STRONG CONVERGENCE FOR EULER–MARUYAMA AND MILSTEIN SCHEMES WITH ASYMPTOTIC METHOD

Hideyuki Tanaka () and Toshihiro Yamada ()
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Hideyuki Tanaka: Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan
Toshihiro Yamada: Graduate School of Economics, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan;

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 02, 1-22

Abstract: Motivated by weak convergence results in the paper of Takahashi & Yoshida (2005), we show strong convergence for an accelerated Euler–Maruyama 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 analyze the multi-level Monte Carlo method originally developed by M.B. Giles. Several numerical experiments for the stochastic alpha-beta-rho (SABR) model of stochastic volatility are presented in order to confirm the efficiency of the schemes.

Keywords: Strong convergence; asymptotic method; multi-level Monte Carlo (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024914500149

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