Volatility Models and their Performance in Indian Capital Markets

Abstract

Estimation and forecasting of volatility of asset returns is important in various applications related to financial markets such as valuation of derivatives, risk management, etc. Till early eighties, it was commonly assumed that the volatility of an asset is constant and estimation procedures were based on this assumption even though some of the pioneering studies on property of stock market returns did not support this assumption. Following the pioneering work of Engle and Bollerslev in eighties on developing models (ARCH/GARCH type models) to capture time-varying characteristics of volatility and other stock return properties, extensive research has been done world over in modeling volatility for estimation and forecasting.

There are broadly four possible approaches for estimating and forecasting volatility. These are:

Traditional Volatility Estimators — These estimators assume that ‘true’ volatility is unconditional and constant. The estimation is based on either squared returns or standard deviation of returns over a period.

Extreme Value Volatility Estimators — These estimators are similar to traditional estimators except that these also incorporate high and low prices observed unlike traditional estimators which are based on closing prices of the asset.

Conditional Volatility Models — These models (ARCH/GARCH type models) take into account the time-varying nature of volatility. There have been quite a few extensions of the basic conditional volatility models to incorporate ‘observed’ characteristics of asset/stock returns.

Implied Volatility — In case of options, most of the parameters relevant for their valuation can be directly observed or estimated, except volatility. Volatility is, therefore, backed out from the observed option values and is used as volatility forecast.

The empirical research across countries and markets has not been equivocal about the effectiveness of using these approaches. This study compares the result of the first three approaches in estimating and forecasting Nifty returns.

Based on four different criteria related to bias and efficiency of the various estimators and models, this study analysed the estimation and forecasting ability of three different traditional estimators, four extreme value estimators, and two conditional volatility models. As a benchmark, it used ‘realized’ volatility estimates. The findings of this study are as follows:

For estimating the volatility, the extreme value estimators perform better on efficiency criteria that the conditional volatility models.

In terms of bias, conditional volatility models perform better than the extreme value estimators.

As far as predictive power is concerned, extreme value estimators estimated from sample of length equal to forecast period perform better than the conditional volatility estimators in providing five-day and month ahead volatility forecasts.