Valuation of European Currency Options in Financial Engineering

In this paper, we try to solve the valuation of currency option in financial engineering. We use a generalized jump-diffusion system to describe the spot Foreign Exchange (FX) rate and apply regime switching model to describe the domestic and foreign risk-free interest rate and the appreciation rate and the volatility. And the regime switching model is based on a continuous time finite state Markov process. Under the minimal martingale measure, we obtain a system of partial-differential-integral-equations satisfied by the European currency option prices. Our model provides the flexibility to model different kinds of dynamics in FX rate. At last, we present a simulation of option pricing with the special case of compound Poisson jump and we can find the effects of the parameters on the prices.