The Minimal Entropy Martingale Measure (MEMM) for a Markov-Modulated Exponential Lévy Model

Abstract

This paper deals with the characterization problem of the minimal entropy martingale measure (MEMM) for a Markov-modulated exponential Lévy model. This model is characterized by the presence of a background process modulating the risky asset price movements between different regimes or market environments. This allows to stress the strong dependence of financial assets price with structural changes in the market conditions. Our main results are obtained from the key idea of working conditionally on the modulator-factor process. This reduces the problem to studying the simpler case of processes with independent increments. Our work generalizes some previous works in the literature dealing with either the exponential Lévy case or the exponential-additive case.

On the Price of Risk Under a Regime Switching CGMY Process

“…The Esscher transform is taken conditional on the information available on the Markov chain. The result by Momeya and Ben-Salah (2012) can be used to justify the choice of our pricing result by the minimal entropy martingale measure. It is also worth mentioning that the work Gerber and Shiu (1994) introduces Esscher transform in actuarial science as the pricing measure for option valuation and justify this choice by maximizing the expected utility of power type of an investor.…”