Geometric Shape To Brown Motion, Foreign Exchange Option Pricing

Along with Breton woods system's disintegration, Western various countries began to implement the floating exchange rate system universally. The exchange rate question becomes the concerned matter and the foreign exchange option arises at the historic moment for guarding the exchange risk.The foreign exchange option is one very good tool to keeping away from risks. The Multinational Corporation competing in the superheating time, it already became one of each company important work to control and shift the exchange rate risks. Whether to control the good exchange rate risk well becomes the crucial matter for enterprises.In the traditional option price, it is general to consider the stock price following the geometry Brown movement, but in fact the geometry Brown movement is not portrays the stock price process the ideal tool. In the empirical study, we discovered that the stock price movement has characteristics such as similarity, long-term dependence which belongs to geometry fractional Brown movement not geometry Brown movement. It makes geometry fractional Brownian motion depicts the process of stock price better then geometry Brownian motion.Under the assumption of no arbitrage, complete and balanced foreign exchange market, by means of fair premium in insurance and random analysis, this paper studied the foreign exchange option price question which obey the geometry fractal Brown movement. The main result as follows:1. Assumpting that the domestic and foreign interest rates are stochastic based on a single geometry the Brown movement that is Single-factor model, using fair premium in insurance, we obtain the formula of Europe foreign exchange option price and so the fair price formula is.2. Assumpting that both the domestic and foreign interest rates are based on two different geometry the Brown movement, that is double-factor model, using the linear attribute of geometry fractal Brown movement, we transform the double-dimensional geometry fractal Brown movement to the single dimension geometry fractal Brown movement and solve the priced problem for double-factor geometry fractal Brown movement to foreign exchange option.3. Based on the classics R/S method to analysis foreign currency, it pointes out that our country foreign exchange's deficiency and puts forward the constructive proposal.