Scaling and long-range dependence in option pricing II: Pricing European option with transaction costs under the mixed Brownian–fractional Brownian model

Abstract

This paper deals with the problem of discrete-time option pricing by the mixed Brownian–fractional Brownian model with transaction costs. By a mean-self-financing delta hedging argument in a discrete-time setting, a European call option pricing formula is obtained. In particular, the minimal pricing c min ( t , s t ) of an option under transaction costs is obtained, which shows that timestep δ t and Hurst exponent H play an important role in option pricing with transaction costs. In addition, we also show that there exists fundamental difference between the continuous-time trade and discrete-time trade and that continuous-time trade assumption will result in underestimating the value of a European call option.