We consider some applications of the volatility models in this chapter. For simplicity, we focus on GARCH(1,1) models with Gaussian innovations. The applications, of course, can be extended to other GARCH models with different types of innovations. An obvious advantage of GARCH models over the constant volatility model is that the former allow for time-varying volatility and volatility cluster. Our first application then is to consider GARCH volatility forecasts and their financial applications. The volatility forecasts enable us to construct volatility term structure for an asset returns. We demonstrate that the volatility estimates from a GARCH model can be used in portfolio selection and in obtaining time-varying betas of an asset. We also show that a fitted GARCH model can be used in pricing options. More specifically, in this chapter, we use daily log returns to demonstrate the GARCH volatility term structure and the GARCH applications in option pricing and hedging.
Furthermore, we show that GARCH models can be used to improve the modeling and prediction of pure ARMA models. Using backtesting, we showed that incorporating a simple GARCH(1,1) model can produce more accurate forecasts of the change in weekly US crude oil price. Finally, applications of GARCH models in risk management such as calculating value at risk and expected shortfall are discussed in a later chapter.