Abstract:
In the mathematical modeling of the classical option pricing models it is assumed that the underlying stock price process follows a geometric Brownian motion, but through statistical analysis persistency was found in the log-returns of some South African stocks and Brownian motion does not have persistency. We suggest the replacement of Brownian motion with fractional Brownian motion which is a Gaussian process that depends on the Hurst parameter that allows for the modeling of autocorrelation in price returns. Three fractional Black-Scholes (Black) models were investigated where the underlying is assumed to follow a fractional Brownian motion. Using South African options on futures and warrant prices these models were compared to the classical models.
