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

Toshihiro Yamada and Kenta Yamamoto

Quantitative Finance, 2020, vol. 20, issue 11, 1825-1837

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.

Date: 2020
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DOI: 10.1080/14697688.2018.1430371

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