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Application of Malliavin calculus to exact and approximate option pricing under stochastic volatility

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  • S. Kuchuk-Iatsenko
  • Y. Mishura
  • Y. Munchak

Abstract

The article is devoted to models of financial markets with stochastic volatility, which is defined by a functional of Ornstein-Uhlenbeck process or Cox-Ingersoll-Ross process. We study the question of exact price of European option. The form of the density function of the random variable, which expresses the average of the volatility over time to maturity is established using Malliavin calculus.The result allows calculate the price of the option with respect to minimum martingale measure when the Wiener process driving the evolution of asset price and the Wiener process, which defines volatility, are uncorrelated.

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  • S. Kuchuk-Iatsenko & Y. Mishura & Y. Munchak, 2016. "Application of Malliavin calculus to exact and approximate option pricing under stochastic volatility," Papers 1608.00230, arXiv.org.
    • Handle: RePEc:arx:papers:1608.00230
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    References listed on IDEAS

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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.
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    5. Mark. B. Garman., 1976. "A General Theory of Asset Valuation under Diffusion State Processes," Research Program in Finance Working Papers 50, University of California at Berkeley.
    6. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
    7. Sergii Kuchuk-Iatsenko & Yuliya Mishura, 2015. "Pricing the European call option in the model with stochastic volatility driven by Ornstein--Uhlenbeck process. Exact formulas," Papers 1510.01848, arXiv.org.
    8. Josep Perello & Ronnie Sircar & Jaume Masoliver, 2008. "Option pricing under stochastic volatility: the exponential Ornstein-Uhlenbeck model," Papers 0804.2589, arXiv.org, revised May 2008.
    9. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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    Cited by:

    1. Ayub Ahmadi & Mahdieh Tahmasebi, 2024. "Pricing and delta computation in jump-diffusion models with stochastic intensity by Malliavin calculus," Papers 2405.00473, arXiv.org, revised Feb 2025.

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