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Previous studies have explored the seasonal behaviour of commodity prices as a deterministic factor. This paper goes further by proposing a general (n+2m)-factor model for the stochastic behaviour of commodity prices, which nests the deterministic seasonal model by Sorensen (2002). We consider seasonality as a stochastic factor, with n non-seasonal and m seasonal factors. The nonseasonal factors are as defined in Schwartz (1997), Schwartz and Smith (2000) and Cortazar and Schwartz (2003). The seasonal factors are trigonometric components generated by stochastic processes. The model has been applied to the Henry Hub natural gas futures contracts listed by NYMEX. We find that models allowing for stochastic seasonality outperform standard models with deterministic seasonality. We obtain similar results with other energy commodities. Moreover, we find that stochastic seasonality implies that the volatility of futures returns follows a seasonal pattern. This result has important implications in terms of option pricing. This paper is the sole responsibility of its authors. The views represented here do not necessarily reflect those of the Banco de España. We thank John Doukas (the editor), an anonymous referee,

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It is well known that market prices of risk play an important role in commodity derivative valuation. There is an extensive literature showing that market prices of risk vary through time. Based on these results, a factor model, with two long-and short-term factors, with market prices of risk depending on these underlying asset factors is proposed and estimated, using data from crude oil, heating oil, unleaded gasoline and natural gas futures prices traded at NYMEX. The valuation results obtained with an extensive sample of commodity American options traded at NYMEX show that this model with time-varying market prices of risk outperforms standard models with constant market prices of risk.

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