Scaling and long range dependence in option pricing, IV: Pricing European options with transaction costs under the multifractional Black–Scholes model

Abstract

This paper deals with the problem of discrete time option pricing using the multifractional Black–Scholes model with transaction costs. Using a mean self-financing delta hedging argument in a discrete time setting, a European call option pricing formula is obtained. The minimal price of an option under transaction costs is obtained. In addition, we show that scaling and long range dependence have a significant impact on option pricing.