A consistent two-factor model for pricing temperature derivatives

Abstract

We analyze a consistent two-factor model for pricing temperature derivatives that incorporates the forward looking information available in the market by specifying a model for the dynamics of the complete meteorological forecast curve. The two-factor model is a generalization of the Nelson-Siegel curve model by allowing factors with mean-reversion to a stochastic mean for structural changes and seasonality for periodic patterns. Based on the outcomes of a statistical analysis of forecast data we conclude that the two-factor model captures well the stylized features of temperature forecast curves. In particular, a functional principal component analysis reveals that the model re ects reasonably well the dynamical structure of forecast curves by decomposing their shapes into a tilting and a bending factor. We continue by developing an estimation procedure for the model, before we derive explicit prices for temperature derivatives and calibrate the market price of risk (MPR) from temperature futures derivatives (CAT, HDD, CDD) traded at the Chicago Mercantile Exchange (CME). The factor model shows that the behavior of the implied MPR for futures traded in and out of the measurement period is more stable than other estimates obtained in the literature. This confirms that at least parts of the irregularity of the MPR is not due to irregular risk perception but rather due to information misspecification. Similar to temperature derivatives, this approach can be used for pricing other non-tradable assets.