Risk premia and seasonality in commodity futures

Abstract

Summary We develop and estimate a multifactor affine model of commodity futures that allows for stochastic seasonality. We document the existence of stochastic seasonal fluctuations in commodity futures and that properly accounting for the cost‐of‐carry curve requires at least three factors. We estimate the model using data on heating oil futures and analyze the contribution of the factors to risk premia. Correctly specifying seasonality as stochastic is important to avoid erroneously assigning those fluctuations to other risk factors. We also estimate a nonlinear version of the model that imposes the zero lower bound on interest rates and find similar results.

Commodity prices and inflation risk

“…(where S jt corresponds to the spot price and F jt,n to the futures contract price with maturity to expiration of n months). In practice, when constructing these proxies one needs to deal with two important features of commodity markets: (a) the uneven availability of futures contracts, 10 and (b) the well documented and often pronounced seasonality present in most futures prices (see, e.g., Hevia et al, 2018).…”

“…11 To address both of the issues highlighted above, we construct convenience yields from interpolated futures curves. Specifically, following Hevia et al (2018), we model the futures curve imposing Nelson and Siegel (1987)'s parametric restrictions to the loadings and explicitly accounting for stochastic seasonality in the futures prices. Specifically,…”

“…To address this issues we construct proxies of the convenience yields using information from the entire futures curve (see, e.g. Hevia et al, 2018). The forecast densities from the set of (likely mis-specified) models are combined using the Linear Opinion Pool and the Logarithmic Opinion Pool (see e.g.…”

Real‐time forecast combinations for the oil price

“…To avoid dropping the futures-based forecasts in the combinations at these horizons, we fill in missing data by estimating a real-time factor-based model for crude oil price futures. Following Hevia, Petrella, and Sola (2016) and Garratt and Petrella (2018), we assume that futures prices are a function of two factors-the level and slope-and impose Nelson and Siegel's (1987) parametric restrictions to the loadings. A VAR(1) is assumed for the dynamics, estimation exploits the Kalman filter, and we use the estimated model to fill in the missing values.…”

Real-Time Forecast Combinations for the Oil Price

“…To avoid dropping the futures-based forecasts in the combinations at these horizons, we fill in missing data by estimating a real-time factor-based model for crude oil price futures. Following Hevia et al (2016) and Garratt and Petrella (2018), we assume that futures prices are a function of two factors, the level and slope, and impose Nelson and Siegel's (1987) parametric restrictions to the loadings. A VAR(1) is assumed for the dynamics, estimation exploits the Kalman filter, and we use the estimated model to fill in the missing values.…”