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 Itô 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.
- Asymptotic expansion
- Malliavin calculus
- Small disturbance asymptotics
- Valuation of financial contingent claims
- Watanabe-Yoshida theory