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Stochastic Modelling of Temperature Variations with a View Towards Weather Derivatives |
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| Authors: | Fred Espen Benth Jūratė Šaltytė‐Benth |
| Institution: | 1. Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, N‐0316 Oslo, Norway and Agder University College , Department of Economics and Business Administration , Serviceboks 422, N‐4604 Kristiansand, Norway;2. Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, N‐0316 Oslo, Norway and Department of System Research , Klaip?da University , H. Manto 84, LT‐5808 Klaip?da, Lithuania |
| Abstract: | Daily average temperature variations are modelled with a mean‐reverting Ornstein–Uhlenbeck process driven by a generalized hyperbolic Lévy process and having seasonal mean and volatility. It is empirically demonstrated that the proposed dynamics fits Norwegian temperature data quite successfully, and in particular explains the seasonality, heavy tails and skewness observed in the data. The stability of mean‐reversion and the question of fractionality of the temperature data are discussed. The model is applied to derive explicit prices for some standardized futures contracts based on temperature indices and options on these traded on the Chicago Mercantile Exchange (CME). |
| Keywords: | Temperature modelling stochastic processes Lévy processes mean‐reversion seasonality fractionality temperature futures and options |