A control variate method for weak approximation of SDEs via discretization of numerical error of asymptotic expansion

Okano Yusuke () and Yamada Toshihiro ()
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Okano Yusuke: Hitotsubashi University, TokyoJapan(current affiliation: SMBC Nikko Securities Inc., Tokyo, Japan)
Yamada Toshihiro: Hitotsubashi University, Tokyo, Japan

Monte Carlo Methods and Applications, 2019, vol. 25, issue 3, 239-252

Abstract: The paper shows a new weak approximation method for stochastic differential equations as a generalization and an extension of Heath–Platen’s scheme for multidimensional diffusion processes. We reformulate the Heath–Platen estimator from the viewpoint of asymptotic expansion. The proposed scheme is implemented by a Monte Carlo method and its variance is much reduced by the asymptotic expansion which works as a kind of control variate. Numerical examples for the local stochastic volatility model are shown to confirm the efficiency of the method.

Keywords: Heath–Platen estimator; weak approximation; stochastic differential equation; asymptotic expansion; Monte Carlo simulation (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1515/mcma-2019-2044

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