Malliavin differentiability of the Heston volatility and applications to option pricing. (English) Zbl 1137.91422
Summary: 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 E. Alòs [Finance Stoch. 10, No. 3, 353–365 (2006; Zbl 1101.60044)] in order to derive approximate option pricing formulae in the context of the Heston model. Numerical results are given.
MSC:
91G80 | Financial applications of other theories |
60H07 | Stochastic calculus of variations and the Malliavin calculus |
60H30 | Applications of stochastic analysis (to PDEs, etc.) |
91G20 | Derivative securities (option pricing, hedging, etc.) |
Keywords:
Malliavin calculus; stochastic volatility model; Heston model; Cox-Ingersoll-Ross process; Hull and White formula; option pricingCitations:
Zbl 1101.60044References:
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