Option pricing on foreign exchange in a Markov-modulated, incomplete-market economy

In this study, we investigate the currency option pricing in a Markov-modulated, incomplete-market economy. Specifically, the dynamics of the spot foreign exchange rate and the domestic/foreign instantaneous forward interest rates are, respectively, governed by a two-factor Markov-modulated stochastic volatility model with jumps and a Markov-modulated Heath-Jarrow-Morton model. The analytical expressions are obtainable using the random Esscher transform. Numerical examples are also given.