Looking into the relationship between implied and realized volatility: a study on S & amp;P CNX Nifty index option

Abstract

This paper looks into the robustness of implied volatility against the backward looking volatility of S & P CNX Nifty index option in India by considering both ‘in the sample’ and ‘out of the sample’ framework. The backward looking volatility is measured by employing Moving Average (MA), Exponential Weighted Moving Average (EWMA), Generalized Auto Regressive Conditional Heteroskedisticity (GARCH) and Exponential Generalized Auto Regressive Conditional Heteroskedisticity (EGARCH) model with Generalized Error Distribution (GED). The study computed the realized volatility of S & P CNX Nifty by using the overlapping database to match with the expiration of the corresponding option contract. This leads to the problem of minimizing the standard error of the estimator as per the OLS method. This problem has been resolved by employing Generalized Methods of Moments (GMM). The study period of the analysis is spanning over the period from 4th June 2001 to 23rd June 2011. The determinations of the study suggest that Conditional Volatility gives a superior forecast of realized volatility than forward looking volatility and other backward looking volatility. At the same time the analysis shows that implied volatilities are biased and inefficient estimates over the remaining life of the option contract. In ‘out of the sample analysis’, the family of ARCH models outperformed all other forecasting models with respect to predicting 30 days ahead volatility.