Pricing European put currency options in a two-factor regime-switching market

In the real spot foreign exchange market, it is obvious that the jumps of the exchange rate do exist due to the rare catastrophic economic crisis or the macroeconomic regime switching between "recession" and "boom". In addition, the foreign rate and the domestic/foreign interest rate all depend on the states of the economy. This paper we will exploit the two-factor regime-switching processes with Heston's stochastic volatility to characterize the exchange rate dynamics. In this situation, the market is incomplete and there are infinitely many equivalent martingale measures. We will adopt the risk minimizing approach to find the equivalent domestic martingale measure condition and determine the equivalent domestic martingale measure for pricing contingent claims on European put currency options.