Option pricing of a bi-fractional Black–Merton–Scholes model with the Hurst exponent HH in [12,1]

A model for option pricing of a (γ,2H)(γ,2H)-fractional Black–Merton–Scholes equation driven by the dynamics of a stock price S(t)S(t) satisfying (dS)2H=μS2H(dt)2H+σS2HdBH(t), where BH(t)BH(t) is a fractional Brownian motion with Hurst exponent H∈(0,1)H∈(0,1), is established. We obtain the explicit option pricing formulas for the European call option and put option for γ>0,12≤H≤1.