A WEAK APPROXIMATION WITH ASYMPTOTIC EXPANSION AND MULTIDIMENSIONAL MALLIAVIN WEIGHTS

• 成果类型: Article
• 署名作者: Takahashi, Akihiko; Yamada, Toshihiro
• 署名单位: University of Tokyo; Mitsubishi International Corporation (MIC)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1105
• 发表日期: 2016
• 页码: 818-856
• 关键词: cubature

摘要

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).