Currency Option Pricing Under Jump-diffusion Model

Since 1970s,after Bretton woods system collapsed, western countries began to implement floating exchange rate system universally,so has China since July 2005. In the floating exchange rate system,the exchange rate changes frequently and largely, the following currency risk control problem becomes a serious problem that every participant has to be faced with and concerned for,so does the financier. Recently, some research on the use of trade strategies and tools to avoid currency risk effectively develops quickly ,especially on the financial derivatives as risk management tools. With the depth of financial creativity,there exists many different kinds of financial derivatives the financial market, forward contracts,futures and options are the most basic. They all have the ability to speculate,arbitrage,hedge,but options attract more people. Because of the disparity between rights and obligations, the holders could always choose the best price for them, but have to pay for :premium.Then the currency option pricing problem becomes a problem that we have to solve.Under the assumption of complete market,by means of martingale method, this paper does some research on the currency option pricing in a jump-diffusion model. The main results are as follows:1.Assuming that both domestic and foreign interest rates are non-stochastic, we get the pricing formula for currency call option, so does the currency put option.As the financial market is unstable, interest rates changes all the time, so this thesis pays more attention to the stochastic models.2.Assuming that both domestic and foreign interest rates are stochastic, and based on a single source of uncertainty, that is Single-factor model, we get the pricing formulas for both currency call and put option, then the put-call parity relationship is derived.3.Assuming that both domestic and foreign interest rates are based on two different sources of uncertainty, that is two-factor model. we also get the pricing formulas for both currency call and put option, then the put-call parity relationship is derived.