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Malliavin differentiability of the Heston volatility and applications to option pricing

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  • Alos, Elisa
  • Ewald, Christian-Oliver

Abstract

We prove that the Heston volatility is Malliavin differentiable under the classical Novikov condition and give an explicit expression for the derivative. This result guarantees the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model. Furthermore we derive conditions on the parameters which assure the existence of the second Malliavin derivative of the Heston volatility. This allows us to apply recent results of the first author [3] in order to derive approximate option pricing formulas in the context of the Heston model. Numerical results are given.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 3237.

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Date of creation: 14 May 2007
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Handle: RePEc:pra:mprapa:3237

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Keywords: Malliavin calculus; stochastic volatility models; Heston model; Cox- Ingersoll-Ross process; Hull and White formula; Option pricing;

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  1. Jérôme Detemple & René Garcia & Marcel Rindisbacher, 2005. "Representation formulas for Malliavin derivatives of diffusion processes," Finance and Stochastics, Springer, vol. 9(3), pages 349-367, 07.
  2. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375.
  3. 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.
  4. 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.
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Cited by:
  1. Christian-Oliver Ewald & Zhaojun Yang, 2008. "Utility based pricing and exercising of real options under geometric mean reversion and risk aversion toward idiosyncratic risk," Computational Statistics, Springer, vol. 68(1), pages 97-123, August.
  2. Romain Bompis & Emmanuel Gobet, 2012. "Asymptotic and non asymptotic approximations for option valuation," Post-Print hal-00720650, HAL.
  3. Elisa Alòs, 2012. "A decomposition formula for option prices in the Heston model and applications to option pricing approximation," Finance and Stochastics, Springer, vol. 16(3), pages 403-422, July.

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