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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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  • 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