A Control Variate Method for Weak Approximation of SDEs via Discretization of Numerical Error of Asymptotic Expansion

Monte Carlo Methods and Applications, Volume 25, Issue 3, 239-252

Posted: 18 Jun 2020

See all articles by Yusuke Okano

Yusuke Okano

SMBC Nikko Securities

Toshihiro Yamada

Hitotsubashi University

Date Written: August 19, 2019

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

Suggested Citation

Okano, Yusuke and Yamada, Toshihiro, A Control Variate Method for Weak Approximation of SDEs via Discretization of Numerical Error of Asymptotic Expansion (August 19, 2019). Monte Carlo Methods and Applications, Volume 25, Issue 3, 239-252. Available at SSRN: https://ssrn.com/abstract=3609099

Yusuke Okano

SMBC Nikko Securities ( email )

Shin-Marunouchi Bldg
1-5-1 Marunouchi
Chiyoda-ku, Tokyo 100-6519
Japan

Toshihiro Yamada (Contact Author)

Hitotsubashi University ( email )

2-1 Naka Kunitachi-shi
Tokyo 186-8601
Japan

Here is the Coronavirus
related research on SSRN

Paper statistics

Abstract Views
16
PlumX Metrics