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Hedging electricity swaptions using partial integro-differential equations

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  • Hepperger, Peter
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    Abstract

    The basic contracts traded on energy exchanges are swaps involving the delivery of electricity for fixed-rate payments over a certain period of time. The main objective of this article is to solve the quadratic hedging problem for European options on these swaps, known as electricity swaptions. We consider a general class of Hilbert space valued exponential jump-diffusion models. Since the forward curve is an infinite-dimensional object, but only a finite set of traded contracts are available for hedging, the market is inherently incomplete. We derive the optimization problem for the quadratic hedging problem under the risk neutral measure and state a representation of its solution, which is the starting point for numerical algorithms.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304414911002286
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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 2 ()
    Pages: 600-622

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:2:p:600-622

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    Related research

    Keywords: Swaptions; Quadratic hedging; Hilbert space valued jump-diffusion; Infinite-dimensional stochastic analysis; Partial integro-differential equation;

    References

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    1. Rudiger Kiesel & Gero Schindlmayr & Reik Borger, 2009. "A two-factor model for the electricity forward market," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 279-287.
    2. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    3. Benth, Fred Espen & Koekebakker, Steen, 2008. "Stochastic modeling of financial electricity contracts," Energy Economics, Elsevier, vol. 30(3), pages 1116-1157, May.
    4. Fred Espen Benth & Alvaro Cartea & Ruediger Kiesel, 2006. "Pricing Forward Contracts in Power Markets by the Certainty Equivalence Principle: Explaining the Sign of the Market Risk Premium," Birkbeck Working Papers in Economics and Finance 0611, Birkbeck, Department of Economics, Mathematics & Statistics.
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