Malliavin differentiability of the Heston volatility and applications to option pricing
AbstractWe 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  in order to derive approximate option pricing formulas in the context of the Heston model. Numerical results are given.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 3237.
Date of creation: 14 May 2007
Date of revision:
Malliavin calculus; stochastic volatility models; Heston model; Cox- Ingersoll-Ross process; Hull and White formula; Option pricing;
Find related papers by JEL classification:
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-05-19 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375.
- 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.
- 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.
- 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.
- Romain Bompis & Emmanuel Gobet, 2012. "Asymptotic and non asymptotic approximations for option valuation," Post-Print hal-00720650, HAL.
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