Modeling and Forecasting Volatility: An Empirical Evidence from the Bombay Stock Exchange

Volatility is unobservable and an indispensible contribution to the pricing models and for risk management purposes. A number of previous studies have been dedicated to scrutinize the characteristics of volatility in emerging markets. In an attempt to contribute to literature, this dissertation examines stock return volatility on Bombay stock exchange (BSE). Historical volatility is an inappropriate indicator of future volatility and in the literature the GARCH model of Bollerslev and Taylor (1986), time after time has been demonstrated to be most precise in forecasting future volatility which also led to the extension of other GARCH models overcoming its limitations. The main purpose of taking this research into contemplation was to determine how correctly the methods (models) predict the future volatilities. This study examines which is the most suitable method an investor can rely on for forecasting the future volatility and hence avoid getting drawn into higher risk. In order to accomplish this analysis, historical data on BSE SENSEX (^BSESN) has been considered for a span of 6 years from April, 2005 to March, 2011. The study is undertaken by giving a gist of the different methods for forecasting volatility proposed by varied economists namely, Historical Simulation Method, Parkinson’s Extreme Value Estimator (PEVE), Exponentially Weighted Moving Average (EWMA), Auto Regressive Heteroscedasticity Model (ARCH), General Auto Regressive Heteroscedasticity Model [GARCH (1,1)], Exponentially Generalized Auto Regressive Heteroscedasticity Model [EGARCH(1,1)] and the GJR-GARCH (1,1). The findings for these methods are calculated using Microsoft Excel (MSEXCEL) and the statistical software STATA 11. Furthermore, comparison between the models has been made by doing graphical representation, error test statistics, regression analysis of the parameters, the Lagrange multiplier test, ljung-box statistical test etc. The three types of error statistics test namely, RMSE, MAPE and MAE have been employed to case of forecasting volatility with the help of historical data it was documented that even after GARCH (1,1) model comprising of few limitations, it was still universally accepted to be the finest and the most accurate predictor of volatility. To summon it up, the reasons for the best method of forecasting volatility have been illustrated with the help of empirical evidences. Keywords: PEVE, EWMA, ARCH, GARCH (1,1), EGARCH (1,1), GJR-GARCH (1,1), RMSE, MAPE, MAE, Volatility