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

CHAPTER 12 Estimating Commodity Term Structure Volatilities

Andrea Roncoroni, Rachid Id Brik and Mark Cummins

12.1 INTRODUCTION

This chapter introduces two leading methods used in estimating the term structure of volatility in energy and commodity futures markets. The first of these methods is the Kalman filter and the second is principal components analysis. Technical definitions are provided and the methods are illustrated using historical futures data.

12.2 MODEL ESTIMATION USING THE KALMAN FILTER

The literature in financial modelling offers a large number of models to draw on in determining commodity prices. Several papers are based on spot prices, where the spot price is for immediate delivery of a commodity, while others are based on forward or futures prices, where delivery or cash settlement occurs at a date in the future. The no-arbitrage relationship between futures and spot prices introduces the concept of convenience yield. This new variable allows us to reproduce the term structure of futures prices from a spot price model. However, this variable is not observable in the market and so must be measured from observable market price information. The convenience yield only has an economic interpretation and can be linked with the level of inventories. Spot price and convenience yield as a pair have been well studied by Gibson and Schwartz (1990), Schwartz (1997), Casassus and Collin-Dufresne (2005) and many others. In this context, since the convenience yield is ...