Volatility in Indian Stock Market: An Empirical Analysis

Many economic models assume that the variance, as a measure of uncertainty, is constant through time. However, empirical evidence rejects this assumption. Financial time series such as stock returns or exchange rates exhibit so-called volatility clustering. This means that large changes in these series tend to be followed by large changes and small changes by small changes. The technical term given to this behavior is autoregressive conditional heteroskedasticity (ARCH). In this paper, firstly the data set which comprises of two market indices are described. Then, an appropriate GARCH model, to predict the time-varying volatility of daily returns, is fitted. The estimation of GARCH (1, 1) model and subsequently the evaluation of its forecasting accuracy are made at the macro level on two major stock indices, namely, S&P CNX Nifty and BSE Sensex.

The sample data used here consists of two sets which comprise of the S&P CNX Nifty and the BSE Sensex compiled and published by NSE India and Bombay Stock Exchange respectively for the period from January, 2000 to December, 2010. Volatility has been estimated on return (Rt) which is defined as:

Rt = log (Pt/Pt-1)

where Rt is logarithmic daily return at time t and Pt-1 and Pt are daily price of an asset at two successive days t-1 and t respectively.

Jarque-Bera test and Augmented Dickey Fuller tests are applied to check the normality and stationarity of the data.

The GARCH (1, 1) model has been fitted to both the market indices. It was found that there is a strong evidence of time-varying volatility. Also there is a tendency of the periods of high and low volatility to cluster and finally that there is a high persistence and predictability of volatility.