>The resulting VIX index formulation provides a measure of market volatility on which expectations of further stock market volatility in the near future might be based. The current VIX index value quotes the expected annualized change in the S&P 500 index over the following 30 days, as computed from options-based theory and current options-market data. </p><p>To summarize, VIX is a volatility index derived from S&P 500 options for the 30 days following the measurement date,<sup id="cite_ref-:0_5-0" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> with the price of each option representing the market's expectation of 30-day forward-looking volatility.<sup id="cite_ref-:0_5-1" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-auto_6-0" class="reference"><a href="#cite_note-auto-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The resulting VIX index formulation provides a measure of expected market volatility on which expectations of further stock market <a href="/wiki/Volatility_(finance)" title="Volatility (finance)">volatility</a> in the near future might be based.<sup id="cite_ref-auto_6-1" class="reference"><a href="#cite_note-auto-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Like conventional indexes, the VIX Index calculation employs rules for selecting component options and a formula to calculate index values.<sup id="cite_ref-auto_6-2" class="reference"><a href="#cite_note-auto-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_7-0" class="reference"><a href="#cite_note-:1-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Unlike other market products, VIX cannot be bought or sold directly.<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> Instead, VIX is traded and exchanged via <a href="/wiki/Derivative_(finance)" title="Derivative (finance)">derivative</a> contract, derived <a href="/wiki/Exchange-traded_fund" title="Exchange-traded fund">ETFs</a>, and <a href="/wiki/Exchange-traded_notes" class="mw-redirect" title="Exchange-traded notes">ETNs</a> which most commonly track VIX futures indexes.<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>In addition to VIX, CBOE uses the same methodology to compute the following related products:<sup id="cite_ref-auto_6-3" class="reference"><a href="#cite_note-auto-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_7-1" class="reference"><a href="#cite_note-:1-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <ul><li>CBOE ShortTerm Volatility Index (VIX9DSM), which reflects 9-day expected volatility of the S&P 500 Index</li> <li>CBOE S&P 500 3-Month Volatility Index (VIX3MSM)</li> <li>CBOE S&P 500 6-Month Volatility Index (VIX6MSM)</li> <li>CBOE S&P 500 1-Year Volatility Index (VIX1YSM)</li> <li>CBOE 1-Day Volatility Index (VIX1D)</li></ul> <p>CBOE also calculates the Nasdaq-100 Volatility Index (VXNSM), CBOE DJIA Volatility Index (VXDSM) and the CBOE Russell 2000 Volatility Index (RVXSM).<sup id="cite_ref-auto_6-4" class="reference"><a href="#cite_note-auto-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> There is even a VIX on VIX (VVIX) which is a volatility of volatility measure in that it represents the expected volatility of the 30-day forward price of the CBOE Volatility Index (the VIX).<sup id="cite_ref-Cboe_Index_Dashboard_10-0" class="reference"><a href="#cite_note-Cboe_Index_Dashboard-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Specifications">Specifications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=VIX&action=edit&section=1" title="Edit section: Specifications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The concept of computing implied volatility or an implied volatility index dates to the publication of the Black and Scholes' 1973 paper, "The Pricing of Options and Corporate Liabilities," published in the <i>Journal of Political Economy,</i> which introduced the seminal <a href="/wiki/Black%E2%80%93Scholes_model" title="Black–Scholes model">Black–Scholes model</a> for valuing options.<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> Just as a bond's implied yield to maturity can be computed by equating a bond's market price to its valuation formula, an option-implied volatility of a financial or physical asset can be computed by equating the asset option's market price to its valuation formula.<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> In the case of VIX, the option prices used are the S&P 500 index option prices.<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><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><p>The VIX takes as inputs the market prices of the call and put options on the S&P 500 index for near-term options with more than 23 days until expiration, next-term options with less than 37 days until expiration, and risk-free U.S. treasury bill interest rates. Options are ignored if their bid prices are zero or where their strike prices are outside the level where two consecutive bid prices are zero.<sup id="cite_ref-auto_6-5" class="reference"><a href="#cite_note-auto-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (February 2020)">page needed</span></a></i>]</sup> The goal is to estimate the <a href="/wiki/Implied_volatility" title="Implied volatility">implied volatility</a> of S&P 500 index options at an average expiration of 30 days.<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> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Vix_historical_1990-2024.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Vix_historical_1990-2024.png/220px-Vix_historical_1990-2024.png" decoding="async" width="220" height="132" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Vix_historical_1990-2024.png/330px-Vix_historical_1990-2024.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Vix_historical_1990-2024.png/440px-Vix_historical_1990-2024.png 2x" data-file-width="1439" data-file-height="862" /></a><figcaption>Chicago Board of Exchange volatility index 1990-2024 on a logarithmic scale.</figcaption></figure> <p>Given that it is possible to create a hedging position equivalent to a <a href="/wiki/Variance_swap" title="Variance swap">variance swap</a> using only vanilla puts and calls (also called "static replication"),<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> the VIX can also be seen as the square root of the implied volatility of a <a href="/wiki/Variance_swap" title="Variance swap">variance swap</a><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> – and not that of a <a href="/wiki/Volatility_swap" title="Volatility swap">volatility swap</a>, volatility being the square root of variance, or <a href="/wiki/Standard_deviation" title="Standard deviation">standard deviation</a>. </p><p>The VIX is the square root of the risk-neutral expectation of the S&P 500 variance over the next 30 calendar days and is quoted as an annualized standard deviation.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p>The VIX is calculated and disseminated in real-time by the <a href="/wiki/Chicago_Board_Options_Exchange" class="mw-redirect" title="Chicago Board Options Exchange">Chicago Board Options Exchange</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (February 2020)">citation needed</span></a></i>]</sup> On March 26, 2004, trading in futures on the VIX began on CBOE Futures Exchange (CFE).<sup id="cite_ref-lin_19-0" class="reference"><a href="#cite_note-lin-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>On February 24, 2006, it became possible to trade options on the VIX.<sup id="cite_ref-lin_19-1" class="reference"><a href="#cite_note-lin-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Several <a href="/wiki/Exchange-traded_fund" title="Exchange-traded fund">exchange-traded funds</a> hold mixtures of VIX futures that attempt to enable stock-like trading in those futures. The correlation between these ETFs and the actual VIX index is very poor, especially when the VIX is moving.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="VIX_Formula">VIX Formula</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=VIX&action=edit&section=2" title="Edit section: VIX Formula"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The VIX is the 30-day expected volatility of the SP500 index, more precisely the square root of a 30-day expected realized variance of the index. It is calculated as a weighted average of out-of-the-money call and <a href="/wiki/Put_options" class="mw-redirect" title="Put options">put options</a> on the S&P 500: </p><p><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 VIX={\sqrt {{\frac {2e^{r\,\!\tau }}{\tau }}\left(\int _{0}^{F}{\frac {P(K)}{K^{2}}}dK+\int _{F}^{\infty }{\frac {C(K)}{K^{2}}}dK\right)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mi>I</mi> <mi>X</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> <mi>τ</mi> </mrow> </msup> </mrow> <mi>τ</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>P</mi> <mo stretchy="false">(</mo> <mi>K</mi> <mo stretchy="false">)</mo> </mrow> <msup> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mi>d</mi> <mi>K</mi> <mo>+</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>C</mi> <mo stretchy="false">(</mo> <mi>K</mi> <mo stretchy="false">)</mo> </mrow> <msup> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mi>d</mi> <mi>K</mi> </mrow> <mo>)</mo> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle VIX={\sqrt {{\frac {2e^{r\,\!\tau }}{\tau }}\left(\int _{0}^{F}{\frac {P(K)}{K^{2}}}dK+\int _{F}^{\infty }{\frac {C(K)}{K^{2}}}dK\right)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56ed7ce70405a969dba83bdd93043f0a511a0eaa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:50.455ex; height:7.509ex;" alt="{\displaystyle VIX={\sqrt {{\frac {2e^{r\,\!\tau }}{\tau }}\left(\int _{0}^{F}{\frac {P(K)}{K^{2}}}dK+\int _{F}^{\infty }{\frac {C(K)}{K^{2}}}dK\right)}}}"></span> </p><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 {\tau }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>τ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tau }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d2cbbb2bd6bed8835c6a57e58a152568e6f7fa8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle {\tau }}"></span> is the number of average days in a month (30 days), <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 risk-free rate, <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}"></span> is the 30-day forward price on the S&P 500, 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 P(K)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <mi>K</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P(K)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cb37597a811ca35e5cf78722f93a6fed0faea97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.621ex; height:2.843ex;" alt="{\displaystyle P(K)}"></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 C(K)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo stretchy="false">(</mo> <mi>K</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C(K)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b823cba8d0220d7bd670bace88a3fe7fd07e6659" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.642ex; height:2.843ex;" alt="{\displaystyle C(K)}"></span> are prices for puts and calls with strike <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 30 days to maturity.<sup id="cite_ref-auto_6-6" class="reference"><a href="#cite_note-auto-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=VIX&action=edit&section=3" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The following is a timeline of key events in the history of the VIX Index:<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions" title="Wikipedia:Manual of Style/Words to watch"><span title="The material near this tag may use weasel words or too-vague attribution. (February 2020)">according to whom?</span></a></i>]</sup> </p> <ul><li>1987 – The Sigma Index was introduced in an academic paper by Brenner and Galai, published in Financial Analysts Journal, July/August 1989.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> Brenner and Galai wrote, "Our volatility index, to be named Sigma Index, would be updated frequently and used as the underlying asset for futures and options... A volatility index would play the same role as the market index play for options and futures on the index."<sup id="cite_ref-:3_3-1" class="reference"><a href="#cite_note-:3-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li> <li>1989 – Brenner and Galai's paper is published in Financial Analysts Journal.<sup id="cite_ref-:3_3-2" class="reference"><a href="#cite_note-:3-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Brenner and Galai develop their research further in graduate symposia at <a href="/wiki/Hebrew_University_of_Jerusalem" title="Hebrew University of Jerusalem">The Hebrew University of Jerusalem</a><sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (February 2020)">citation needed</span></a></i>]</sup> and at the <a href="/wiki/New_York_University_Stern_School_of_Business" title="New York University Stern School of Business">Leonard M. Stern School of Business</a> at <a href="/wiki/New_York_University" title="New York University">New York University</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (February 2020)">citation needed</span></a></i>]</sup></li> <li>1992 – The <a href="/wiki/American_Stock_Exchange" class="mw-redirect" title="American Stock Exchange">American Stock Exchange</a> announced it is conducting a feasibility study on a volatility index, proposed as the "Sigma Index."<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></li> <li>1993 – On January 19, 1993, the Chicago Board Options Exchange held a press conference to announce the launch of real-time reporting of the CBOE Market Volatility Index or VIX. The formula that determines the VIX is tailored to the CBOE S&P 100 Index (OEX) option prices, and was developed by Professor Robert E. Whaley of <a href="/wiki/Duke_University" title="Duke University">Duke University</a> (now at <a href="/wiki/Vanderbilt_University" title="Vanderbilt University">Vanderbilt University</a>), whom the CBOE had commissioned.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> This index, now known as the VXO, is a measure of implied volatility calculated using 30-day <a href="/wiki/S%26P_100" title="S&P 100">S&P 100</a> index at-the-money options.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup></li> <li>1993 – Professors Brenner and Galai develop their 1989 proposal for a series of volatility index in their paper, "Hedging Volatility in Foreign Currencies," published in The Journal of Derivatives in the fall of 1993.<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources"><span title="A complete citation is needed. (February 2020)">full citation needed</span></a></i>]</sup></li> <li>2003 – The CBOE introduces a new methodology for the VIX. Working with <a href="/wiki/Goldman_Sachs" title="Goldman Sachs">Goldman Sachs</a>, the CBOE developed further computational methodologies, and changed the underlying index the CBOE S&P 100 Index (OEX) to the CBOE S&P 500 Index (SPX). The old methodology was renamed the VXO.<sup id="cite_ref-auto_6-7" class="reference"><a href="#cite_note-auto-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="The material near this tag needs to be fact-checked with the cited source(s). (February 2020)">verification needed</span></a></i>]</sup></li> <li>2004 – On March 26, 2004, the first-ever trading in futures on the VIX Index began on the CBOE Futures Exchange (CFE).<sup id="cite_ref-:2_26-0" class="reference"><a href="#cite_note-:2-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> VIX is now proposed<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (February 2020)">clarification needed</span></a></i>]</sup> on different trading platforms, like XTB.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (February 2020)">citation needed</span></a></i>]</sup></li> <li>2006 – VIX options were launched in February of this year.<sup id="cite_ref-:2_26-1" class="reference"><a href="#cite_note-:2-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup></li> <li>2008 – On October 24, 2008, the VIX reached an intraday high of 89.53.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup></li> <li>2008 – On November 21, 2008, the VIX closed at a record 80.74.<sup id="cite_ref-autogenerated1_28-0" class="reference"><a href="#cite_note-autogenerated1-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup></li> <li>2018 – On February 5, 2018, the VIX closed 37.32 (up 103.99% from previous close).<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup></li> <li>2020 – On March 9, 2020, the VIX hit 62.12, the highest level since the 2008 financial crisis due to a combination of the <a href="/wiki/2020_Russia%E2%80%93Saudi_Arabia_oil_price_war" title="2020 Russia–Saudi Arabia oil price war">2020 Russia–Saudi Arabia oil price war</a> and the <a href="/wiki/COVID-19_pandemic" title="COVID-19 pandemic">COVID-19 pandemic</a>.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li> <li>2020 – During the <a href="/wiki/COVID-19_pandemic" title="COVID-19 pandemic">COVID-19 pandemic</a>, on March 12, 2020, the VIX hit and closed at 75.47, exceeding the previous <a href="/wiki/Black_Monday_(1987)" title="Black Monday (1987)">Black Monday</a> value, as a travel ban to the US from <a href="/wiki/Europe" title="Europe">Europe</a> was announced by <a href="/wiki/President_Trump" class="mw-redirect" title="President Trump">President Trump</a>.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup></li> <li>2020 – On March 16, the VIX closed at 82.69, the highest level since its inception in 1990.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup></li> <li>2021 – The <a href="/wiki/U.S._Securities_and_Exchange_Commission" title="U.S. Securities and Exchange Commission">U.S. Securities and Exchange Commission</a> fined the <a href="/wiki/S%26P_Dow_Jones_Indices" title="S&P Dow Jones Indices">S&P Dow Jones Indices</a> for halting data on February 5, 2018.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Interpretation">Interpretation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=VIX&action=edit&section=4" title="Edit section: Interpretation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Vix.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Vix.png/440px-Vix.png" decoding="async" width="440" height="198" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Vix.png/660px-Vix.png 1.5x, //upload.wikimedia.org/wikipedia/commons/e/ed/Vix.png 2x" data-file-width="721" data-file-height="324" /></a><figcaption>Performance of VIX (left) compared to past volatility (right) as 30-day volatility predictors, for the period of Jan. 1990–Sep. 2009. Volatility is measured as the standard deviation of S&P500 one-day returns over a month's period. The blue lines indicate linear regressions, resulting in the <a href="/wiki/Correlation" title="Correlation">correlation coefficients</a> <i>r</i> shown. Note that VIX has virtually the same predictive power as past volatility, insofar as the shown correlation coefficients are nearly identical.</figcaption></figure> <p>VIX is sometimes criticized as a prediction of future volatility. Instead it is described as a measure of the current price of index options.<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions" title="Wikipedia:Manual of Style/Words to watch"><span title="The material near this tag may use weasel words or too-vague attribution. (February 2020)">according to whom?</span></a></i>]</sup><sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (February 2020)">citation needed</span></a></i>]</sup> </p><p>Critics claim that, despite a sophisticated formulation, the predictive power of most volatility forecasting models is similar to that of plain-vanilla measures, such as simple past volatility.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> However, other works have countered that these critiques failed to correctly implement the more complicated models.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p><p>Some practitioners and <a href="/wiki/Portfolio_managers" class="mw-redirect" title="Portfolio managers">portfolio managers</a> have questioned the depth of our understanding of the fundamental concept of volatility, itself. For example, <a href="/wiki/Daniel_Goldstein" title="Daniel Goldstein">Daniel Goldstein</a> and <a href="/wiki/Nassim_Taleb" class="mw-redirect" title="Nassim Taleb">Nassim Taleb</a> famously titled one of their research articles, <i>We Don't Quite Know What We are Talking About When We Talk About Volatility</i>.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> Relatedly,<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="The material near this tag needs to be fact-checked with the cited source(s). (February 2020)">verification needed</span></a></i>]</sup> <a href="/wiki/Emanuel_Derman" title="Emanuel Derman">Emanuel Derman</a> has expressed disillusion with empirical models that are unsupported by theory.<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (February 2020)">clarification needed</span></a></i>]</sup><sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (February 2020)">citation needed</span></a></i>]</sup><sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (February 2020)">page needed</span></a></i>]</sup> He argues that, while "theories are attempts to uncover the hidden principles underpinning the world around us... [we should remember that] models are metaphors—analogies that describe one thing relative to another."<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (February 2020)">page needed</span></a></i>]</sup> </p><p><a href="/wiki/Mike_Harris_(entrepreneur)" title="Mike Harris (entrepreneur)">Michael Harris</a>, the trader, programmer, price pattern theorist, and author, has argued that VIX just tracks the inverse of price and has no predictive power.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template noprint noexcerpt Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:NOTRS" class="mw-redirect" title="Wikipedia:NOTRS"><span title="This claim needs references to better sources. (February 2020)">better source needed</span></a></i>]</sup> </p><p>According to some,<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions" title="Wikipedia:Manual of Style/Words to watch"><span title="The material near this tag possibly uses too-vague attribution or weasel words. (February 2020)">who?</span></a></i>]</sup> VIX should have predictive power as long as the prices computed by the <a href="/wiki/Black-Scholes_equation" class="mw-redirect" title="Black-Scholes equation">Black–Scholes equation</a> are valid assumptions about the volatility predicted for the future lead time (the remaining time to maturity).<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (February 2020)">citation needed</span></a></i>]</sup> <a href="/wiki/Robert_J._Shiller" title="Robert J. Shiller">Robert J. Shiller</a> has argued that it would be <a href="/wiki/Circular_reasoning" title="Circular reasoning">circular reasoning</a> to consider VIX to be proof of Black–Scholes, because they both express the same implied volatility, and has found that calculating VIX retrospectively in 1929 did not predict the surpassing volatility of the <a href="/wiki/Great_Depression" title="Great Depression">Great Depression</a>—suggesting that in the case of anomalous conditions, VIX cannot even weakly predict future severe events.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> </p><p>An academic study from the <a href="/wiki/University_of_Texas_at_Austin" title="University of Texas at Austin">University of Texas at Austin</a> and <a href="/wiki/Ohio_State_University" title="Ohio State University">Ohio State University</a> examined potential methods of VIX manipulation.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> On February 12, 2018, a letter was sent to the Commodity Futures Trading Commission and Securities and Exchange Commission by a law firm representing an anonymous whistleblower alleging manipulation of the VIX.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Volatility_of_volatility">Volatility of volatility</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=VIX&action=edit&section=5" title="Edit section: Volatility of volatility"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="anchor" id="VVIX"></span>In 2012, the CBOE introduced the "VVIX index" (also referred to as "vol of vol"), a measure of the VIX's expected volatility.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> VVIX is calculated using the same methodology as VIX, except the inputs are market prices for VIX options instead of stock market options.<sup id="cite_ref-Cboe_Index_Dashboard_10-1" class="reference"><a href="#cite_note-Cboe_Index_Dashboard-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>The VIX can be thought of as the velocity of investor fear. The VVIX measures how much the VIX changes and hence can be thought of as the acceleration of investor fear.<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Other_Volatility_indexes_in_the_world">Other Volatility indexes in the world</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=VIX&action=edit&section=6" title="Edit section: Other Volatility indexes in the world"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Tradable: </p><p>VSTOXX </p><p>Deribit BTCDVOL </p><p>Brazil Volatility Index<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<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=VIX&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{clear:left;float:left;margin:0.5em 1em 0.5em 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href="/wiki/Option_on_realized_variance" title="Option on realized variance">Option on realized variance</a></li> <li><a href="/wiki/Probability_of_default" title="Probability of default">Probability of default</a></li> <li><a href="/wiki/S%26P/ASX_200_VIX" title="S&P/ASX 200 VIX">S&P/ASX 200 VIX</a></li> <li><a href="/wiki/SKEW" title="SKEW">SKEW</a></li> <li><a href="/wiki/Volfefe_index" title="Volfefe index">Volfefe index</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=VIX&action=edit&section=8" title="Edit section: References"><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-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</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 .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBrennerGalai1989" class="citation journal cs1">Brenner, Menachem; Galai, Dan (July–August 1989). <a rel="nofollow" class="external text" href="http://people.stern.nyu.edu/mbrenner/research/FAJ_articleon_Volatility_Der.pdf">"New Financial Instruments for Hedging Changes in Volatility"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Financial_Analysts_Journal" title="Financial Analysts Journal">Financial Analysts Journal</a></i>. <b>45</b> (4): 61–65. <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.v45.n4.61">10.2469/faj.v45.n4.61</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=New+Financial+Instruments+for+Hedging+Changes+in+Volatility&rft.volume=45&rft.issue=4&rft.pages=61-65&rft.date=1989-07%2F1989-08&rft_id=info%3Adoi%2F10.2469%2Ffaj.v45.n4.61&rft.aulast=Brenner&rft.aufirst=Menachem&rft.au=Galai%2C+Dan&rft_id=http%3A%2F%2Fpeople.stern.nyu.edu%2Fmbrenner%2Fresearch%2FFAJ_articleon_Volatility_Der.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVIX" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrennerGalai1993" class="citation journal cs1">Brenner, Menachem; Galai, Dan (Fall 1993). <a rel="nofollow" class="external text" href="http://people.stern.nyu.edu/mbrenner/research/JOD_article_of_Vol_Index_Computation.pdf">"Hedging Volatility in Foreign Currencies"</a> <span class="cs1-format">(PDF)</span>. <i>The Journal of Derivatives</i>. <b>1</b> (1): 53–58. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3905%2Fjod.1993.407870">10.3905/jod.1993.407870</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Journal+of+Derivatives&rft.atitle=Hedging+Volatility+in+Foreign+Currencies&rft.ssn=fall&rft.volume=1&rft.issue=1&rft.pages=53-58&rft.date=1993&rft_id=info%3Adoi%2F10.3905%2Fjod.1993.407870&rft.aulast=Brenner&rft.aufirst=Menachem&rft.au=Galai%2C+Dan&rft_id=http%3A%2F%2Fpeople.stern.nyu.edu%2Fmbrenner%2Fresearch%2FJOD_article_of_Vol_Index_Computation.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVIX" class="Z3988"></span></span> </li> <li id="cite_note-:3-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-:3_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:3_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:3_3-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrennerGalai1989" class="citation journal cs1">Brenner, Menachem; Galai, Dan (1989). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://www.jstor.org/stable/4479241">"New Financial Instruments for Hedging Changes in Volatility"</a></span>. <i>Financial Analysts Journal</i>. <b>45</b> (4): 61–65. <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.v45.n4.61">10.2469/faj.v45.n4.61</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN 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Retrieved <span class="nowrap">25 February</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Models+Behaving+Badly%3A+Why+Confusing+Illusion+With+Reality+Can+Lead+to+Disaster%2C+on+Wall+Street+and+in+Life&rft.place=New+York%2C+NY&rft.pages=unknown+page+nos&rft.pub=Simon+and+Schuster&rft.date=2011&rft.isbn=9781439165010&rft.au=Derman%2C+Emanuel&rft_id=https%3A%2F%2Fwww.google.com%2Fsearch%3Ftbm%3Dbks%26hl%3Den%26q%3D9781439164983&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVIX" class="Z3988"></span></span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarris,_Michael2012" class="citation web cs1">Harris, Michael (21 August 2012). <a rel="nofollow" class="external text" href="http://www.priceactionlab.com/Blog/2012/08/on-the-zero-predictive-capacity-of-vix/">"On the Zero Predictive Capacity of VIX—Price Action Lab Blog"</a> <span class="cs1-format">(self-published blog)</span>. <i>PriceActionLab.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">25 February</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=PriceActionLab.com&rft.atitle=On+the+Zero+Predictive+Capacity+of+VIX%E2%80%94Price+Action+Lab+Blog&rft.date=2012-08-21&rft.au=Harris%2C+Michael&rft_id=http%3A%2F%2Fwww.priceactionlab.com%2FBlog%2F2012%2F08%2Fon-the-zero-predictive-capacity-of-vix%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVIX" class="Z3988"></span></span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarris,_Michael2012" class="citation web cs1">Harris, Michael (25 August 2012). <a rel="nofollow" class="external text" href="http://www.priceactionlab.com/Blog/2012/08/further-analytical-evidence-that-vix-just-tracks-the-inverse-of-price/">"Further Analytical Evidence that VIX Just Tracks the Inverse of Price"</a> <span class="cs1-format">(self-published blog)</span>. <i>PriceActionLab.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">25 February</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=PriceActionLab.com&rft.atitle=Further+Analytical+Evidence+that+VIX+Just+Tracks+the+Inverse+of+Price&rft.date=2012-08-25&rft.au=Harris%2C+Michael&rft_id=http%3A%2F%2Fwww.priceactionlab.com%2FBlog%2F2012%2F08%2Ffurther-analytical-evidence-that-vix-just-tracks-the-inverse-of-price%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVIX" class="Z3988"></span></span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShiller,_Robert2011" class="citation web cs1"><a href="/wiki/Robert_J._Shiller" title="Robert J. Shiller">Shiller, Robert</a> (30 March 2011). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160922071546/http://oyc.yale.edu/transcript/1086/econ-252-11">"Econ 252-11: Financial Markets [Lecture 17—Options Markets]"</a>. New Haven, CT: Yale University. Archived from <a rel="nofollow" class="external text" href="http://oyc.yale.edu/transcript/1086/econ-252-11">the original</a> <span class="cs1-format">(college course content)</span> on 22 September 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">26 February</span> 2020</span> – via OYC.Yale.edu.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Econ+252-11%3A+Financial+Markets+%5BLecture+17%E2%80%94Options+Markets%5D&rft.place=New+Haven%2C+CT&rft.pub=Yale+University&rft.date=2011-03-30&rft.au=Shiller%2C+Robert&rft_id=http%3A%2F%2Foyc.yale.edu%2Ftranscript%2F1086%2Fecon-252-11&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVIX" class="Z3988"></span></span> </li> <li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGriffin,_John_M.Shams,_Amin2017" class="citation journal cs1">Griffin, John M.; Shams, Amin (May 23, 2017). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://ssrn.com/abstract=2972979">"Manipulation in the VIX?"</a></span>. <i>SSRN.com</i>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2139%2Fssrn.2972979">10.2139/ssrn.2972979</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:157586475">157586475</a>. <a href="/wiki/SSRN_(identifier)" class="mw-redirect" title="SSRN (identifier)">SSRN</a> <a rel="nofollow" class="external text" href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2972979">2972979</a><span class="reference-accessdate">. Retrieved <span class="nowrap">25 February</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=SSRN.com&rft.atitle=Manipulation+in+the+VIX%3F&rft.date=2017-05-23&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A157586475%23id-name%3DS2CID&rft_id=https%3A%2F%2Fpapers.ssrn.com%2Fsol3%2Fpapers.cfm%3Fabstract_id%3D2972979%23id-name%3DSSRN&rft_id=info%3Adoi%2F10.2139%2Fssrn.2972979&rft.au=Griffin%2C+John+M.&rft.au=Shams%2C+Amin&rft_id=https%3A%2F%2Fssrn.com%2Fabstract%3D2972979&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVIX" class="Z3988"></span></span> </li> <li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCornish,_Chloe2018" class="citation journal cs1">Cornish, Chloe (13 February 2018). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://www.ft.com/content/a89eba68-10b4-11e8-940e-08320fc2a277">"Anonymous 'Whistleblower' Claims 'Rampant Manipulation' of Vix Index"</a></span>. <i><a href="/wiki/Financial_Times" title="Financial Times">Financial Times</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">26 February</span> 2020</span> – via FT.com.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Financial+Times&rft.atitle=Anonymous+%27Whistleblower%27+Claims+%27Rampant+Manipulation%27+of+Vix+Index&rft.date=2018-02-13&rft.au=Cornish%2C+Chloe&rft_id=https%3A%2F%2Fwww.ft.com%2Fcontent%2Fa89eba68-10b4-11e8-940e-08320fc2a277&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVIX" class="Z3988"></span></span> </li> <li id="cite_note-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-46">^</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="http://www.cboe.com/micro/vvix/documents/vvix-termstructure.pdf">"Double the Fun with CBOE's VVIX Index"</a> <span class="cs1-format">(PDF)</span>. <i>CBOE.com</i>. March 13, 2012<span class="reference-accessdate">. Retrieved <span class="nowrap">November 19,</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=CBOE.com&rft.atitle=Double+the+Fun+with+CBOE%27s+VVIX+Index&rft.date=2012-03-13&rft_id=http%3A%2F%2Fwww.cboe.com%2Fmicro%2Fvvix%2Fdocuments%2Fvvix-termstructure.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVIX" class="Z3988"></span></span> </li> <li id="cite_note-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-47">^</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.vixfaq.com/what-is-the-cboe-vvix-index/">"What is the VVIX (Cboe VVIX Index)?"</a>. <i>VIXFAQ.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-04-29</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=VIXFAQ.com&rft.atitle=What+is+the+VVIX+%28Cboe+VVIX+Index%29%3F&rft_id=https%3A%2F%2Fwww.vixfaq.com%2Fwhat-is-the-cboe-vvix-index%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVIX" class="Z3988"></span></span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</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.cboe.com/us/indices/dashboard/vxewz/">"Cboe Brazil ETF Volatility Index"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Cboe+Brazil+ETF+Volatility+Index&rft_id=https%3A%2F%2Fwww.cboe.com%2Fus%2Findices%2Fdashboard%2Fvxewz%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVIX" class="Z3988"></span></span> </li> </ol></div></div> <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=VIX&action=edit&section=9" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Fischer_Black" title="Fischer Black">Black, Fischer</a> and <a href="/wiki/Myron_Scholes" title="Myron Scholes">Myron Scholes</a>. "The Pricing of Options and Corporate Liabilities." Journal of Political Economy (May/June 1973), pp. 637–659.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrennerGalai1989" class="citation journal cs1">Brenner, Menachem; Galai, Dan (July–August 1989). <a rel="nofollow" class="external text" href="http://people.stern.nyu.edu/mbrenner/research/FAJ_articleon_Volatility_Der.pdf">"New Financial Instruments for Hedging Changes in Volatility"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Financial_Analysts_Journal" title="Financial Analysts Journal">Financial Analysts Journal</a></i>. <b>45</b> (4): 61–65. <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.v45.n4.61">10.2469/faj.v45.n4.61</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=New+Financial+Instruments+for+Hedging+Changes+in+Volatility&rft.volume=45&rft.issue=4&rft.pages=61-65&rft.date=1989-07%2F1989-08&rft_id=info%3Adoi%2F10.2469%2Ffaj.v45.n4.61&rft.aulast=Brenner&rft.aufirst=Menachem&rft.au=Galai%2C+Dan&rft_id=http%3A%2F%2Fpeople.stern.nyu.edu%2Fmbrenner%2Fresearch%2FFAJ_articleon_Volatility_Der.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVIX" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrennerGalai1993" class="citation journal cs1">Brenner, Menachem; Galai, Dan (Fall 1993). <a rel="nofollow" class="external text" href="http://people.stern.nyu.edu/mbrenner/research/JOD_article_of_Vol_Index_Computation.pdf">"Hedging Volatility in Foreign Currencies"</a> <span class="cs1-format">(PDF)</span>. <i>The Journal of Derivatives</i>. <b>1</b> (1): 53–58. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3905%2Fjod.1993.407870">10.3905/jod.1993.407870</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Journal+of+Derivatives&rft.atitle=Hedging+Volatility+in+Foreign+Currencies&rft.ssn=fall&rft.volume=1&rft.issue=1&rft.pages=53-58&rft.date=1993&rft_id=info%3Adoi%2F10.3905%2Fjod.1993.407870&rft.aulast=Brenner&rft.aufirst=Menachem&rft.au=Galai%2C+Dan&rft_id=http%3A%2F%2Fpeople.stern.nyu.edu%2Fmbrenner%2Fresearch%2FJOD_article_of_Vol_Index_Computation.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVIX" class="Z3988"></span></li> <li>"Amex Explores Volatility Options," <a rel="nofollow" class="external text" href="http://people.stern.nyu.edu/mbrenner/research/IFR_report_on_Brenner-Galai_Sigma_Index.pdf">International Financing Review</a>, August 8, 1992.</li> <li>Black, Keith H. "Improving Hedge Fund Risk Exposures by Hedging Equity Market Volatility, or How the VIX Ate My Kurtosis." The Journal of Trading. (Spring 2006).</li> <li>Connors, Larry. "A Volatile Idea." Futures (July 1999): pp. 36–37.</li> <li>Connors, Larry. "Timing Your S&P Trades with the VIX." Futures (June 2002): pp. 46–47.</li> <li>Copeland, Maggie. "Market Timing: Style and Size Rotation Using the VIX." Financial Analysts Journal, (Mar/Apr 1999); pp. 73–82.</li> <li>Daigler, Robert T., and Laura Rossi. "A Portfolio of Stocks and Volatility." The Journal of Investing. (Summer 2006).</li> <li>Fleming, Jeff, Barbara Ostdiek, and <a href="/wiki/Robert_E._Whaley" title="Robert E. Whaley">Robert E. Whaley</a>, "Predicting Stock Market Volatility: A New Measure," The Journal of Futures Markets 15 (May 1995), pp. 265–302.</li> <li><a href="/wiki/Mark_Hulbert" title="Mark Hulbert">Hulbert, Mark</a>, <a rel="nofollow" class="external text" href="http://online.barrons.com/article/SB50001424052748703464104576616983309689062.html">"The Misuse of the Stock Market's Fear Index,"</a> Barron's, October 7, 2011.</li> <li>Mele, Antonio and Yoshiki Obayashi. "The Price of Fixed Income Market Volatility." Springer Verlag: Springer Finance Series, New York (2015).</li> <li>Moran, Matthew T., "Review of the VIX Index and VIX Futures.," Journal of Indexes, (October/November 2004). pp. 16–19.</li> <li>Moran, Matthew T. and Srikant Dash. "VIX Futures and Options: Pricing and Using Volatility Products to Manage Downside Risk and Improve Efficiency in Equity Portfolios." The Journal of Trading. (Summer 2007).</li> <li>Szado, Ed. "VIX Futures and Options—A Case Study of Portfolio Diversification During the 2008 Financial Crisis." (June 2009).</li> <li>Tan, Kopin. "The ABCs of VIX." Barron's (Mar 15, 2004): p. MW16.</li> <li>Tracy, Tennille. "Trading Soars on Financials As Volatility Index Hits Record." Wall Street Journal. (Sept. 30, 2008) p. C6.</li> <li><a href="/wiki/Robert_E._Whaley" title="Robert E. Whaley">Whaley, Robert E</a>., <a rel="nofollow" class="external text" href="http://rewconsulting.files.wordpress.com/2012/09/jd93.pdf">"Derivatives on Market Volatility: Hedging Tools Long Overdue,"</a> The Journal of Derivatives 1 (Fall 1993), pp. 71–84.</li> <li><a href="/wiki/Robert_E._Whaley" title="Robert E. Whaley">Whaley, Robert E</a>., "The Investor Fear Gauge," The Journal of Portfolio Management 26 (Spring 2000), pp. 12–17.</li> <li><a href="/wiki/Robert_E._Whaley" title="Robert E. Whaley">Whaley, Robert E</a>., "Understanding the VIX." The Journal of Portfolio Management 35 (Spring 2009), pp. 98–105.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=VIX&action=edit&section=10" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://www.cboe.com/tradable_products/vix/">Official website</a> at CBOE</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl 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href="/wiki/Market_trend" title="Market trend">Market trend</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Charts</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Candlestick_chart" title="Candlestick chart">Candlestick</a></li> <li><a href="/wiki/Renko_chart" title="Renko chart">Renko</a></li> <li><a href="/wiki/Kagi_chart" title="Kagi chart">Kagi</a></li> <li><a href="/wiki/Line_chart" title="Line chart">Line</a></li> <li><a href="/wiki/Open-high-low-close_chart" title="Open-high-low-close chart">Open-high-low-close</a></li> <li><a href="/wiki/Point_and_figure_chart" title="Point and figure chart">Point and figure</a></li> <li><a href="/wiki/Line_break_chart" title="Line break chart">Line break</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Patterns</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" 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%"><a href="/wiki/Chart_pattern" title="Chart pattern">Chart</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/Broadening_top" title="Broadening top">Broadening top</a></li> <li><a href="/wiki/Cup_and_handle" title="Cup and handle">Cup and handle</a></li> <li><a href="/wiki/Double_top_and_double_bottom" title="Double top and double bottom">Double top and double bottom</a></li> <li><a href="/wiki/Flag_and_pennant_patterns" title="Flag and pennant patterns">Flag and pennant</a></li> <li><a href="/wiki/Gap_(chart_pattern)" title="Gap (chart pattern)">Gap</a></li> <li><a href="/wiki/Head_and_shoulders_(chart_pattern)" title="Head and shoulders (chart pattern)">Head and shoulders</a></li> <li><a href="/wiki/Island_reversal" title="Island reversal">Island reversal</a></li> <li><a href="/wiki/Price_channels" title="Price channels">Price channels</a></li> <li><a href="/wiki/Triangle_(chart_pattern)" title="Triangle (chart pattern)">Triangle</a></li> <li><a href="/wiki/Triple_top_and_triple_bottom" title="Triple top and triple bottom">Triple top and triple bottom</a></li> <li><a href="/wiki/Wedge_pattern" title="Wedge pattern">Wedge pattern</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Candlestick_pattern" title="Candlestick pattern">Candlestick</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%"><a href="/wiki/Candlestick_pattern#Simple_patterns" title="Candlestick pattern">Simple</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/Doji" title="Doji">Doji</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Candlestick_pattern#Complex_patterns" title="Candlestick pattern">Complex</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/Hikkake_pattern" title="Hikkake pattern">Hikkake pattern</a></li> <li><a href="/wiki/Morning_star_(candlestick_pattern)" title="Morning star (candlestick pattern)">Morning star</a></li> <li><a href="/wiki/Three_black_crows" title="Three black crows">Three black crows</a></li> <li><a href="/wiki/Three_white_soldiers" title="Three white soldiers">Three white soldiers</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/Point_and_figure_chart" title="Point and figure chart">Point and figure</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/Bull_trap" title="Bull trap">Bull trap</a></li> <li><a href="/wiki/Bear_market" class="mw-redirect" title="Bear market">Bear trap</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/Technical_indicator" title="Technical indicator">Indicators</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" 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%"><a href="/wiki/Support_and_resistance" title="Support and resistance">Support &<br />resistance</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/Fibonacci_retracement" title="Fibonacci retracement">Fibonacci retracement</a></li> <li><a href="/wiki/Pivot_point_(technical_analysis)" title="Pivot point (technical analysis)">Pivot point</a> (PP)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Market_trend" title="Market trend">Trend</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/Average_directional_movement_index" title="Average directional movement index">Average directional index</a> (A.D.X.)</li> <li><a href="/wiki/Commodity_channel_index" title="Commodity channel index">Commodity channel index</a> (CCI)</li> <li><a href="/wiki/Detrended_price_oscillator" title="Detrended price oscillator">Detrended price oscillator</a> (DPO)</li> <li><a href="/wiki/KST_oscillator" title="KST oscillator">Know sure thing oscillator</a> (KST)</li> <li><a href="/wiki/Ichimoku_Kink%C5%8D_Hy%C5%8D" title="Ichimoku Kinkō Hyō">Ichimoku Kinkō Hyō</a></li> <li><a href="/wiki/MACD" title="MACD">Moving average convergence/divergence</a> (MACD)</li> <li><a href="/wiki/Mass_index" title="Mass index">Mass index</a></li> <li><a href="/wiki/Moving_average" title="Moving average">Moving average</a> (MA)</li> <li><a href="/wiki/Parabolic_SAR" title="Parabolic SAR">Parabolic SAR</a> (SAR)</li> <li><a href="/wiki/Smart_money_index" title="Smart money index">Smart money index</a> (SMI)</li> <li><a href="/wiki/Trend_line_(technical_analysis)" title="Trend line (technical analysis)">Trend line</a></li> <li><a href="/wiki/Trix_(technical_analysis)" title="Trix (technical analysis)">Trix</a></li> <li><a href="/wiki/Vortex_indicator" title="Vortex indicator">Vortex indicator</a> (VI)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Momentum_(finance)" title="Momentum (finance)">Momentum</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/Money_flow_index" title="Money flow index">Money flow index</a> (MFI)</li> <li><a href="/wiki/Relative_strength_index" title="Relative strength index">Relative strength index</a> (RSI)</li> <li><a href="/wiki/Stochastic_oscillator" title="Stochastic oscillator">Stochastic oscillator</a></li> <li><a href="/wiki/True_strength_index" title="True strength index">True strength index</a> (TSI)</li> <li><a href="/wiki/Ultimate_oscillator" title="Ultimate oscillator">Ultimate oscillator</a></li> <li><a href="/wiki/Williams_%25R" title="Williams %R">Williams %R</a> (%R)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Volume_(finance)" title="Volume (finance)">Volume</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/Accumulation/distribution_index" title="Accumulation/distribution index">Accumulation/distribution line</a></li> <li><a href="/wiki/Ease_of_movement" title="Ease of movement">Ease of movement</a> (EMV)</li> <li><a href="/wiki/Force_index" title="Force index">Force index</a> (FI)</li> <li><a href="/wiki/Negative_volume_index" title="Negative volume index">Negative volume index</a> (NVI)</li> <li><a href="/wiki/On-balance_volume" title="On-balance volume">On-balance volume</a> (OBV)</li> <li><a href="/wiki/Put/call_ratio" title="Put/call ratio">Put/call ratio</a> (PCR)</li> <li><a href="/wiki/Volume%E2%80%93price_trend" title="Volume–price trend">Volume–price trend</a> (VPT)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Volatility_(finance)" title="Volatility (finance)">Volatility</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/Average_true_range" title="Average true range">Average true range</a> (ATR)</li> <li><a href="/wiki/Bollinger_Bands" title="Bollinger Bands">Bollinger Bands</a> (BB)</li> <li><a href="/wiki/Donchian_channel" title="Donchian channel">Donchian channel</a></li> <li><a href="/wiki/Keltner_channel" title="Keltner channel">Keltner channel</a></li> <li><a class="mw-selflink selflink">CBOE Market Volatility Index</a> (VIX)</li> <li><a href="/wiki/Standard_deviation" title="Standard deviation">Standard deviation</a> (σ)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Breadth_of_market" title="Breadth of market">Breadth</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/Advance%E2%80%93decline_line" title="Advance–decline line">Advance–decline line</a> (ADL)</li> <li><a href="/wiki/TRIN_(finance)" title="TRIN (finance)">Arms index</a> (TRIN)</li> <li><a href="/wiki/McClellan_oscillator" title="McClellan oscillator">McClellan oscillator</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</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/Coppock_curve" title="Coppock curve">Coppock curve</a></li> <li><a href="/wiki/Ulcer_index" title="Ulcer index">Ulcer index</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Analysts</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/John_Bollinger" title="John Bollinger">John Bollinger</a></li> <li><a href="/wiki/Ned_Davis_(analyst)" title="Ned Davis (analyst)">Ned Davis</a></li> <li><a href="/wiki/Charles_Dow" title="Charles Dow">Charles Dow</a></li> <li><a href="/wiki/Ralph_Nelson_Elliott" title="Ralph Nelson Elliott">Ralph Nelson Elliott</a></li> <li><a href="/wiki/Robert_Farrell_(technical_analyst)" class="mw-redirect" title="Robert Farrell (technical analyst)">Bob Farrell</a></li> <li><a href="/wiki/John_Murphy_(technical_analyst)" title="John Murphy (technical analyst)">John Murphy</a></li> <li><a href="/wiki/Mark_Hulbert" title="Mark Hulbert">Mark Hulbert</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=VIX&oldid=1255823716">https://en.wikipedia.org/w/index.php?title=VIX&oldid=1255823716</a>"</div></div> <div id="catlinks" class="catlinks" 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