Putting a price on temperature

This paper analyzes the weather derivatives traded at the Chicago Mercantile Exchange (CME), with futures and options written on different temperature indices. We propose to model the temperature dynamics as a continuous-time autoregressive process with lag p and seasonal variation. The choice p=3 turns out to be sufficient to explain the temperature dynamics observed in Stockholm, Sweden, where we fit the model to more than 40 years of daily observations. The main finding is a clear seasonal variation in the regression residuals, where temperature shows high variability in winter, low in autumn and spring, and increasing variability towards the early summer. Our model allows for derivations of explicit prices for several futures and options. Note that the volatility term structure of futures written on the cumulative average temperature has a modified Samuelson effect, where the volatility prior to the measurement period increases, except for the last part, where it may decrease.