Abstract
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.
Citation
Naoto Kunitomo. Akihiko Takahashi. "On validity of the asymptotic expansion approach in contingent claim analysis." Ann. Appl. Probab. 13 (3) 914 - 952, August 2003. https://doi.org/10.1214/aoap/1060202831
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