A weak approximation with asymptotic expansion and multidimensional Malliavin weights (Revised version of CARF-F-335; Forthcoming in Annals of Applied Probability”)”
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).