The stylised facts of the behaviour of spot prices of commodities have been extensively studied. The main two features are: the presence of a seasonal trend; and that deviations from this trend, for instance jumps, tend to mean revert in the short-term. But what are the stylised facts under the risk-neutral measure? In this paper we set out to answer this question. We analyse how risk averse investors adjust the statistical measure of price dynamics when pricing risky securities written on commodities.

Spot (or day-ahead) price dynamics are much easier to model than dynamics under the risk-neutral measure because the former are observed whereas the latter can only be inferred from the price dynamics of instruments written on the spot commodity; for instance forward contracts. We model the market price of risk so that market participants bearing spot commodity risk are compensated for: jump arrival risk; jump size risk; and speed of mean reversion risk of both diffusion and/or jumps. Our approach can also be viewed as a special case of stochastic discount factors that not only affect the mean of the process but also its variance via the persistence of shocks to the economy.

We consider three models: the Schwartz (1997) pure diffusion model, the short- and long-term two-factor model of Schwartz and Smith (2000) and a three-factor arithmetic model that includes positive and negative jumps in the prices of commodities. We show that when spot dynamics exhibit mean reversion to a seasonal trend market participants are averse to deviations from this seasonal trend. Consequently, when pricing under the risk-adjusted measure agents will: over-state the time it takes to return to the seasonal trend; alter the mean of the process; and change the intensity of the jumps and their average size.