The Pricing Of European Foreign Exchange Option Underlying Fraction Brownian Motion And Empirical Analysis

Floating exchange rate system is generally carried out, which leads to exchange rate risk has become increasingly exposed in financial market. Foreign exchange option has become more prominent as a hedging tool.B-S formula solves the problem of option pricing well, but it depends on the underlying assets subject to the normal distribution. However, the fraction Brow-nian motion inosculates well with the change of financial assets price by its unique long-term and the like character, so it describes the change of financial assets price more realistic.This article established a stochastic differential equation of rate based on frac-tion Brownian motion, it used the theory of fractal integral and risk-neutral pricing to get a new model of foreign exchange rate option pricing. In the new model, we assume that the risk-free interest rate of domestic and foreign are functions of time, which makes the new model more close to reality. In addition, the modified R/S analysis is applied to study China’s foreign exchange market, the conclusion indi-cates that China’s foreign exchange market has a clear fractal structure. The result provides a realistic basis for the new model. At last, this article compares the new model and the traditional model by empirical analysis and gets that the new model is superior.