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

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.

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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

Information

Published: August 2003
First available in Project Euclid: 6 August 2003

zbMATH: 1091.91037
MathSciNet: MR1994041
Digital Object Identifier: 10.1214/aoap/1060202831

Subjects:
Primary: 90A09
Secondary: 60H07

Keywords: asymptotic expansion , Malliavin calculus , small disturbance asymptotics , validity , Valuation of financial contingent claims , Wanatabe-Yoshida theory

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.13 • No. 3 • August 2003
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