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April 2016 A weak approximation with asymptotic expansion and multidimensional Malliavin weights
Akihiko Takahashi, Toshihiro Yamada
Ann. Appl. Probab. 26(2): 818-856 (April 2016). DOI: 10.1214/15-AAP1105


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 with multidimensional Malliavin weights 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. Especially, our weak approximation substantially improves the accuracy at deep Out-of-The-Moneys (OTMs).


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Akihiko Takahashi. Toshihiro Yamada. "A weak approximation with asymptotic expansion and multidimensional Malliavin weights." Ann. Appl. Probab. 26 (2) 818 - 856, April 2016.


Received: 1 December 2013; Revised: 1 September 2014; Published: April 2016
First available in Project Euclid: 22 March 2016

zbMATH: 1339.60099
MathSciNet: MR3476626
Digital Object Identifier: 10.1214/15-AAP1105

Primary: 60H07, 91G20, 91G60

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.26 • No. 2 • April 2016
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