Path-dependent options in semi-Markov regime switching models

Abstract

The aim of this thesis is to study option pricing of continuously sampled arithmetic Asian options in a semi-Markov Modulated market. As per the best of our knowledge this has not been done before. We start by reviewing the fundamentals of option pricing theory including the application of Follmer-Schweizer decomposition in incomplete markets to find the locally risk minimizing price of contingent claims. We then re-examine the pricing of path dependent options in markets where there are no regime switching and using the knowledge of pricing of vanilla options in regime switching markets we try to study the pricing of Asian options in the semi-Markov regime switching market. We show that the price function satisfies a PDE by deriving the Follmer-Schweizer decomposition of the claim. We also show that the PDE is equivalent to an integral solution using which the existence and uniqueness of classical solution to the PDE is proved.