Weather Derivatives with Applications to Canadian Data

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 Lévy process with seasonal mean and volatility. As an extension to the first model, Continuous Autoregressive (CAR) model driven by Lévy 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 Lévy process, futures pricing of CDD and HDD indices.

Cite this paper

A. Swishchuk and K. Cui, "Weather Derivatives with Applications to Canadian Data,"*Journal of Mathematical Finance*, Vol. 3 No. 1, 2013, pp. 81-95. doi: 10.4236/jmf.2013.31007.

A. Swishchuk and K. Cui, "Weather Derivatives with Applications to Canadian Data,"

References

[1] L. Zeng, “Weather Derivatives and Weather Insurance: Concept, Application and Analysis,” Bulletin of the American Meteorological Society, Vol. 81, No. 9, 2000, pp. 2075-2081. doi:10.1175/1520-0477(2000)081<2075:WDAWIC>2.3.CO;2

[2] M. Cao and J. Wei, “Pricing the Weather,” Risk Magazine, May 2000, pp. 67-70.

[3] F. Dornier and M. Queruel, “Caution to the Wind,” Energy and Power Risk Management, 2000, pp. 30-32.

[4] M. H. A. Davis, “Pricing Weather Derivative by Marginal Value,” Quantitative Finance, Vol. 1, No. 3, 2001, pp. 305308. doi:10.1080/713665730

[5] D. C. Brody, J. Syroka and M. Zervos, “Dynamical Pricing of Weather Derivatives,” Quantitative Finance, Vol. 2, No. 3, 2002, pp. 189-198. doi:10.1088/1469-7688/2/3/302

[6] F. E. Benth, “On Arbitrage-Free Pricing of Weather Derivatives Based on Fractional Brownian Motion,” Applied Mathematical Finance, Vol. 10, No. 4, 2003, pp. 303324. doi:10.1080/1350486032000174628

[7] F. E. Benth and J. Saltyte-Benth, “Sthochastic Modeling of Temperature Variations with a View towards Weather Derivatives,” Applied Mathematical Finance, Vol. 12, No. 1, 2005, pp. 53-85. doi:10.1080/1350486042000271638

[8] F. E. Benth and J. Saltyte-Benth, “The Volatility of Temperature and Pricing of Weather Derivatives,” Quantitative Finance, Vol. 7, No. 5, 2007, pp. 553-561. doi:10.1080/14697680601155334

[9] F. E. Benth, J. Saltyte-Benth and S. Koekebakker, “Putting a Price on Temperature,” Scandinavian Journal of Statistics, Vol. 34, No. 4, 2007, pp. 746-767.

[10] A. D. Zapranis and A. Alexandridis, “Modeling the Temperature Time-Dependent Spped of Mean Reversion in the Context of Weather Derivatives Pricing,” Applied Mathematical Finance, Vol. 15, No. 4, 2008, pp. 355-386. doi:10.1080/13504860802006065

[11] A. Papapantoleon, “An Introduction to Lévy Processes with Applications in Finance,” Lecture Notes, Berlin, 2008. http://page.math.tu-berlin.de/~papapan/papers/introduction.pdf

[12] P. Alaton, B. Djehiche and D. Stillberger, “On Modeling and Pricing Weather Derivatives,” Applied Mathematical Finance, Vol. 9, No. 8, 2002, pp. 1-20. doi:10.1080/13504860210132897

[13] A. J. McNeil, R. Frey and P. Embrechts, “Quantitative Risk Management: Concepts, Techniques and Tools,” Princeton University Press, Princeton, 2005.

[14] P. J. Brockwell and T. Marquardt, “Lévy-Driven and Fractionally Integrated ARMA Processes with Continuous Time Parameter,” Statistica Sinica, Vol. 15, No. 2, 2005, pp. 477-494.

[15] F. E. Benth, J. Saltyte-Benth and S. Koekebakker, “Stochastic Modeling of Electricity and Related Markets,” World Scientific Press, The Singapore City, 2008.

[16] F. E. Benth and J. Saltyte-Benth, “The Normal Inverse Gaussian Distribution and Spot Price Modeling in Energy Markets,” International Journal of Theoretical Applied Finance, Vol. 7, No. 2, 2004, pp. 177-192. doi:10.1142/S0219024904002360

[17] E. Hewitt and K. R. Stromberg, “Real and Abstract Analysis: A Modern Treatment of the Theory of Functions of a Real Variable,” Springer-Verlag, Berlin, 1965.

[18] K. Chourdakis, “Option Pricing Using the Fractional FFT,” Journal of Computational Finance, Vol. 8, No. 2, 2004, pp. 1-18.

[1] L. Zeng, “Weather Derivatives and Weather Insurance: Concept, Application and Analysis,” Bulletin of the American Meteorological Society, Vol. 81, No. 9, 2000, pp. 2075-2081. doi:10.1175/1520-0477(2000)081<2075:WDAWIC>2.3.CO;2

[2] M. Cao and J. Wei, “Pricing the Weather,” Risk Magazine, May 2000, pp. 67-70.

[3] F. Dornier and M. Queruel, “Caution to the Wind,” Energy and Power Risk Management, 2000, pp. 30-32.

[4] M. H. A. Davis, “Pricing Weather Derivative by Marginal Value,” Quantitative Finance, Vol. 1, No. 3, 2001, pp. 305308. doi:10.1080/713665730

[5] D. C. Brody, J. Syroka and M. Zervos, “Dynamical Pricing of Weather Derivatives,” Quantitative Finance, Vol. 2, No. 3, 2002, pp. 189-198. doi:10.1088/1469-7688/2/3/302

[6] F. E. Benth, “On Arbitrage-Free Pricing of Weather Derivatives Based on Fractional Brownian Motion,” Applied Mathematical Finance, Vol. 10, No. 4, 2003, pp. 303324. doi:10.1080/1350486032000174628

[7] F. E. Benth and J. Saltyte-Benth, “Sthochastic Modeling of Temperature Variations with a View towards Weather Derivatives,” Applied Mathematical Finance, Vol. 12, No. 1, 2005, pp. 53-85. doi:10.1080/1350486042000271638

[8] F. E. Benth and J. Saltyte-Benth, “The Volatility of Temperature and Pricing of Weather Derivatives,” Quantitative Finance, Vol. 7, No. 5, 2007, pp. 553-561. doi:10.1080/14697680601155334

[9] F. E. Benth, J. Saltyte-Benth and S. Koekebakker, “Putting a Price on Temperature,” Scandinavian Journal of Statistics, Vol. 34, No. 4, 2007, pp. 746-767.

[10] A. D. Zapranis and A. Alexandridis, “Modeling the Temperature Time-Dependent Spped of Mean Reversion in the Context of Weather Derivatives Pricing,” Applied Mathematical Finance, Vol. 15, No. 4, 2008, pp. 355-386. doi:10.1080/13504860802006065

[11] A. Papapantoleon, “An Introduction to Lévy Processes with Applications in Finance,” Lecture Notes, Berlin, 2008. http://page.math.tu-berlin.de/~papapan/papers/introduction.pdf

[12] P. Alaton, B. Djehiche and D. Stillberger, “On Modeling and Pricing Weather Derivatives,” Applied Mathematical Finance, Vol. 9, No. 8, 2002, pp. 1-20. doi:10.1080/13504860210132897

[13] A. J. McNeil, R. Frey and P. Embrechts, “Quantitative Risk Management: Concepts, Techniques and Tools,” Princeton University Press, Princeton, 2005.

[14] P. J. Brockwell and T. Marquardt, “Lévy-Driven and Fractionally Integrated ARMA Processes with Continuous Time Parameter,” Statistica Sinica, Vol. 15, No. 2, 2005, pp. 477-494.

[15] F. E. Benth, J. Saltyte-Benth and S. Koekebakker, “Stochastic Modeling of Electricity and Related Markets,” World Scientific Press, The Singapore City, 2008.

[16] F. E. Benth and J. Saltyte-Benth, “The Normal Inverse Gaussian Distribution and Spot Price Modeling in Energy Markets,” International Journal of Theoretical Applied Finance, Vol. 7, No. 2, 2004, pp. 177-192. doi:10.1142/S0219024904002360

[17] E. Hewitt and K. R. Stromberg, “Real and Abstract Analysis: A Modern Treatment of the Theory of Functions of a Real Variable,” Springer-Verlag, Berlin, 1965.

[18] K. Chourdakis, “Option Pricing Using the Fractional FFT,” Journal of Computational Finance, Vol. 8, No. 2, 2004, pp. 1-18.