Empirical Study of the Effect of Including Skewness and Kurtosis in Black Scholes Option Pricing Formula on S&P CNX Nifty Index Options

Abstract

The most popular model for pricing options, both in financial literature as well as in practice has been the Black-Scholes model. In spite of its wide spread use the model appears to be deficient in pricing deep in the money and deep out of the money options using statistical estimates of volatility. This limitation has been taken into account by practitioners using the concept of implied volatility. The value of implied volatility for different strike prices should theoretically be identical, but is usually seen in the market to vary. In most markets across the world it has been observed that the implied volatilities of different strike prices form a pattern of either a ‘smile’ or ‘skew’. Theoretically, since volatility is a property of the underlying asset it should be predicted by the pricing formula to be identical for all derivatives based on that same asset. Hull [1993] and Nattenburg [1994] have attributed the volatility smile to the non normal Skewness and Kurtosis of stock returns. Many improvements to the Black-Scholes formula have been suggested in academic literature for addressing the issue of volatility smile. This paper studies the effect of using a variation of the BS model (suggested by Corrado & Sue [1996] incorporating non-normal skewness and kurtosis) to price call options on S&P CNX Nifty. The results strongly suggest that the incorporation of skewness and kurtosis into the option pricing formula yields values much closer to market prices. Based on this result and the fact that this approach does not add any further complexities to the option pricing formula, we suggest that this modified approach should be considered as a better alternative.