Two-Asset Option Pricing With Transaction Costs Under The Fractional Black-Scholes Model

Classic Black-Scholes option pricing formula is built on a series of strict assumptions。These assumptions are not consistent with the actual operation law in the real financial market, so the pricing results were not ideal when using Black-Scholes option pricing formula in practice. Therefore, relaxing the assumptions of the Black-Scholes option pricing model to get the option pricing formula which can reveal the actual operation rules in the real financial market is the hotspot in mathematical financial research, and is also the main problem in this paper.This paper first reviews systematically the research on option pricing. Then briefly introduced the useful knowledge of Random process and Behavioral finance, and presented the main two-asset options and their pricing formulas in the classic Black-Scholes model.The main results are in the following:according to the points of Behavioral finance, under the hypothesis of bounded rational investors we replaced the standard Brownian motion by the fractional Brownian motion in the classical Black-Scholes model, anchoring-adjustment by the Bayes theorem when estimating the probability, Taylor's formula by Ito formula in the continuous trading environment, and we solved the problem of discrete-time two-asset option pricing by the fractional Black-Scholes model with transaction costs. About this problem, we has not yet seen the similar papers at present. By a mean-self-financing delta-hedging argument in a discrete time setting, a two-asset option pricing differential equation is obtained. As an application of it, we get the pricing formulas of exchange option, outer performance option and better-of option. Furthermore, the minimal prices of these three options under transaction costs are obtained. In fact, these minimal prices are the super-hedging prices which can be used as the actual prices of them. In addition, we also know that scaling and long-range dependence have a significant impact on option pricing.