Title: Pricing Asian Options under a General Jump Diffusion Model

Steven Kou, Columbia University

Abstract:
We obtain a closed-form solution for the double-Laplace transform of Asian 
options under the hyper-exponential jump diffusion model (HEM).

Similar results are only available previously in the special case of Black-
Scholes model (BSM). Even in the case of BSM, our approach is simpler as we 
essentially use only the Ito's formula and do not need more advanced results 
such as those of Bessel processes and Lamperti's representation. Furthermore, 
our approach is more general as it applies to the HEM. 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 transforms can be 
inverted numerically via a two-sided Euler inversion algorithm. Numerical 
results indicate that our pricing method is fast, stable, and accurate.



This is a joint work with Ning Cai, Hong Kong Univ. of Science and Technology