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Geometrical Considerations on Heston's Market Model

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  • Dell'Era, Mario
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    Abstract

    We propose to discuss a new technique to derive an good approximated solution for the price of a European call and put options, in a market model with stochastic volatility. In particular, the model that we have considered is the Heston's model. This allows arbitrary correlation between volatility and spot asset returns. We are able to write the price of European call and put, in the same form in which one can see in the Black-Scholes model. The solution technique is based upon coordinate transformations that reduce the initial PDE in a straightforward one-dimensional heat equation.

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    File URL: http://mpra.ub.uni-muenchen.de/21523/
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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 21523.

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    Date of creation: 10 Mar 2010
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    Handle: RePEc:pra:mprapa:21523

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    Keywords: Quantitative methods in Finance;

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    1. Roger Lord & Remmert Koekkoek & Dick van Dijk, 2006. "A Comparison of Biased Simulation Schemes for Stochastic Volatility Models," Tinbergen Institute Discussion Papers 06-046/4, Tinbergen Institute, revised 07 Jun 2007.
    2. Vladimir Piterbarg, 2005. "Stochastic Volatility Model with Time-dependent Skew," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(2), pages 147-185.
    3. Christian Kahl & Peter Jackel, 2006. "Fast strong approximation Monte Carlo schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 513-536.
    4. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
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