Weather Derivatives with Applications to Canadian Data

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.

[1]  Edwin Hewitt,et al.  Real and Abstract Analysis: A Modern Treatment of the Theory of Functions of a Real Variable , 1965 .

[2]  L. Zeng.  Weather Derivatives and Weather Insurance: Concept, Application, and Analysis. , 2000 .

[3]  Mark H. A. Davis.  Pricing weather derivatives by marginal value , 2001 .

[4]  Boualem Djehiche,et al.  On modelling and pricing weather derivatives , 2002 .

[5]  D. Brody,et al.  Dynamical pricing of weather derivatives , 2002 .

[6]  Fred Espen Benth,et al.  On arbitrage‐free pricing of weather derivatives based on fractional Brownian motion , 2003 .

[7]  Fred Espen Benth,et al.  THE NORMAL INVERSE GAUSSIAN DISTRIBUTION AND SPOT PRICE MODELLING IN ENERGY MARKETS , 2004 .

[8]  Kyriakos Chourdakis.  Option Pricing Using the Fractional FFT , 2004 .

[9]  Fred Espen Benth,et al.  Stochastic Modelling of Temperature Variations with a View Towards Weather Derivatives , 2005 .

[10]  Peter J. Brockwell,et al.  Lévy-driven and fractionally integrated ARMA processes with continuous time parameter , 2005 .

[11]  Christine M. Anderson-Cook,et al.  Book review: quantitative risk management: concepts, techniques and tools, revised edition, by A.F. McNeil, R. Frey and P. Embrechts. Princeton University Press, 2015, ISBN 978-0-691-16627-8, xix + 700 pp. , 2017, Extremes.

[12]  F. Benth,et al.  The volatility of temperature and pricing of weather derivatives , 2007 .

[13]  J. Šaltytė Benth,et al.  Putting a Price on Temperature * , 2007 .

[14]  F. Benth,et al.  'Preface to' Stochastic Modeling of Electricity and Related Markets , 2008 .

[15]  Achilleas Zapranis,et al.  Modeling Temperature Time- Dependent Speed of Mean Reversion in the Context of Weather Derivatives Pricing , 2014 .

[16]  F. Benth,et al.  Stochastic Modeling of Electricity and Related Markets , 2008 .

[17]  A. Papapantoleon.  An introduction to Lévy processes with applications in finance , 2008, 0804.0482.