Quanto Option Pricing With Transaction Costs Under The Fractional Black-scholes Model

With the gradual opening up of China's financial markets, domestic investors will get more foreign investment opportunities. But Investing in foreign investment in domestic financial assets and financial assets are not the same. Investing in foreign financial assets measured in foreign currency earnings, which need to be converted into RMB. So the investment income not only by foreign financial assets price changes, but also by the effects of changes in exchange rates. In this paper, I studied the quanto option which is the most representative of this type of financial derivatives.As the classic B-S option pricing formula is based on the efficient market hypothesis. But the assumption is too idealistic ,thus quanto option pricing formula is not practical, and it can not provide investors with a good basis. Therefore, relaxing the assumptions of the B-S option pricing formula is the main problem in this paper.The main results are in the following: In the process of option pricing, consider the investor's judgments play a role in pricing,based on the anchoring and adjustment heuristic in behavioral finance, we replaced the standard Brownian motion by the fractional Brownian motion in the classical Black- Scholes model. Construct a replicating portfolio of quanto option and obtain a quanto option pricing formula under the Brownian-fractional Brownian model in the discrete-time trade setting by a mean-self-financing Delta-hedging argument. In order to be closer to real financial markets, the paper also considers the European stock exchange transaction fees, then obtained a quanto option pricing formula with transaction costs under the Brownian-fractional Brownian model. Further illustrates the Brownian motion is a special case of the fractional Brownian motion in the time of H=1/2.The studies of using of fractional Brownian motion to study the quanto option pricing, have not yet seen in other reports.