Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model

Authors:
Ning Cai;Steven Kou
Affiliations:
Department of Industrial Engineering and Logistics Management, Hong Kong University of Science and Technology, Kowloon, Hong Kong;Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
Venue:
Operations Research
Year:
2012

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Abstract

We obtain a closed-form solution for the double-Laplace transform of Asian options under the hyper-exponential jump diffusion model. Similar results were available previously only in the special case of the Black-Scholes model (BSM). Even in the case of the BSM, our approach is simpler as we essentially use only Itô's formula and do not need more advanced results such as those of Bessel processes and Lamperti's representation. As a by-product we also show that a well-known recursion relating to Asian options has a unique solution in a probabilistic sense. The double-Laplace transform can be inverted numerically via a two-sided Euler inversion algorithm. Numerical results indicate that our pricing method is fast, stable, and accurate; and it performs well even in the case of low volatilities.