IDEAS home Printed from
   My bibliography  Save this article

On Modelling and Pricing Rainfall Derivatives with Seasonality


  • Gunther Leobacher
  • Philip Ngare


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

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112,
    2. Ales Černý & Jan Kallsen, 2008. "Mean-Variance Hedging And Optimal Investment In Heston'S Model With Correlation," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 473-492.
    3. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    4. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 385-413.
    5. Jan Kallsen & Richard Vierthauer, 2009. "Quadratic hedging in affine stochastic volatility models," Review of Derivatives Research, Springer, vol. 12(1), pages 3-27, April.
    6. Flavio Angelini & Stefano Herzel, 2007. "Measuring the error of dynamic hedging: a Laplace transform approach," Quaderni del Dipartimento di Economia, Finanza e Statistica 33/2007, Università di Perugia, Dipartimento Economia.
    7. repec:dau:papers:123456789/1392 is not listed on IDEAS
    8. Helyette Geman & P. Carr & D. Madan & M. Yor, 2003. "Stochastic Volatility for Levy Processes," Post-Print halshs-00144385, HAL.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. repec:gam:jijfss:v:5:y:2017:i:4:p:23-:d:115840 is not listed on IDEAS
    5. 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.
    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. 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.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:apmtfi:v:18:y:2011:i:1:p:71-91. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.