The Non-Uniqueness of Partial Differential Equations Options Price Valuation Formula for Heston Stochastic Volatility Model

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Differential Equations Options Price Valuation Formula for Heston Stochastic Volatility Model</title> <meta name="description" content="The Non-Uniqueness of Partial Differential Equations Options Price Valuation Formula for Heston Stochastic Volatility Model"> <meta name="keywords" content="Black-Scholes partial differential equations, Ito process, option price valuation, partial differential equations"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar 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class="card-body"><strong>Paper Count:</strong> 87356</div> </div> </div> </div> <div class="card publication-listing mt-3 mb-3"> <h5 class="card-header" style="font-size:.9rem">The Non-Uniqueness of Partial Differential Equations Options Price Valuation Formula for Heston Stochastic Volatility Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20D.%20Ibrahim">H. D. Ibrahim</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20C.%20Chinwenyi"> H. C. Chinwenyi</a>, <a href="https://publications.waset.org/abstracts/search?q=T.%20Danjuma"> T. Danjuma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation. <iframe src="https://publications.waset.org/abstracts/131307.pdf" style="width:100%; height:400px;" frameborder="0"></iframe> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Black-Scholes%20partial%20differential%20equations" title="Black-Scholes partial differential equations">Black-Scholes partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Ito%20process" title=" Ito process"> Ito process</a>, <a href="https://publications.waset.org/abstracts/search?q=option%20price%20valuation" title=" option price valuation"> option price valuation</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equations" title=" partial differential equations"> partial differential equations</a> </p> <a href="https://publications.waset.org/abstracts/131307/the-non-uniqueness-of-partial-differential-equations-options-price-valuation-formula-for-heston-stochastic-volatility-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/131307.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">145</span> </span> </div> </div> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational 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The Non-Uniqueness of Partial Differential Equations Options Price Valuation Formula for Heston Stochastic Volatility Model