CIRJE-F-909 | "A Weak Approximation with Asymptotic Expansion and Multidimensional Malliavin Weights" |
Author Name | Yamada and Toshihiro, Akihiko Takahashi |
Date | December 2013 |
Full Paper | PDF file |
Remarks | Revised in January 2014 and February 2015; Subsequently published in Annals of Applied Probability, Vol. 26, No.2, pp.818–856, April 2016. |
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 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 improve the accuracy at deep Out-of-The-Moneys (OTMs). |