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A second-order discretization with Malliavin weight and Quasi-Monte Carlo method for option pricing

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  • Toshihiro Yamada
  • Kenta Yamamoto

Abstract

This paper shows a second-order discretization scheme for expectations of stochastic differential equations. We introduce a smart Malliavin weight which is given by a sum of simple polynomials of Brownian motions as an improvement of the scheme of Yamada [J. Comput. Appl. Math., 2017, 321, 427–447]. A new quasi-Monte Carlo simulation is proposed to obtain an efficient option pricing scheme. Numerical examples for the SABR model are shown to illustrate the validity of the scheme.

Suggested Citation

  • Toshihiro Yamada & Kenta Yamamoto, 2020. "A second-order discretization with Malliavin weight and Quasi-Monte Carlo method for option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 20(11), pages 1825-1837, November.
    • Handle: RePEc:taf:quantf:v:20:y:2020:i:11:p:1825-1837
    DOI: 10.1080/14697688.2018.1430371
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    Cited by:

    1. Yoshifumi Tsuchida, 2023. "Control Variate Method for Deep BSDE Solver Using Weak Approximation," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 30(2), pages 273-296, June.

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