Strong Convergence for Euler-Maruyama and Milstein Schemes with Asymptotic Method (Forthcoming in "International Journal of Theoretical and Applied Finance")

Hideyuki Tanaka and Toshihiro Yamada
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Hideyuki Tanaka: Ritsumeikan University
Toshihiro Yamada: The University of Tokyo

No CARF-F-333, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: Motivated by weak convergence results in the paper of Takahashi and Yoshida (2005), we show strong convergence for an accelerated Euler- aruyama scheme applied to perturbed stochastic differential equations. The Milstein scheme with the same acceleration is also discussed as an extended result. The theoretical results can be applied to analyzing the multi-level Monte Carlo method originally developed by M.B. Giles. Several numerical experiments for the SABR stochastic volatility model are presented in order to confirm the efficiency of the schemes.

Pages: 22
Date: 2013-11
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Citations: View citations in EconPapers (1)

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