Estimating Stock Market Volatility with Asymmetric Arch, GARCH and Expanded GARCH Models

Traditional econometric models assume a constant one period forecast variance. However, many financial time series display volatility clustering, that is, autoregressive conditional heteroskedasticity (ARCH). The aim of this paper is to estimate conditional volatility models in an effort to capture the salient features of stock market volatility in India and evaluate the models in terms of out-ofsample forecast accuracy. The paper also investigates whether there is any leverage effect in Indian companies. The estimation of volatility is made at the macro level on two major market indices, namely, S&P CNX Nifty and BSE Sensex. The fitted model is then evaluated in terms of its forecasting accuracy on these two indices. In addition, 50 individual companies' share prices currently included in S&P CNX Nifty are used to examine the heteroskedastic behaviour of the Indian stock market at the micro level. The vanilla GARCH (1, 1) model has been fitted to both the market indices. We find: a strong evidence of time-varying volatility a tendency of the periods of high and low volatility to cluster a high persistence and predictability of volatility. Conditional volatility of market return series from January 1991 to June 2003 shows a clear evidence of volatility shifting over the period where violent changes in share prices cluster around the boom of 1992. Though the higher price movement started in response to strong economic fundamentals, the real cause for abrupt movement appears to be the imperfection of the market. The forecasting ability of the fitted GARCH (1, 1) model has been evaluated by estimating parameters initially over trading days of the in-sample period and then using the estimated parameters to later data, thus forming out-of-sample forecasts on two market indices. These out-of-sample volatility forecasts have been compared to true realized volatility. Three alternative methods have been followed to measure three pairs of forecast and realized volatility. In each method, the volatility forecasts are evaluated and compared through popular measures. To examine the information content of forecasts, a regression-based efficiency test has also been performed. It is observed that the GARCH (1, 1) model provides reasonably good forecasts of market volatility. While turning to 50 individual underlying shares, it is observed that the GARCH (1, 1) model has been fitted for almost all companies. Only for four companies, GARCH models of higher order may be more successful. In general, volatility seems to be of a persistent nature. Only eight out of 50 shares show significant leverage effects and really need an asymmetric GARCH model such as EGARCH to capture their volatility clustering which is left for future research. The implications of the study are as follows: The various GARCH models provide good forecasts of volatility and are useful for portfolio allocation, performance measurement, option valuation, etc. Given the anticipated high growth of the economy and increasing interest of foreign investors towards the country, it is important to understand the pattern of stock market volatility in India which is time-varying, persistent, and predictable. This may help diversify international portfolios and formulate hedging strategies.

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