Empirical Performance of the Black-Scholes Model in India

Abstract

In this paper we empirically investigate the performance of the Black-Scholes (BS) model and its skewness-kurtosis adjusted modified version in Indian stock market using data on Nifty index call & put options over the period July, 2007 to June 2009. The presence of volatility smile in index options indicates that benchmark BS model is mis-specified. We also find that the pricing performance of the modified BS model is not significantly better than that of the benchmark BS model. In addition to the BS model, nine specifications of the ad-hoc Black-Scholes (AHBS) model are also examined. Among the nine model specifications examined only the model with standardized moneyness as independent variable best describes the smile pattern. The mis-pricing (measured in terms of MAPE) is highest in out-of-the-money and near maturity call and put options, while mis-pricing is lowest for the model with standardized moneyness as independent variable.