A Weak Approximation with Asymptotic Expansion and Multidimensional Malliavin Weights

Akihiko Takahashi and Toshihiro Yamada
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Akihiko Takahashi: Faculty of Economics, The University of Tokyo
Toshihiro Yamada: Graduate School of Economics, The University of Tokyo & MTEC

No CIRJE-F-909, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: 　　 This paper develops a new efficient scheme for approximations of expectations of the solutions to stochastic differential equations (SDEs). In particular, we present a method for connecting approximate operators based on an asymptotic expansion to compute a target expectation value precisely. The mathematical validity is given based on Watanabe and Kusuoka theories in Malliavin calculus. Moreover, numerical experiments for option pricing under local and stochastic volatility models confirm the effectiveness of our scheme.

Pages: 21 pages
Date: 2013-12
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2013cf909

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