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Pricing Precipitation Based Derivatives

Author

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  • RENÉ CARMONA

    (Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544, USA;
    Bendheim Center for Finance and the Applied and Computational Mathematics Program, USA)

  • PAVEL DIKO

    (Electrabel S.A., Trading & Portfolio Management, Boulevard du Régent 8, Bruxelles 1000, Belgium)

Abstract

We consider the problem of pricing a derivative contract written on precipitation at a specific location during a given period of time. We propose a jump Markov process model for the stochastic dynamics of the underlying precipitation. Our model is based on pulse Poisson process models widely used in hydrology. We develop maximum likelihood parameter estimation procedures to fit our model to rainfall data. In order to price derivatives, we assume the existence of a traded asset whose price dynamics are influenced by the precipitation at the location in question, and we rely on the utility indifference approach. Two utility functions are considered: exponential and power utility. We derive explicit solutions for the exponential and bounds for the power utility.Finally, we apply our model fitting and pricing techniques to a sample rainfall contract in Norway.

Suggested Citation

  • René Carmona & Pavel Diko, 2005. "Pricing Precipitation Based Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(07), pages 959-988.
    • Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:07:n:s0219024905003311
    DOI: 10.1142/S0219024905003311
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    References listed on IDEAS

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    1. Les Clewlow & Chris Strickland, 1999. "Valuing Energy Options in a One Factor Model Fitted to Forward Prices," Research Paper Series 10, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Cited by:

    1. Härdle, Wolfgang Karl & Osipenko, Maria, 2017. "Dynamic valuation of weather derivatives under default risk," SFB 649 Discussion Papers 2017-005, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    2. López Cabrera, Brenda & Odening, Martin & Ritter, Matthias, 2013. "Pricing rainfall derivatives at the CME," SFB 649 Discussion Papers 2013-005, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    3. repec:hum:wpaper:sfb649dp2013-005 is not listed on IDEAS
    4. Wolfgang Karl Härdle & Maria Osipenko, 2017. "A Dynamic Programming Approach for Pricing Weather Derivatives under Issuer Default Risk," IJFS, MDPI, vol. 5(4), pages 1-18, October.
    5. López Cabrera, Brenda & Odening, Martin & Ritter, Matthias, 2013. "Pricing rainfall futures at the CME," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4286-4298.
    6. Markus Hess, 2016. "Modeling And Pricing Precipitation Derivatives Under Weather Forecasts," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(07), pages 1-29, November.
    7. Fred Espen Benth & Jūratė Šaltytė Benth, 2012. "Modeling and Pricing in Financial Markets for Weather Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8457, August.
    8. Nelson Christopher Dzupire & Philip Ngare & Leo Odongo, 2019. "Pricing Basket Weather Derivatives on Rainfall and Temperature Processes," IJFS, MDPI, vol. 7(3), pages 1-14, June.
    9. Tong, Zhigang & Liu, Allen, 2021. "A censored Ornstein–Uhlenbeck process for rainfall modeling and derivatives pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    10. repec:hum:wpaper:sfb649dp2017-005 is not listed on IDEAS
    11. Ragnhild Noven & Almut Veraart & Axel Gandy, 2015. "A Lévy-driven rainfall model with applications to futures pricing," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(4), pages 403-432, October.

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