Market Risk Analysis Volume II: Practical Financial Econometrics

II.4

Introduction to GARCH Models

II.4.1 INTRODUCTION

The moving average models described in the previous chapter are based on the assumption that returns are independent and identically distributed (i.i.d.). So the volatility and correlation forecasts that are made from these models are simply equal to the current estimates. But we know that the i.i.d. assumption is very unrealistic. The volatility of financial asset returns changes over time, with periods when volatility is exceptionally high interspersed with periods when volatility is unusually low. This volatility clustering behaviour does, of course, depend on the frequency of the data – it would hardly occur in annual data, and may not be very evident in monthly data – but it is normally very obvious in daily data and even more obvious in intraday data.

There is a large body of empirical evidence on volatility clustering in financial markets that dates back to Mandelbrot (1963). Volatility clustering has important implications for risk measurement and for pricing and hedging options. Following a large shock to the market, volatility changes and the probability of another large shock is greatly increased. Portfolio risk measurement and option prices both need to take this into account. Unfortunately the moving average models that we have considered above, though simple, provide only a crude picture of the time variation in volatility. This is because the models assume volatility is constant and the only reason why estimates ...