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  • Print publication year: 2011
  • Online publication date: June 2012

4 - The Empirical Performance of the Two-Factor Storage Model



The previous chapter showed how continuously produced commodities' prices, volatilities, and correlations behave in a competitive market with two homoscedastic net demand shocks of differing persistences. The model studied there implies that these prices can exhibit rich dynamics, with time-varying correlations and volatilities that depend on the shape of the forward curve and, hence, with underlying fundamental supply-and-demand conditions.

Empirically observed commodity prices also exhibit rich dynamics, including time-varying – and often extreme – volatilities. Commodity forward curves exhibit a variety of shapes, including backwardation, contango, and “humps,” and correlations between forward prices of different maturities are time varying (Ng and Pirrong 1994). Hence the question: How well do the dynamics generated by the model match with the dynamics observed for actual commodity prices?

Empirical work on the theory has lagged its theoretical development. In some respects, this is not surprising, given the complexity of the problem and the associated computational costs.

Heretofore, confrontations between the theory and the data have involved modest calibration exercises based on relatively simple one-factor versions of the model of Routledge et al. (2000) (RSS), or more ambitious estimations involving low-frequency (annual) data (Deaton and Laroque 1992, 1995, or 1996). These empirical investigations have not been particularly kind to the theory. RSS find that the theory has difficulty explaining the dynamics of longer-term forward prices. Deaton-Laroque claim that storage apparently has little role in explaining commodity price dynamics; instead, autocorrelation in the underlying net demand process, rather than speculative storage, seems to be the main source of autocorrelation in commodity prices.