On validity of the asymptotic expansion approach in contingent claim analysis

• 成果类型: Article
• 署名作者: Kunitomo, N; Takahashi, A
• 署名单位: University of Tokyo; University of Tokyo
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2003
• 页码: 914-952
• 关键词: malliavin calculus; valuation

摘要

Kunitomo and Takahashi (1995, 2001) have proposed a new methodology, called small disturbance asymptotics, for the valuation problem of financial contingent claims when the underlying asset prices follow a general class of continuous Ito processes. It can be applicable to a wide range of valuation problems, including complicated contingent claims associated with the Black-Scholes model and the term structure model of interest rates in the Heath-Jarrow-Morton framework. Our approach can be rigorously justified by an infinite-dimensional analysis called the Watanabe-Yoshida theory on the Malliavin calculus recently developed in stochastic analysis.