R Programming for Actuarial Science

31 Volatility Models – GARCH

Peter McQuire

library(moments)
library(tseries)
library(rugarch)

31.1 Introduction

In this chapter we will look at a special family of time series models known as GARCH models. Generalised Auto Regressive Conditional Heteroskedastic models have been extensively used by financial analysts since their introduction in the 1980s, particularly when studying equity market returns and movements in exchange rates.

We will study the characteristics of GARCH models first by simulating and fitting appropriate models, and comparing them with the Normal distribution. We then proceed, in the form of an exercise, to analyse US daily equity return data over the period from 2001 to 2020 (a period which included the Global Financial Crisis 2008 and the COVID-19 pandemic).

31.2 Why Use GARCH Models?

It is worth first highlighting two key aspects of typical GARCH models to provide motivation for their use in modelling equity markets. After all, many analysts simply use a Normal distribution to model equity market returns; why should we use these more advanced GARCH models?

1. GARCH models exhibit a phenomenon known as “volatility clustering”. It may be that, for a period of time, it appears that the data comes from a distribution with a higher variance than is usually the case, with many relatively large values occurring over a small period of time. GARCH models exhibit the characteristic of non-constant variance (or “heteroskedasticity”); we tend to see periods ...