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A weak approximation for Bismut’s formula: An algorithmic differentiation method

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  • Akiyama, Naho
  • Yamada, Toshihiro

Abstract

The paper provides a novel algorithmic differentiation method by constructing a weak approximation for Bismut’s formula. A new operator splitting method based on Gaussian Kusuoka-approximation is introduced for an enlarged semigroup describing “differentiation of diffusion semigroup”. The effectiveness of the new algorithmic differentiation is checked through numerical examples.

Suggested Citation

  • Akiyama, Naho & Yamada, Toshihiro, 2024. "A weak approximation for Bismut’s formula: An algorithmic differentiation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 386-396.
    • Handle: RePEc:eee:matcom:v:216:y:2024:i:c:p:386-396
    DOI: 10.1016/j.matcom.2023.09.003
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    References listed on IDEAS

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    1. Syoiti Ninomiya & Nicolas Victoir, 2008. "Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 107-121.
    2. Mariko Ninomiya & Syoiti Ninomiya, 2009. "A new higher-order weak approximation scheme for stochastic differential equations and the Runge–Kutta method," Finance and Stochastics, Springer, vol. 13(3), pages 415-443, September.
    3. Martin I. Reiman & Alan Weiss, 1989. "Sensitivity Analysis for Simulations via Likelihood Ratios," Operations Research, INFORMS, vol. 37(5), pages 830-844, October.
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