Realized Volatility and India VIX

Abstract

While the market return of a stock is difficult to predict, there are well established models to predict return volatility. It has been observed in early sixties of the last century (Mandelbrot 1963) that stock market volatility exhibits clustering, where periods of large returns are followed by periods of small returns .Later popular models of volatility clustering were developed by Engle (1982) and Bollerslev (1986). The autoregressive conditional heteroskedastic (ARCH) models (Engle, 1982) and generalized ARCH (GARCH) models (Bollerslev, 1986) have been extensively used in capturing volatility clustering in financial time series (Bollerslev et al. 1992). Using data on developed market, several empirical studies (Akgiray, 1989; West et al, 1993) have confirmed the superiority of GARCHtype models in volatility predictions over models such as the naïve historical average, moving average and exponentially weighted moving average (EWMA). GARCH models can replicate the fat tails observed in many high frequency financial asset return series, where large changes occur more often than a normal distribution would imply. Financial markets also demonstrate that volatility is higher in a falling market than it is in a rising market. This asymmetry or leverage effect was first documented by Black (1976) and Christie (1982). Empirical results also show that augmenting GARCH models with information like market volume or number of trades may lead to modest improvement in forecasting volatility (Brooks, 1998; Jones et al, 1994).