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 widespread 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. 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 Black-Scholes model (suggested by Corrado and Sue 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, it is suggested that this modified approach should be considered as a better alternative.

Publication
ICFAI Journal of Derivatives Markets

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