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A weak approximation with Malliavin weights for local stochastic volatility model

Author

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  • Toshihiro Yamada

    (Hitotsubashi University, 2-1, Kunitachi, Tokyo, Japan)

Abstract

This paper introduces a new efficient and practical weak approximation for option price under local stochastic volatility model as marginal expectation of stochastic differential equation, using iterative asymptotic expansion with Malliavin weights. The explicit Malliavin weights for SABR model are shown. Numerical experiments confirm the validity of our discretization with a few time steps.

Suggested Citation

  • Toshihiro Yamada, 2017. "A weak approximation with Malliavin weights for local stochastic volatility model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-17, March.
    • Handle: RePEc:wsi:ijfexx:v:04:y:2017:i:01:n:s2424786317500025
    DOI: 10.1142/S2424786317500025
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    References listed on IDEAS

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    1. Akihiko Takahashi, 2015. "Asymptotic Expansion Approach in Finance," CARF F-Series CARF-F-356, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2015.
    2. Akihiko Takahashi & Toshihiro Yamada, 2015. "On Error Estimates for Asymptotic Expansions with Malliavin Weights: Application to Stochastic Volatility Model," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 513-541, March.
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    Cited by:

    1. Mishari Al-Foraih & Jan Posp'iv{s}il & Josep Vives, 2023. "Computation of Greeks under rough Volterra stochastic volatility models using the Malliavin calculus approach," Papers 2312.00405, arXiv.org.

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