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A general decomposition formula for derivative prices in stochastic volatility models

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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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  • 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.
    • Handle: RePEc:upf:upfgen:665
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    1. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    5. 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 637-654, May-June.
    6. 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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    Cited by:

    1. Elisa Alòs, 2004. "A generalization of Hull and White formula and applications to option pricing approximation," Economics Working Papers 740, Department of Economics and Business, Universitat Pompeu Fabra.

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    More about this item

    Keywords

    Continuous-time option pricing model; stochastic volatility; Ito's formula; incomplete markets;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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