On Validity of the Asymptotic Expansion Approach in Contingent Claim Analysis
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 p...
| Veröffentlicht in: | The Annals of Applied Probability. - Institute of Mathematical Statistics. - 13(2003), 3, Seite 914-952 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2003
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| Zugriff auf das übergeordnete Werk: | The Annals of Applied Probability |
| Schlagworte: | Primary 90A09 Secondary 60H07 Valuation of financial contingent claims Asymptotic expansion Small disturbance asymptotics Validity Watanabe-Yoshida theory Malliavin calculus Business Mathematics mehr... |
| Zusammenfassung: | 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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| ISSN: | 10505164 |