Effectiveness of the Black and Scholes Model in Pricing Nifty Call Options

Abstract

Derivatives  today  constitute  the  most  important  segment  of  the  Indian  securities  market. Fischer Black and Myron Scholes (1973) made a major contribution in the subject matter of derivatives when they developed the theoretical model for the pricing of European options. The model influenced  the  academicians  and  practitioners  in  a  great  way  to  price  European  options. This study uses S&P CNX NIFTY call and put options for analysis for the sample period starting from January 1, 2003 through December 24, 2008. The objectives of the present study are to check whether implied volatility is a better predictor of volatility of future stock returns than historical volatility or not, to check whether there exists any correlation between historical volatility and implied volatility, to examine whether Black and Scholes model is misspecified or not by investigating the existence of volatility smile in case of S&P CNX Nifty options traded at NSE and to examine the predictive accuracy of the Black-Scholes model in pricing the Nifty index option contracts. The results show that implied volatility is more efficient predictor of option prices than historical volatility and there is a significant and positive correlation between historical volatility and implied volatility in case of the near month call and put option contracts. The implied volatility graphs for different samples depict the shape of a ‘Smile' which indicates that out-of-the money options and in-the-money options are having high volatility values while near-the-money options are having low volatility values, The BS model provides pricing errors but pricing errors are less in the case of near-the-money call options, errors slowly increase as moneyness increases.