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Hedging Expected Losses on Derivatives in Electricity Futures Markets

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  • Adrien Nguyen Huu

    (FiME Lab, IMPA)

  • Nadia Oudjane

    (FiME Lab)

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    Abstract

    We investigate the problem of pricing and hedging derivatives of Electricity Futures contract when the underlying asset is not available. We propose to use a cross hedging strategy based on the Futures contract covering the larger delivery period. A quick overview of market data shows a basis risk for this market incompleteness. For that purpose we formulate the pricing problem in a stochastic target form along the lines of Bouchard and al. (2008), with a moment loss function. Following the same techniques as in the latter, we avoid to demonstrate the uniqueness of the value function by comparison arguments and explore convex duality methods to provide a semi-explicit solution to the problem. We then propose numerical results to support the new hedging strategy and compare our method to the Black-Scholes naive approach.

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    Paper provided by arXiv.org in its series Papers with number 1401.8271.

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    Date of creation: Jan 2014
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    Handle: RePEc:arx:papers:1401.8271

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    Web page: http://arxiv.org/

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    1. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    2. Benth, Fred Espen & Koekebakker, Steen, 2008. "Stochastic modeling of financial electricity contracts," Energy Economics, Elsevier, vol. 30(3), pages 1116-1157, May.
    3. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
    4. Föllmer Hans & Penner Irina, 2006. "Convex risk measures and the dynamics of their penalty functions," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 36, July.
    5. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    6. Ludovic Moreau, 2011. "Stochastic target problems with controlled loss in jump diffusion models," Post-Print hal-00515522, HAL.
    7. Lindell, Andreas & Raab, Mikael, 2009. "Strips of hourly power options--Approximate hedging using average-based forward contracts," Energy Economics, Elsevier, vol. 31(3), pages 348-355, May.
    8. Bruno Bouchard & Marcel Nutz, 2011. "Weak Dynamic Programming for Generalized State Constraints," Papers 1105.0745, arXiv.org, revised Oct 2012.
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