Empirical Study of the effect of including Skewness and Kurtosis in Black Scholes option pricing formula on S&P CNX Nifty index Options

Saurabha, Rritu and Tiwari, Manvendra (2007): 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: black scholes, skewness, kurtosis, nse, nifty, india
• Subjects: G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing

References

1. Data on option prices, Retrieved October 30, 2007 from http://www.nseindia.com/ 2. Barone-Adesi, G. and R.E. Whaley (1986): “The Valuation of American Call Options and the Expected Ex-Dividend Stock Price Decline,” Journal of Financial Economics, 17:91-111. 3. Black, F. and Scholes, M. (1973): “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, 81:637-659. 4. Black, F. (1975): “Fact and Fantasy in the Use of Options,” Financial Analysts Journal, 31:36-72. 5. Brown, Christine A. and Robinson, David M. (2002): “Skewness and kurtosis implied by option prices: A correction,” Journal of Financial Research, Vol. XXV No. 2, 279-282. 6. Corrado, C. and Sue, T. (1997): “Implied Volatility Skews and Stock Index Skewness and Kurtosis in S&P 500 Index Option Prices,” European Journal of Finance, Vol. 3 No. 1, 73-85. 7. Corrado, C. and Sue, T. (1996): “Skewness and Kurtosis in S&P 500 Index Returns Implied by Option Prices,” Journal of Financial Research, Vol. XIX No. 2, 175-192. 8. Corrado, C. and Sue, T. (1996): “S&P 500 Index Option Tests of Jarrow and Rudd's Approximate Option Valuation Formula,” Journal of Futures Markets, Vol. 16 No. 6, 611-629. 9. Hull, J.C. (1993): Options, Futures, and Other Derivative Securities, Englewood Cliffs, N.J.: Prentice Hall. 10. Jarrow, R. and Rudd, A. (1982): “Implied Volatility Skews and Skewness and Kurtosis In Stock Option Prices,” Journal of Financial Economics, 10:347-369. 11. Longstaff, F. A. (1995): “Option pricing and the martingale restriction,” Review of Financial Studies, 8(4):1091-1124. 12. Madam, D. and Milne, F. (1991): “Option pricing with VG martingale components,” Mathematical Finance, 39-55 13. Misra, D., Kannan,R. and Misra, Sangeeta D. (2006): “Implied Volatility Surfaces: A study of NSE Nifty Options,” International Research Journal of Finance & Economics. 14. Merton, R.C. (1973): “The Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science, 4:141-183. 15. Nattenburg, S. (1994): Option Volatility and Pricing, Chicago: Probus Publishing. 16. Rubinstein, M. (1994): “Implied Binomial Trees,” Journal of Finance, 49:771-818. 17. Stuart, A. and Ord, J.K. (1987): Kendall's Advanced Theory of Statistics, New York: Oxford University Press. 18. Whaley, R.E. (1982): “Valuation of American Call Options on Dividend Paying Stocks,” Journal of Financial Economics, 10:29-58.