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A general decomposition formula for derivative prices in stochastic volatility models

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  • Elisa Alòs

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    Abstract

    We see that the price of an european call option in a stochastic volatility framework can be decomposed in the sum of four terms, which identify the main features of the market that affect to option prices: the expected future volatility, the correlation between the volatility and the noise driving the stock prices, the market price of volatility risk and the difference of the expected future volatility at different times. We also study some applications of this decomposition.

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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 665.

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    Date of creation: Feb 2003
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    Handle: RePEc:upf:upfgen:665

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

    Related research

    Keywords: Continuous-time option pricing model; stochastic volatility; Ito's formula; incomplete markets;

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    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    2. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
    3. 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, Society for Financial Studies, vol. 6(2), pages 327-43.
    4. Comte, F. & Renault, E., 1996. "Long Memory in Continuous Time Stochastic Volatility Models," Papers, Toulouse - GREMAQ 96.406, Toulouse - GREMAQ.
    5. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
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    Cited by:
    1. Elisa Alòs, 2004. "A generalization of Hull and White formula and applications to option pricing approximation," Economics Working Papers, Department of Economics and Business, Universitat Pompeu Fabra 740, Department of Economics and Business, Universitat Pompeu Fabra.

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