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- Title
Valuation of Nifty Options Using Black's Option Pricing Formula.
- Authors
Mitra, Subrata Kumar
- Abstract
The Black and Scholes option pricing formula exhibits certain biases on several parameters used in the model. It has been observed that the implied volatilities are high for 'in-the-money' options and low for 'out-of-the-money' options indicating that the Black-Scholes model underprices 'in-the-money' options and overprices 'out-of-the-money' options. Further, implied volatility also varies with maturity. In addition to the problems of changing implied volatility across moneyness and maturity, Nifty options also suffer from 'cost-of-carry' bias, as future prices of Nifty options are usually less than Nifty spot prices plus interest element. Since the inception of Nifty future trading in India, Nifty future even traded below the Nifty spot value. These deformities obviously cause difference between the actual price of Nifty options and the prices calculated using Black-Scholes formula. Black tried to address this problem of negative cost of carry by using forward prices in the option pricing model instead of spot prices. He argued that actual forward prices not only incorporate cost of carry but also capture various irregularities faced by market forces. In his model, he replaced the spot price term (S) by the discounted value of future price (F.e-rt) in the original Black-Scholes Formula. On the otherhand black's model is widely used for valuing options on physical commodities as the discounted value of a quoted future price is found to be a better proxy of the current spot prices as an input to Black-Scholes formula. In this study, the theoretical options prices of Nifty options are calculated using both the Black formula and Black-Scholes formula, and these theoretical values are compared with the actual quoted prices in the market. It is found that the Black formula provides better result in comparison to Black-Scholes formula for Nifty options.
- Publication
ICFAI Journal of Derivatives Markets, 2008, Vol 5, Issue 1, p50
- ISSN
0972-9119
- Publication type
Academic Journal