Subdiffusive fractional Black–Scholes model for pricing currency options under transaction costs

Abstract

A new framework for pricing European currency option is developed in the case where the spot exchange rate follows a subdiffusive fractional Black–Scholes. An analytic formula for pricing European currency call option is proposed by a mean self-financing delta-hedging argument in a discrete time setting. The minimal price of a currency option under transaction costs is obtained as time-step [formula], which can be used as the actual price of an option. In addition, we also show that time-step and long-range dependence have a significant impact on option pricing.