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The asymptotic expansion approach to the valuation of interest rate contingent claims. (English) Zbl 0994.91023

A new methodology for the valuation problem of financial contingent claims is proposed, when the underlying asset prices follow a general class of continuous Itô processes. The method proposed can be applied to a wide range of valuation problems. It is illustrated by two examples: the valuation problems of swaptions and Asian options for interest rates. Some explicit formulas for solutions being sufficiently numerically accurate for practical purposes in most cases are given. The continuous stochastic processes for spot or forward interest rates are not necessarily Markovian nor diffusion processes in the usual sense. Nevertheless the approach can be rigorously justified by the Malliavin-Watanabe calculus in stochastic analysis.

MSC:

91B28 Finance etc. (MSC2000)
60H99 Stochastic analysis
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