Calibration of Temperature Futures by Changing the Mean Reversion

In this work we conduct a study on the calibration of futures contracts on temperature indices. We consider a continuous-time autoregressive dynamics for the deseasonalized temperatures and a pricing measure allowing for a simultaneous change of the level and speed of mean reversion in the risk neutral dynamics. We compare this pricing measure with the one provided by the classical Girsanov's transform. Our study shows that the new pricing measure provides better calibration errors and more realistic risk premium profiles.