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On Modelling and Pricing Rainfall Derivatives with Seasonality

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Listed:
  • Gunther Leobacher
  • Philip Ngare

Abstract

We are interested in pricing rainfall options written on precipitation at specific locations. We assume the existence of a tradeable financial instrument in the market whose price process is affected by the quantity of rainfall. We then construct a suitable 'Markovian gamma' model for the rainfall process which accounts for the seasonal change of precipitation and show how maximum likelihood estimators can be obtained for its parameters. We derive optimal strategies for exponential utility from terminal wealth and determine the utility indifference price of the claim. The method is illustrated with actual measured data on rainfall from a location in Kenya and spot prices of Kenyan electricity companies.

Suggested Citation

  • Gunther Leobacher & Philip Ngare, 2011. "On Modelling and Pricing Rainfall Derivatives with Seasonality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(1), pages 71-91.
    • Handle: RePEc:taf:apmtfi:v:18:y:2011:i:1:p:71-91
    DOI: 10.1080/13504861003795167
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    References listed on IDEAS

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    1. A. Zapranis & A. Alexandridis, 2008. "Modelling the Temperature Time-dependent Speed of Mean Reversion in the Context of Weather Derivatives Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(4), pages 355-386.
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    Cited by:

    1. Brenda López Cabrera & Martin Odening & Matthias Ritter, 2013. "Pricing Rainfall Derivatives at the CME," SFB 649 Discussion Papers SFB649DP2013-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Yuji Yamada & Takuji Matsumoto, 2021. "Going for Derivatives or Forwards? Minimizing Cashflow Fluctuations of Electricity Transactions on Power Markets," Energies, MDPI, vol. 14(21), pages 1-28, November.
    3. Andrea Martínez Salgueiro & Maria-Antonia Tarrazon-Rodon, 2021. "Weather derivatives to mitigate meteorological risks in tourism management: An empirical application to celebrations of Comunidad Valenciana (Spain)," Tourism Economics, , vol. 27(4), pages 591-613, June.
    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. Andrea Martínez Salgueiro & Maria-Antonia Tarrazon-Rodon, 2020. "Approaching rainfall-based weather derivatives pricing and operational challenges," Review of Derivatives Research, Springer, vol. 23(2), pages 163-190, July.
    6. 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.
    7. 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.
    8. 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, January.
    9. Yeny E. Rodríguez & Miguel A. Pérez-Uribe & Javier Contreras, 2021. "Wind Put Barrier Options Pricing Based on the Nordix Index," Energies, MDPI, vol. 14(4), pages 1-14, February.
    10. 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.
    11. 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).
    12. CMaria Osipenko & Wolfgang Karl Härdle, 2017. "Dynamic Valuation of Weather Derivatives under Default Risk," SFB 649 Discussion Papers SFB649DP2017-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Yuji Yamada & Takuji Matsumoto, 2023. "Construction of Mixed Derivatives Strategy for Wind Power Producers," Energies, MDPI, vol. 16(9), pages 1-26, April.
    14. Martínez-Salgueiro, Andrea & Tarrazón-Rodón, María-Antonia, 2020. "Is diversification effective in reducing the systemic risk implied by a market for weather index-based insurance in Spain?," MPRA Paper 119924, University Library of Munich, Germany, revised 19 May 2021.
    15. Luiz Vitiello & Ivonia Rebelo, 2015. "A note on the pricing of multivariate contingent claims under a transformed-gamma distribution," Review of Derivatives Research, Springer, vol. 18(3), pages 291-300, October.
    16. 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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