Abstract
We applied two daily average temperature models to Canadian cities data and derived their derivative pricing applications. The first model is characterized by mean-reverting Ornstein-Uhlenbeck process driven by general Levy process with seasonal mean and volatility. As an extension to the first model, Continuous Autoregressive (CAR) model driven by Levy process is also considered and calibrated to Canadian data. It is empirically proved that the proposed dynamics fitted CalgaryandTorontotemperature data successfully. These models are also applied to derivation of an explicit price of CAT futures, and numerical prices of CDD and HDD futures using fast Fourier transform. The novelty of this paper lies in the applications of daily average temperature models to Canadian cities data and CAR model driven by Levy process, futures pricing of CDD and HDD indices.
Highlights
Over the last decade, weather derivatives have emerged as an attractive and interesting new derivative class for risk management and other related fields
As an extension to the first model, Continuous Autoregressive (CAR) model driven by Lévy process is considered and calibrated to Canadian data
The novelty of this paper lies in the applications of daily average temperature models to Canadian cities data and CAR model driven by Lévy process, futures pricing of cooling degree days (CDD) and heating degree days (HDD) indices
Summary
Weather derivatives have emerged as an attractive and interesting new derivative class for risk management and other related fields. CDD are used in summer to measure the demand of energy used for cooling and a measure of how hot the weather is They are usually used in United States, Canada and Australia. Benth and Šaltytė-Benth [7] proposed an Ornstein-Uhlenbeck model with seasonal mean and volatility, where the residuals are generated by the class of generalized hyperbolic Lévy process rather than Brownian motion family. A similar model driven by Brownian motion was applied for pricing CAT, HDD and CDD futures in Benth and Šaltytė-Benth [8], they gave discussions about options written upon these futures.
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