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
Date Written: August 19, 2019
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
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