Option Pricing With Proportional Transaction Cost Under The Fractional Black-Scholes

In classic Black-Scholes option pricing model, the movement of asset price is assumed by following the geometric Brownian motion, so the movement of underlying assets price have the same properties. But a large number of empirical studies have shown that the underlying assets price do not follow random walk,but present the scaling laws and long-range dependence. So people put forward using fractional Brownian motion process with characteristics of these two views instead of the geometric Brownian motion of classical Black-Scholes model, better illustrated in process of the movement of asset price.In a real financial market,the financial data are discrete in nature.The transaction is carried out in discrete time the to pay certain transaction costs. if the investors trade continuous then they will face huge sums and cannot be ignored of the transaction costs.Thus, we assume that the trading occurs in a discrete time.In a discrete time, we assume that the investors are bounded rational investors.They adopt anchoring-adjustment strategy in making decisions by Delta-hedging argument under the mean-self-financing. Using a replicating portfolio with underlying asset and the riskless bond, we obtain the pricing formulas of European option pricing with proportional transaction costs under the fractional Black-Scholes model. With this model, The minimal price),(min tSt C of an option under transaction costs is obtained as timestepHk-ps-=D, which can be used as the actual price of an option.and also have the corresponding European option price. In addition,we also show that timestep and long-range dependence have a significant impact on option pricing.