Temperature models for pricing weather derivatives

Abstract

We present four models for predicting temperatures that can be used for pricing weather derivatives. Three of the models have been suggested in previous literature, and we propose another model that uses splines to remove trend and seasonality effects from temperature time series in a flexible way. Using historical temperature data from 35 weather stations across the United States, we test the performance of the models by evaluating virtual heating degree days (HDD) and cooling degree days (CDD) contracts. We find that all models perform better when predicting HDD indices than predicting CDD indices. However, all models based on a daily simulation approach significantly underestimate the variance of the errors.

Keywords:

• Weather derivative pricing
• Stochastic processes
• Temperature dynamics
• Daily simulation

Acknowledgements

We thank Gregor Dorfleitner, Robert Ferstl, Josef Hayden, Christian Heigl, and the seminar participants at the Department of Mathematics, Ludwig-Maximilians-Universität Munich for insightful comments and discussions. We also acknowledge the helpful comments given by the anonymous referees.

Notes

†Technically, we have deleted all leap days from the temperature data for our analysis.

†As in the Alaton model, we delete all leap days to obtain years of equal length.

†In fact, weather derivatives with such low expected indices are rarely traded.

‡The fact that the error of the Index Modelling approach is slightly below 50% results from the fact that, due to rounding, we evaluate the contract one half-day after the middle of the measurement period if the measurement period is uneven.

†In fact, we also tested the Benth model with parameters I ₁ = 4 and J ₁ = 4, which improved the overall performance in the expected value, albeit with an increased error in the variance.