Scaling and long-range dependence in option pricing III: A fractional version of the Merton model with transaction costs

Abstract

A model for option pricing of fractional version of the Merton model with ‘Hurst exponent’ H being in [ 1 / 2 , 1 ) is established with transaction costs. In particular, for H ∈ ( 1 / 2 , 1 ) the minimal price C min ( t , S t ) of an option under transaction costs is obtained, which displays that the timestep δ t and the ‘Hurst exponent’ H play an important role in option pricing with transaction costs.