A comparison of European and Asian options under Markov additive processes

TL;DR

This paper extends exponential Levy models to Markov additive processes (MAPs), analyzing their integrability properties and applying Mellin transform and PDE methods to value European options, then comparing European and Asian call option prices.

Contribution

It introduces integrability analysis for exponential MAPs and develops valuation methods for European options within this framework, including a comparison with Asian options.

Findings

Exponential MAPs exhibit specific integrability properties.

Valuation of European options using Mellin transform and PDE methods.

European call options are compared with Asian call options in this model.

Abstract

We provide results relating to the integrability, uniform integrability and local integrability of exponential MAPs, which are natural extensions of exponential Levy models. Then, we use Mellin transform and partial integro-differential equation methods to value European options under a such a model. Finally, a comparison is made between the price of a European call option and that of an Asian call option.