Malliavin differentiability of the Heston volatility and applications to option pricing

Alos, Elisa and Ewald, Christian-Oliver (2007): Malliavin differentiability of the Heston volatility and applications to option pricing.

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.

• Item Type: MPRA Paper
• Institution: University of St.Andrews, School of Economics and Finance
• Language: English
• Keywords: Malliavin calculus; stochastic volatility models; Heston model; Cox- Ingersoll-Ross process; Hull and White formula; Option pricing
• Subjects: G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing; G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods

References

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