Fractional black-scholes models: complete mle with application to fractional option pricing

Abstract

Geometric fractional Brownian motion (GFBM) is an extended model of the traditional geometric Brownian motion that is widely used for Black-Scholes option pricing. By considering GFBM, we are now able to capture the memory dependency. This method will enable us to derive the estimators of the drift, μ, volatility, !2, and also the index of self similarity, H, simultaneously. This will enable us to use the fractional Black-Scholes model with all the needed parameters. Simulation outcomes illustrate that our methodology is efficient and reliable. Empirical application to stock exchange index with option pricing under GFBM is also made.