"On Validity of the Asymptotic Expansion Approach in Contingent Claim Analysis"

Kunitomo and Takahashi (1995), and Takahashi (1997) 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.