Modes of Fluctuation in Metal Futures Prices (2000)
This article examines the stochastic behaviour of copper, gold and silver futures prices, which is important to analyze the hedging and risk modelling on the underlying commodity.
The “modes of fluctuation” in this article refers to two shift functions of the futures price curves, i.e. a combination of a change in the level of the curve and a change in the slope of the curve. The shift functions describe the way that the curve shifts.
Earlier studies assume that interest rates and convenience yields are constant and the volatility of prices is stationary. This paper extends Cortazar and Schwartz (1994) analysis of the stationary multi-factor model of movements in the term structure of copper futures prices in the following ways:
1) the price fluctuations are modeled as fluctuations in a curve instead of fluctuations in a set of discrete points;
2) the model allows for time variation in the modes of fluctuation;
3) new data from gold and silver are used
Model: Multifactor model, principle component analysis
Data: The data are daily prices for the COMEX futures contracts for copper, gold, and silver from January 3, 1990 to December 31, 1996.
Abstract: This article examines the stochastic structure of metal futures prices. First, this article presents a stationary multi-factor model of fluctuations in the futures price curve. Next, the model is extended to allow for time variation in the factors or “modes” of fluctuation. The model is estimated using futures price data for three very different metals: copper, which is an industrial metal; gold, which is a precious metal; and silver, which is in transition from a precious metal to an industrial metal. The estimation results show that the shapes and importance of the various modes of fluctuation for gold and silver are much different from those for copper. Gold and silver futures price curves can be adequately modeled as a time-varying one-factor model. Copper, however, has a more complicated structure and should be modeled as a time-varying two-or three-factor model.
Full Citation: Thomas J. Urich (2000) The Journal of Futures Markets, Vol.20, No.3, 219-241