Malliavin differentiability of the Heston volatility and applications to option pricing

Elisa Alos, Christian-Oliver Ewald

    Research output: Contribution to journalArticlepeer-review

    30 Citations (Scopus)

    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 Alos (2006) in order to derive approximate option pricing formulae in the context of the Heston model. Numerical results are given.

    Original languageEnglish
    Pages (from-to)144-162
    Number of pages19
    JournalAdvances in Applied Probability
    Volume40
    Issue number1
    DOIs
    Publication statusPublished - Mar 2008

    Keywords

    • Malliavin calculus
    • stochastic volatility model
    • Heston model
    • Cox-Ingersoll-Ross process
    • Hull and White formula
    • option pricing
    • STOCHASTIC VOLATILITY
    • FORMULA

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