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Geometrical Considerations on Heston's Market Model

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  • Dell'Era, Mario

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.

Suggested Citation

  • Dell'Era, Mario, 2010. "Geometrical Considerations on Heston's Market Model," MPRA Paper 21523, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:21523
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    File URL: https://mpra.ub.uni-muenchen.de/21523/1/MPRA_paper_21523.pdf
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    References listed on IDEAS

    as
    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    2. Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
    3. Vladimir Piterbarg, 2005. "Stochastic Volatility Model with Time-dependent Skew," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(2), pages 147-185.
    4. 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.
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    More about this item

    Keywords

    Quantitative methods in Finance;

    JEL classification:

    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • C0 - Mathematical and Quantitative Methods - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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