Effectiveness of the Skewness and Kurtosis Adjusted Black-Scholes Model in Pricing Nifty Call Options

Abstract

This paper tests the predictive accuracy of the Black-Scholes (BS) model in pricing the Nifty index option contracts and examines whether the skewness and kurtosis adjusted BS model of Corrado and Su (1996) gives better results than the original BS model. We also examine whether volatility smile in case of NSE Nifty options, if any, can be attributed to the non normal skewness and kurtosis of stock returns. We use S&P CNX NIFTY near-the-month call options for the period January 1, 2003 to December 24, 2008. The results show that BS model is misspecified as the implied volatility graph depicts the shape of a ‘Smile’ for the study period. There is significant underpricing by the original BS model and that the mispricing increases as the moneyness increases. Even the modified BS model misprices options significantly. However, pricing errors are less in case of the modified BS model than in case of the original BS model. On the basis of Mean Absolute Error (MAE) it can be concluded that the modified BS model is performing better than the original BS model. Moreover, volatility smile in case of NSE Nifty options for the study period cannot be attributed to the non normal skewness and kurtosis of stock returns.