Handbook of Multi-Commodity Markets and Products: Structuring, Trading and Risk Management

CHAPTER 15 GARCH Models for Commodity Markets

Eduardo Rossi and Filippo Spazzini

15.1 INTRODUCTION

In this chapter we focus on volatility modelling with special attention paid to the features of volatility of commodities. In general, an important contribution to the understanding of modern financial markets has been the study of the volatility of asset returns. Volatility is considered a measure of risk, and the riskiness of any financial asset is a crucial element in determining its equilibrium price. In its broader sense, volatility can be interpreted as a measure of variability over a period of time. This chapter is devoted to present models for the expectation of volatility.

The autoregressive conditional heteroscedasticity (ARCH, hereafter) class of models have been developed to provide a convenient and accurate methodology to forecast volatility. In particular, this class of models is able to capture several empirical regularities observed in financial data. In brief, some stylized facts common to many financial time series are:

• Asset prices are generally nonstationary. Returns are usually stationary. Some financial time series are fractionally integrated.
• Return series usually show no or little autocorrelation.
• Serial independence between the squared values of the series is often rejected, pointing towards the existence of nonlinear relationships between subsequent observations.
• Volatility of the returns series appears to be clustered.
• Normality has to be rejected in ...