Forecasting Performance of Volatility Models for Pricing S&P CNX Nifty Index Options Via Black-Scholes Model

Though the Black-Scholes model shows systematic maturity-moneyness biases, still this simple and elegant model is used worldwide as a benchmark method to fix the base price of options trading on exchanges. Volatility is the only unknown factor in Black-Scholes model. In this paper, we have used implied and time series econometric volatility models as inputs to Black-Scholes model for forecasting S&P Nifty 50 index option prices. The paper is divided into two main parts. The first one refers to forecasting volatility from actual option prices - Volatility Index (VIX) and implied standard deviation approach [Implied Volatility (IV)]; and the second refers to models based on historical prices, time series GARCH approach, namely, symmetric GARCH, asymmetric PGARCH and GJRGARCH models. The out-of-sample performance of volatility models is closely examined based on moneyness-maturity bias. The parameters of each GARCH model and implied volatility have been estimated on a rolling window, updated daily. It has been shown in the paper that implied volatility outperforms benchmark GARCH volatility and VIX models in most of the moneyness-maturity groups