An empirical application of Black and Scholes option pricing with fractional Brownian motion

Abstract

This thesis examines the empirical properties of a fractional Black and Scholes model developed by Röstek and Schobel. The model is tested and compared to the standard Black and Scholes for Standard and Poor’s 500 call options in the period 10th May to 10th of July 2018. We first go through the theoretical differences of using a geometrical and a fractional Brownian motion. We test the models using three different empirical tests, following the methods of Bakshi, Cao & Chen (1997). The performance is measured using an in-sample test, an out of sample test and running a dynamic delta hedging strategy over a period of 41 trading days. While testing the models, we highlight the importance of estimating the correct Hurst value (long-term dependence) as the model becomes time dependent. We find that the fractional Black and Scholes model is misspecified, but performs slightly better in the out of sample test. In total, we rank the fractional equal to the geometric model.