In this paper, we study the valuation of European currency options when the dynamics of the spot foreign exchange rate are driven by geometric Brownian motions with Markov-modulated Poisson processes. Under such dynamics, the jump events are described as a compound Poisson process with log-normal jump size, and the regime-switching arrival intensity is governed by a continuous-time finite-state Markov chain. Since the market is incomplete, we present a framework for option valuation using the technique of Esscher transforms. After determining the Esscher parameters, we derive the analytical pricing formulas of European currency options under Markov-modulated jump risks.
International Research Journal of Finance and Economics, No.114, 93-101