Calibration of temperature futures by changing the mean reversion

Fred Espen Benth and Salvador Ortiz-Latorre

Journal of Energy Markets

Abstract: In this paper, we study the calibration of futures contracts on temperature indexes. We consider a continuous-time autoregressive dynamics for deseasonalized temperatures along with a pricing measure that allows us to simultaneously change the level and speed of mean reversion in the risk-neutral dynamics. We compare this pricing measure with that provided by the classical Girsanov transformation. Our paper shows that the new pricing measure provides better calibration errors and more realistic risk-premium profiles. Indeed, the empirical evidence indicates that the speed of mean reversion of temperature is slowed down in the forward market; this implies that there is a risk premium not only for the temperature level but also for temperature volatility.

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