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Asia-Pacific Financial Markets

, Volume 20, Issue 2, pp 147–182 | Cite as

Pricing Exotic Options and American Options: A Multidimensional Asymptotic Expansion Approach

  • Masahiro Nishiba
Article

Abstract

This paper introduces a new method for pricing exotic options whose payoff functions depend on several stochastic indices and American options in multidimensional models. This method is based on two ideas. One is an application of the asymptotic expansion method for the law of a multidimensional diffusion process. The other is the combination of the asymptotic expansion method and the method called backward induction. The author applies the method to the problems of pricing call options on the maximum of two assets in the CEV model, average strike options in the Black–Scholes model and American options in the Heston model. Numerical examples show practical effectiveness of the proposed method.

Keywords

American option Asymptotic expansion Average strike option Black–Scholes model CEV model Call option on the maximum of two assets Heston model Monte Carlo Quasi-Monte Carlo Simulation 

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Copyright information

© Springer Japan 2013

Authors and Affiliations

  1. 1.Tokyo Institute of TechnologyTokyoJapan

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