Option pricing of a bi-fractional Black–Merton–Scholes model with the Hurst exponent in

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