Markov modulated jump-diffusions for currency options when regime switching risk is priced

Abstract

In the current literature, regime-switching risk is NOT priced in the Markov-modulated jump-diffusion models for currency options. We therefore develop a hidden Markov-modulated jump-diffusion model under the regime-switching economy where the regime-switching risk is priced. In the model, the dynamics of the spot foreign exchange rate captures both the rare events and the time-inhomogeneity in the fluctuating currency market. In particular, the rare events are described by a compound Poisson process with log-normal jump amplitude, and the time-varying rates are formulated by a continuous-time finite-state Markov chain. Unlike previous research, the proposed model can price regime-switching risk, in addition to diffusion risk and jump risk, based on the Esscher transform conditional on a single initial regime of economy. Numerical experiments are conducted and their results reveal that the impact of pricing regime-switching risk on the currency option prices does not seem significant in contradictory to the findings made by Siu and Yang [Siu, TK and H Yang (2009). Option Pricing When The Regime-Switching Risk is priced. Acta Mathematicae Applicatae Sinica, English Series, Vol. 25, No. 3, pp. 369–388].