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A Non-Gaussian Ornstein-Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing

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  • Fred Espen Benth
  • Jan Kallsen
  • Thilo Meyer-Brandis
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    Abstract

    A mean-reverting model is proposed for the spot price dynamics of electricity which includes seasonality of the prices and spikes. The dynamics is a sum of non-Gaussian Ornstein-Uhlenbeck processes with jump processes giving the normal variations and spike behaviour of the prices. The amplitude and frequency of jumps may be seasonally dependent. The proposed dynamics ensures that spot prices are positive, and that the dynamics is simple enough to allow for analytical pricing of electricity forward and futures contracts. Electricity forward and futures contracts have the distinctive feature of delivery over a period rather than at a fixed point in time, which leads to quite complicated expressions when using the more traditional multiplicative models for spot price dynamics. In a simulation example it is demonstrated that the model seems to be sufficiently flexible to capture the observed dynamics of electricity spot prices. The pricing of European call and put options written on electricity forward contracts is also discussed.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 14 (2007)
    Issue (Month): 2 ()
    Pages: 153-169

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    Handle: RePEc:taf:apmtfi:v:14:y:2007:i:2:p:153-169

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    Web page: http://www.tandfonline.com/RAMF20

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    Related research

    Keywords: Electricity markets; spot price modelling; forward and futures pricing; additive processes; Ornstein-Uhlenbeck processes;

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    Cited by:
    1. René Aid & Luciano Campi & Nicolas Langrené, 2010. "A structural risk-neutral model for pricing and hedging power derivatives," Working Papers hal-00525800, HAL.
    2. : Enzo Fanone & Andrea Gamba & Marcel Prokopczuk, 2011. "The Case of Negative Day-Ahead Electricity Prices," Working Papers wpn11-01, Warwick Business School, Finance Group.
    3. Rypdal, Martin & Løvsletten, Ola, 2013. "Modeling electricity spot prices using mean-reverting multifractal processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 194-207.
    4. Benth, Fred Espen & Kiesel, Rüdiger & Nazarova, Anna, 2012. "A critical empirical study of three electricity spot price models," Energy Economics, Elsevier, vol. 34(5), pages 1589-1616.
    5. St\'ephane Goutte & Nadia Oudjane & Francesco Russo, 2012. "Variance Optimal Hedging for discrete time processes with independent increments. Application to Electricity Markets," Papers 1205.4089, arXiv.org.
    6. Ole E. Barndorff-Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2013. "Modelling energy spot prices by volatility modulated L\'{e}vy-driven Volterra processes," Papers 1307.6332, arXiv.org.
    7. St\'ephane Goutte & Nadia Oudjane & Francesco Russo, 2009. "Variance Optimal Hedging for continuous time processes with independent increments and applications," Papers 0912.0372, arXiv.org.
    8. Fred Espen Benth & Claudia Kl\"uppelberg & Gernot M\"uller & Linda Vos, 2012. "Futures pricing in electricity markets based on stable CARMA spot models," Papers 1201.1151, arXiv.org.
    9. Fred Espen Benth & Paul Kr\"uhner, 2014. "Representation of infinite dimensional forward price models in commodity markets," Papers 1403.4111, arXiv.org.

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