European Foreign Exchange Options Pricing Research With Transaction Costs Based On Fraction Browinan Motion

In the1970s, with the collapsing of the Breton Woods System, exchange rate risk was concerned, and the floating exchange rate era came. As a result of option trading strong flexibility, foreign exchange options has become the obstacle to the risk and hedging tool.Using the mathematical model for pricing options is the key of Quantitative economic research. In this paper, with combination of the actual market fluctuation characteristics based on the traditional pricing model, changed the original assumptions, gave a more model consistent with the fluctuation in the foreign exchange market.This study is mainly divided into five parts.The first part is the introduction part. Included the research background, significances, research summary and contents, structure, and innovations.The second part introduced some basic concepts of option and BS option pricing model. From the option of development history, characteristics, classifications and so on, briefly introduced the option of some basic concepts, then introduced the Wiener process and Ito theorem, at last, gave the assumptions of BS option pricing model and BS option pricing formula.The third part is the core of the paper, introducing foreign exchange options pricing. The third part is mainly composed of four sections, the first section introduced the basic concepts of foreign exchange option, included the type and price. In the second section, without consider the transaction costs and any costs from the traditional theory, introduced fractional Brown motion, corrected to establish FBS model in the classical BSGK model. In the third section, from the actually, deduced the European exchange option pricing mode based on FBS with transaction costs. In the section4, considered transaction costs and the payments, established the foreign exchange option model with transaction costs and payments under two hypothesis.In the part4, discussed the foreign exchange option sensitivity analysis. With fractional Brown motion, established four option parameters expression under the FBS model; use the R/S analysis method to compute Hurst exponents, discussed the different parameters change of Hurst index of the model, draw in other conditions remain unchanged, Foreign exchange option price and the Hurst index was inversely proportional to, and maturity; at last, give the analysis model of the two kind of method:average squared deviation percentage ratio and regression analysis.The fifth part is the empirical analysis in this paper.This article took China Merchants Bank foreign exchange options as an example, analysis foreign exchange option price with two different models. Compared the simulated price and the real foreign exchange option price, do error analysis, when the Hurst index is larger, FBS model simulation of foreign exchange option price model is better than BS, when the Hurst index is small tend to the BS model, consistent with the theory.