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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
  • Tiwari, Manvendra

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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 6329.

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Date of creation: Nov 2007
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Handle: RePEc:pra:mprapa:6329
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  1. Barone-Adesi, Giovanni & Whaley, Robert E., 1986. "The valuation of American call options and the expected ex-dividend stock price decline," Journal of Financial Economics, Elsevier, vol. 17(1), pages 91-111, September.
  2. Charles J. Corrado & Tie Su, 1996. "Skewness And Kurtosis In S&P 500 Index Returns Implied By Option Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-192, 06.
  3. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  5. Frank Milne & Dilip Madan, 1991. "Option Pricing With V. G. Martingale Components," Working Papers 1159, Queen's University, Department of Economics.
  6. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
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