Stochastic Volatility and GARCH: a Comparison Based on UK Stock Data

This paper compares two types of volatility models for returns, ARCH-type and stochastic volatility (SV) models, both from a theoretical and an empirical point of view. In particular a GARCH(1,1) model, an EGARCH(1,1) model and a log-normal AR(1) stochastic volatility model are considered. The three models are estimated on UK stock data: a series of the British equity index FTSE100 is used to estimate the relevant parameters. Diagnostic tests are implemented to evaluate how well the models fit the data. The models are used to obtain daily volatility forecasts and these volatilities are used to estimate the “VaR” on a simple one-unit position on FTSE100. The VaR accuracy is tested by means of a backtest. While the results do not lead to a straightforward preference between GARCH(1,1) and SV, the EGARCH shows the best performance.