Exchange Rates In The Target Area Diffusion Model For Option Pricing

Since the 90's in the 20th century, the exchange rate in a target zone was one of the most important and controversial issue about the exchange rate in the international financial community .In this paper, diffusion models for exchange rate in a target zone are applied to China, in order to explore which diffusion model the exchange rate of RMB against U.S. dollar to satisfy.First of all, we select two diffusion models for exchange rate in a target zone,and study the statistical characteristics of them to make preparation for the parameter estimation and empirical analysis.Secondly, the above-mentioned two models were estimated using martingale estimation method and the GMM based on the conditional moments. Through numerical simulation, we educe that the GMM based on the conditional moments is better than the martingale estimation method. Then we choose the exchange rate data of RMB against the U.S. dollar to estimate parameters and draw the fitting pictures. As a result of the correlation coefficient estimated in the second model is out of distortion, so the first model is more suitable for the Chinese short-term exchange rate market.Finally, we study the foreign currency option pricing about the two above-mentioned models. Generally, the option is priced using the martingale method . In this paper, non-payment of dividend of European options,European option to pay dividend and strong path dependence of the Asian foreign exchange options are priced using the method of hedging. In the end, we derive the partial differential equation to satisfy about them. And we preliminary study the pricing of the European foreign exchange option in the diffusion model for exchange rate in a target zone which the volatility meets the CIR model.