Modeling S and P Cnx Nifty Index Volatility with Garch Class Volatility Models- Empirical Evidence from India

Abstract

Theoretically, basic idealization is that returns follow a stationary time series model with stochastic volatility structure. The presence of stochastic volatility implies that returns are not necessarily independent over time. In the year 1982, Engle proposed a volatility process with time varying conditional variance; the Autoregressive Conditional Heteroskedasticity (ARCH) process. Two important characteristics within financial time series, the fat tails and volatility clustering can be analyzed by the GARCH family models. However, empirical evidence shows that high ARCH order has to be selected in order to catch the dynamics of conditional variance. The high ARCH order implies that many parameters have to be estimated and the calculations get burdensome. The development of autoregressive conditional heteroskedasticity (ARCH) and GARCH models has been nothing short ofrevolutionary for modeling financial time series, to the extent that Robert Engle, who first introduced the ARCH model, shared the 2003 Nobel Prize in Economics for his discovery. The original GARCH models have spumed a number of extensions, including multivariate versions and applications to option pricing. Bollerslev, Chou, and Kroner (1992) present a literature review of some of the important academic studies on ARCH and GARCH modeling in finance. Four years after Engel's introduction of the ARCH process, Bollerslev 1986, proposed the Generalized ARCH (GAR CH) model as a natural solution to the problem with the high ARCH orders. This model is based on an infinite ARCH specification and it allows to dramatically reduce the number of estimated parameters from an infinite number to just a few. Financ;~ l time series often exhibit some well-known characteristics. First, large changes tend to be followed by large changes and small changes tend to be followed by small changes. Secondly, financial time series often exhibit leptokurtosis, which means that the distribution of their returns is fat-tailed (i.e. relative high probability for extreme values). The GARCH model successfully captures the first property described above, but fails to capture the fat-tail property of financial data. This has lead to the use of non-normal distributions to a better model of the fat-tailed characteristics. The GAR CH model has been so successful in looking at volatilities of single assets that researchers all over the world have been developing various alternatives -multivariate models -for years. But they tend to be so complicated and relatively unreliable that they haven't actually caught on in the same way that univariate GARCH models have. Ever since Bollerslev introduced the GARCH model, new GARCH models have been proposed, e.g. Exponential GARCH (EGARCH), with different characteristics, advantages and drawbacks. In this paper, we capture financial time series characteristics by employing GARCH (p,q) model, and its extensions. There are several alternatives th,i.t are widely used. GARCH models explicitly are one of them. With the development of the GARCH model, and theAkCH model, steps have been made to make a scientific way of deciding which methods are working better and which ones are not working as well. ARCH is quite a tongue twister. Fortunately, Robert Engle's Nobel Prize-winning ARCH model is much easier to put into practice than to pronounce, according to the many practitioners who today rely on ARCH, and then subsequently developed the GARCH model, to more accurately predict volatility.