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A generalization of Hull and White formula and applications to option pricing approximation

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  • Elisa Alòs

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    Abstract

    By means of Malliavin Calculus we see that the classical Hull and White formula for option pricing can be extended to the case where the noise driving the volatility process is correlated with the noise driving the stock prices. This extension will allow us to construct option pricing approximation formulas. Numerical examples are presented.

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    File URL: http://www.econ.upf.edu/docs/papers/downloads/740.pdf
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    Bibliographic Info

    Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 740.

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    Date of creation: Feb 2004
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    Handle: RePEc:upf:upfgen:740

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    Web page: http://www.econ.upf.edu/

    Related research

    Keywords: Continuous-time option pricing model; stochastic volatility; Malliavin calculus;

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    1. Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(04), pages 589-607, December.
    2. Elisa Alòs, 2003. "A general decomposition formula for derivative prices in stochastic volatility models," Economics Working Papers 665, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    5. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous-time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    7. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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