Performance of the Black-Scholes option pricing model : empirical evidence on S&P 500 call options in 2014

Abstract

This paper evaluates performance of the Black-Scholes option pricing model on European call options that are written on U.S. S&P 500 equity index in year 2014. Main purpose is to show empirical evidence about false assumptions contained in the model and complete it by relaxing unconditional restrictions. Analysis consists of investigating biasedness and heteroscedasticity properties by complementing the Black-Scholes model with GARCH(1,1) method based on maximum likelihood estimations. Varying volatility is studied also through implicit volatility surface.

Depending on their characteristics, call options are categorized into specific groups according to their moneyness and maturity for further analysis. Using common econometrics and statistical methods, the paper shows that assumption about constant volatility is false, that the Black-Scholes model exhibits a bias which leads to mispricing of certain type of options and that assumption about normally distributed error term is false. Volatility is estimated through historical and implicit methods, of which the latter one uses GARCH(1,1) method to capture especially time-series characteristics of varying volatility.

Findings regarding performance of the Black-Scholes option pricing model were expected and are in line with prior literature.