A comparison of European and Asian options under Markov additive processes

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.