Asian options and meromorphic Levy processes

作者：Hackmann D; Kuznetsov A^*

来源：Finance and Stochastics, 2014, 18(4): 825-844.

DOI：10.1007/s00780-014-0237-8

• Asian option
• Meromorphic process
• Hyper-exponential process
• Exponential functional
• Mellin transform
• Gamma function

One method to compute the price of an arithmetic Asian option in a L,vy driven model is based on an exponential functional of the underlying L,vy process: If we know the distribution of the exponential functional, we can calculate the price of the Asian option via the inverse Laplace transform. In this paper, we consider pricing Asian options in a model driven by a general meromorphic L,vy process. We prove that the exponential functional is equal in distribution to an infinite product of independent beta random variables, and its Mellin transform can be expressed as an infinite product of gamma functions. We show that these results lead to an efficient algorithm for computing the price of the Asian option via the inverse Mellin-Laplace transform, and we compare this method with some other techniques.

• 出版日期2014-10