International Journal of Stochastic Analysis
Volume 2011 (2011), Article ID 843246, 14 pages
Research Article

Regime-Switching Risk: To Price or Not to Price?

Department of Applied Finance and Actuarial Studies and the Centre for Financial Risk, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia

Received 8 October 2011; Accepted 13 November 2011

Academic Editor: Lukasz Stettner

Copyright © 2011 Tak Kuen Siu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Should the regime-switching risk be priced? This is perhaps one of the important “normative” issues to be addressed in pricing contingent claims under a Markovian, regime-switching, Black-Scholes-Merton model. We address this issue using a minimal relative entropy approach. Firstly, we apply a martingale representation for a double martingale to characterize the canonical space of equivalent martingale measures which may be viewed as the largest space of equivalent martingale measures to incorporate both the diffusion risk and the regime-switching risk. Then we show that an optimal equivalent martingale measure over the canonical space selected by minimizing the relative entropy between an equivalent martingale measure and the real-world probability measure does not price the regime-switching risk. The optimal measure also justifies the use of the Esscher transform for option valuation in the regime-switching market.