Pricing European Options under Fractional Black-Scholes Model with a Weak Payoff Function

The purpose of this paper is to obtain an explicit solutions of the fractional Black-Scholes model with a weak payoff function. To do this, we derive fractional Black-Scholes equation by creating a self-financing portfolio strategy under Leland's strategy. Then, we use the Mellin transform method for solving this equation and obtain the price of a European option as a particular case of the proposed solution. A sensitivity analysis is carried out through numerical experiments which shows the differences between Black-Scholes model and the fractional Black-Scholes model. Moreover, an empirical analysis shows that the fractional Black-Scholes model with Hurst exponent greater than one-half is more precise to predict the real market prices than the classical Black-Sholes model.