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Determining the Efficiency of the Black and Scholes Model in Pricing of Nifty Stock Call Options After Replacing the Spot Price by the Discounted Value of Future Price


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1 Department of Management Studies, YMCA University of Science and Technology, Faridabad, Haryana, India
     

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The aim of this research paper is to study the Black-Scholes model and the model after bring change in the spot price. The systematic difference between call option market prices and prices calculated under the Black-Scholes model have been observed for the valuation of call option contracts written on eight Indian stocks quoted on NSE. We have seen that Future prices of stocks are traded less than the market price which causes the negative cost of carry bias. The various pricing errors produced by the Black-Scholes model can be attributed to this difference. The negative cost carry problem has been addressed by Black in commodity market by using Future prices instead of spot prices as the Future prices incorporate cost of carry as well as the various mismatches faced by market. This research paper first examines the pricing errors produced by the Black-Scholes model and at the second stage it replaces spot price (S) in the original Black-Scholes model by the Discounting Value of the Future Price (DVFP) to gauge the pricing accuracy. It has been found that the exhibited errors under the Black- Scholes model are high and the model after replacing spot price by the DVFP shows improvement over the Black-Scholes model.

Keywords

Black-Scholes Model, Negative Cost of Carry, DVFP.
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  • Baile, W (1987), “An Empirical Investigation of the Market for comex Gold Future Options”, Journal of Finance, Vol. 42, No. 5, pp 1187-1194.

  • Black F (1975), “Fact and Fantasy in the use of options”. Financial analyst journal, vol. 31, pp. 36-41

  • Black F, and Scholes M (1972), “The valuation of option contracts and a test of market efficiency”, Journal of Finance, vol. 27

  • Black F, and Scholes M (1973), “The Pricing of Options and Corporate Liabilities”, The Journal of Political Economy, Vol. 81, No. 3, pp. 637-654.

  • Blomeyer, E and Boyd, J (1988), “Empirical Test of Boundary Conditions for Options on Treasury Bond Futures”, The Journal of Futures Markets, Vol. 8, pp 185-198.

  • Chiraz, A (2016), “Does the Index Futures Destabilize the Underlying Spot Market? Some Evidence from Frensh Stock Exchange”, Business and Economics Journal, Vol. 7, Issue 3, pp 1-9

  • Gencay Ramazan and Salih Aslihan (2003), “Degree of mispricing with the Black-Scholes model and nonparametric cures”, Annals of Economics and Finance, 4, pp. 73-101,

  • Robert Geske and Richard Roll (1984), “On valuing American call option with the Black-Scholes European Formula”, The Journal of Finance, Volume 39, Issue 2, pp 443-445.

  • Hull JC (2007), “Options, Futures, and other Derivatives”, Sixth Edition, Pearson prentice- Hall, India.

  • Jordan J V, Seale, W E, McCabe, N C and Kenyon (1987), “Transaction Data Tests of the Black model for Soyabean Futures option”, The Journal of Future Markets, Vol. 7, No. 5, pp 535-554

  • Jordan J V, and Seale, W E (1986), “Transaction Data Tests of Minimum Prices and Put Call Parity for Treasury Bond Future Options”, Advances in Futures and Options Research, Vol. 1, pp 63-87.

  • K P Rinalini (2006), “Effectiveness of the Black-Scholes Model for Pricing Options in Indian Option Market”, The ICFAI Journal of Derivatives Market, PP 6-19.

  • LauterBach, B and Schultz, P (2012), “Pricing Warrants: An Empirical Study of the Black-Scholes Model and Its Alternatives”, The Journal of Finance, Vol. 45, 1181-1209

  • MacBeth J D and Merville L J (1979), “An Emperical Examination of the Black-Scholes Call Option Prices”, Journal of Finance, vol. 34, pp. 1173-1186.

  • Mckenzie Scott, Gerace Dionigi Gerace and Subedar Zaffar (2007), “An Empirical Investigation of the Black-Scholes Model: Evidence from the Australian Stock Exchange, The Australasian Accounting Business and Finance Journal, pp page 71

  • Mitra, S K (20012), “Pricing of Index Options Using Black’s Model”, Global Journal of Management Business Research. Vol. 12.

  • Rubinstein M (1985), “Non-parametric Test of Alternative Option Pricing Models Using all Reported Trade and quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 Through August 31, 1978”, Journal of Finance, Vol. 40, N0. 2, pp 445-480.

  • Shastri, K and Tandon, K (1986), “An Empirical Test of a Valuation Model for American Options on Futures Contracts”, Journal of Financial and Quantitative Analysis, Vol. 21, Issue 04, pp 377-392

  • Thenmozhir, M “Future Trading, Information and Spot Price Volatility of Nse-50 Index Future Contract”, NSE Research paper 59, source: https://www.nseindia.com/content/research/Paper59.pdf

  • Thiel H (1961), Economic Forecast and Policy, 2nd Revised Edition, North Holland Publishing co., Amsterdam

  • Whaley, R E (1982), “Valuation of American Call Options on Dividend-Paying Stocks”, Journal of Financial Economics, pp 29-58.


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  • Determining the Efficiency of the Black and Scholes Model in Pricing of Nifty Stock Call Options After Replacing the Spot Price by the Discounted Value of Future Price

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Authors

Rajesh Kumar
Department of Management Studies, YMCA University of Science and Technology, Faridabad, Haryana, India
Rachna Agrawal
Department of Management Studies, YMCA University of Science and Technology, Faridabad, Haryana, India

Abstract


The aim of this research paper is to study the Black-Scholes model and the model after bring change in the spot price. The systematic difference between call option market prices and prices calculated under the Black-Scholes model have been observed for the valuation of call option contracts written on eight Indian stocks quoted on NSE. We have seen that Future prices of stocks are traded less than the market price which causes the negative cost of carry bias. The various pricing errors produced by the Black-Scholes model can be attributed to this difference. The negative cost carry problem has been addressed by Black in commodity market by using Future prices instead of spot prices as the Future prices incorporate cost of carry as well as the various mismatches faced by market. This research paper first examines the pricing errors produced by the Black-Scholes model and at the second stage it replaces spot price (S) in the original Black-Scholes model by the Discounting Value of the Future Price (DVFP) to gauge the pricing accuracy. It has been found that the exhibited errors under the Black- Scholes model are high and the model after replacing spot price by the DVFP shows improvement over the Black-Scholes model.

Keywords


Black-Scholes Model, Negative Cost of Carry, DVFP.

References