On validity of the asymptotic expansion approach in contingent claim analysis

Naoto Kunitomo, Akihiko Takahashi

Research output: Contribution to journalArticle

48 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)914-952
Number of pages39
JournalAnnals of Applied Probability
Issue number3
Publication statusPublished - 1 Aug 2003


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

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