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A Simple Model for Trading Climate Risk

Listed author(s):
  • 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.

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Article provided by DIW Berlin, German Institute for Economic Research in its journal Vierteljahrshefte zur Wirtschaftsforschung.

Volume (Year): 74 (2005)
Issue (Month): 2 ()
Pages: 175-195

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Handle: RePEc:diw:diwvjh:74-2-6
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  1. 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.
  2. M. Davis, 2001. "Pricing weather derivatives by marginal value," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 305-308, March.
  3. 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.
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