Modeling S & P CNX Nifty Index Volatility with GARCH Class Volatility Models: Empirical Evidence from India

Abstract

This paper compares several GARCH family models in order to model and forecast the conditional variance of S&P CNX Nifty Index with special focus on the fitting of first order GARCH models to Nifty financial return series and explaining financial market risk. For empirical analysis, we have used daily return data series of Nifty Index. The study uses family of GARCH techniques to capture the time-varying nature of volatility and volatility clustering phenomenon in the data. We have analyzed, fundamental concepts of Nifty financial return time series and stylized facts. We employed various time series methods to test the robustness of the estimation of the parameters in the model with three different distributional assumptions for the innovations; Gaussian (Normal) distribution, Student-t distribution and GED (Generalized Error Distribution). The maximum-likelihood approach is used for the parameter estimation and log likelihood value used for finding the best fit model. Furthermore, back testing is used to relate the residuals under three different distributional assumptions. Robustness of models and their corresponding residuals behaviors were examined empirically along with forecasting performance of the models. We found that the TGARCH and PGARCH specification to be preferred as it more reliably describes the Nifty index volatility processes.