Foreign Exchange Option Pricing Model Based On Fraction Browinan Motion And Its Empirical Study

In the 1970s, with the collapsing of the Bretton Woods System, floating exchange rate era comes. As one of new financial derivatives, foreign exchange option has become important hedging and investing tool.How to use reasonable mathematical model to price foreign exchange option comes important problem to investor using option to hedge risk of exchange rate. So, in financial field, the pricing problem of option becomes one of important fields of theory and practice research. This paper assumes that the exchange rate return don't obey standards Browinan Motion, but general fraction Browinan Motion, and on this basis, gets the pricing model of exchange rate option.Because the fraction Browinan Motion is not semi-martingale and the theory of stochastic differential can't use directly, so, firstly, the paper introduces and summarizes the theories of fraction Browinan Motion stochastic differential by Yaozhong Hu, Bernt ?ksendal,Christian Bender,Robert J.Elliott and so on, secondly, the paper use risk-neutral pricing method to derivate exchange rate option pricing formula, and analyze the differences of model pricing results and the changing of sensitivity coefficient with different Hurst index underlying fraction Browinan motion.This paper also does empirical analysis with the example of personal exchange rate option issuing by china merchants bank. Using fraction Browinan motion exchange rate option pricing model and traditional pricing model, the paper, firstly, gets theory prices of personal exchange rate option, secondly, gets the pricing errors of the two models with the comparison of market prices, and finally, finds the fraction Browinan motion exchange rate option pricing model is better than traditional model with residual average percentage and regression analysis.