Asian options and meromorphic Levy processes

TL;DR

This paper introduces a novel approach for pricing Asian options in models driven by meromorphic Levy processes by expressing the exponential functional as an infinite product of beta variables, enabling efficient computation.

Contribution

It establishes the distribution of the exponential functional for meromorphic Levy processes as an infinite product of beta variables, facilitating improved pricing algorithms.

Findings

Derived the distribution of the exponential functional as an infinite beta product.

Expressed the Mellin transform as an infinite gamma product.

Developed an efficient algorithm for Asian option pricing.

Abstract

One method to compute the price of an arithmetic Asian option in a Levy driven model is based on the exponential functional of the underlying Levy 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 Levy process. We prove that the exponential functional is equal in distribution to an infinite product of indepedent 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.