Solving Black-Schole Equation Using Standard Fractional Brownian Motion | Njamen Njomen | Journal of Mathematics Research | CCSE

In this paper, we emphasize the Black-Scholes equation using standard fractional Brownian motion BHwith the hurst index H ∈ [0,1]. N. Ciprian (Necula, C. (2002)) and Bright and Angela (Bright, O., Angela, I., & Chukwunezu (2014)) get the same formula for the evaluation of a Call and Put of a fractional European with the different approaches. We propose a formula by adapting the non-fractional Black-Scholes model using a λHfactor to evaluate the european option. The price of the option at time t ∈]0,T[ depends on λH(T ？ t), and the cost of the action St, but not only from t ？ T as in the classical model. At the end, we propose the formula giving the implied volatility of sensitivities of the option and indicators of the financial market