IDEAS home Printed from
   My bibliography  Save this article

A Simple Model for Trading Climate Risk


  • Sébastien Chaumont
  • Peter Imkeller
  • Matthias Müller
  • Ulrich Horst


Short term climate events such as the sea surface temperature anomaly known as El Niño are financial risk sources leading to incomplete markets. To make such risk tradable, we use a market model in which a climate index provides an extra investment option. Given one possible market price of risk each agent can maximize the exponential utility from three sources of income: capital market, additional security, and individual risk exposure. Under an equilibrium condition the market price of risk is uniquely determined by a backward stochastic differential equation. We translate these stochastic equations into semi-linear partial differential equations for the simulation of which numerical schemes are available. We choose two simple models for sea surface temperature, and with ENSO risk exposed fisher and farmer and a non-exposed bank three toy agents. By simulating their optimal investment into the climate index we obtain first insight into the dynamics of the market. Klimaereignisse auf einer kurzen Zeitskala, wie die Anomalie der Oberflächentemperatur im Ozean, bekannt als El Niño, sind finanzielle Risikoquellen, die zu unvollständigen Märkten führen. Um so ein Risiko handelbar zu machen, nutzen wir ein Marktmodell, in dem ein Klimaindex eine zusätzliche Investitionsmöglichkeit schafft. Zu einem gegebenen Marktpreis des Risikos kann jeder Händler seinen exponentiellen Nutzen aus drei Einkommensquellen maximieren: dem Kapitalmarkt, der zusätzlichen Anlagemöglichkeit und der individuellen Risikoexposition. Unter einer Gleichgewichtsbedingung wird der Marktpreis des Klimarisikos durch eine stochastische Rückwärtsgleichung eindeutig bestimmt. Diese stochastischen Gleichungen übertragen wir in semilineare partielle Differentialgleichungen, für die numerische Lösungsmethoden vorhanden sind. Wir wählen zwei einfache Modelle für die Meeresoberflächentemperatur. Dann betrachten wir einen Fischer und einen Farmer, die El Niño- Risiko ausgesetzt sind, sowie eine Bank, die diesem Risiko nicht ausgesetzt ist. Durch Simulation ihrer optimalen Investitionen in den Klimaindex erhalten wir einen ersten Einblick in die Dynamik dieses Marktes.

Suggested Citation

  • Sébastien Chaumont & Peter Imkeller & Matthias Müller & Ulrich Horst, 2005. "A Simple Model for Trading Climate Risk," Vierteljahrshefte zur Wirtschaftsforschung / Quarterly Journal of Economic Research, DIW Berlin, German Institute for Economic Research, vol. 74(2), pages 175-195.
  • Handle: RePEc:diw:diwvjh:74-2-6

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    2. M. Davis, 2001. "Pricing weather derivatives by marginal value," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 305-308, March.
    3. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    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. Lee, Yongheon & Oren, Shmuel S., 2009. "An equilibrium pricing model for weather derivatives in a multi-commodity setting," Energy Economics, Elsevier, vol. 31(5), pages 702-713, September.
    2. Javier Orlando Pantoja Robayo & Andrea Roncoroni, 2012. "Optimal Static Hedging of Energy Price and Volume Risk: Closed-Form Results," DOCUMENTOS DE TRABAJO CIEF 010668, UNIVERSIDAD EAFIT.

    More about this item


    Access and download statistics


    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:diw:diwvjh:74-2-6. 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: (Bibliothek). 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.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with 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.