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Modelling electricity forward markets by ambit fields

Author

Listed:
  • Ole E. Barndorff–Nielsen

    () (Thiele Center, Department of Mathematical Sciences and CREATES)

  • Fred Espen Benth

    () (Centre of Mathematics for Applications, University of Oslo and Faculty of Economics University of Agder)

  • Almut E. D. Veraart

    () (CREATES, School of Economics and Management Aarhus University)

Abstract

This paper proposes a new modelling framework for electricity forward markets, which is based on ambit fields. The new model can capture many of the stylised facts observed in energy markets. One of the main differences to the traditional models lies in the fact that we do not model the dynamics, but the forward price directly, where we focus on models which are stationary in time. We give a detailed account on the probabilistic properties of the new model and we discuss martingale conditions and change of measure within the new model class. Also, we derive a model for the spot price which is obtained from the forward model through a limiting argument.

Suggested Citation

  • Ole E. Barndorff–Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2010. "Modelling electricity forward markets by ambit fields," CREATES Research Papers 2010-41, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2010-41
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    File URL: ftp://ftp.econ.au.dk/creates/rp/10/rp10_41.pdf
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    References listed on IDEAS

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    1. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
    2. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
    3. Erik Schlögl, 2002. "A multicurrency extension of the lognormal interest rate Market Models," Finance and Stochastics, Springer, vol. 6(2), pages 173-196.
    4. Mark Joshi & Alan Stacey, 2008. "New and robust drift approximations for the LIBOR market model," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 427-434.
    5. Ernst Eberlein & Jean Jacod & Sebastian Raible, 2005. "Lévy term structure models: No-arbitrage and completeness," Finance and Stochastics, Springer, vol. 9(1), pages 67-88, January.
    6. Nicolas Merener & Paul Glasserman, 2003. "Numerical solution of jump-diffusion LIBOR market models," Finance and Stochastics, Springer, vol. 7(1), pages 1-27.
    7. Ernst Eberlein & Fehmi Özkan, 2005. "The Lévy LIBOR model," Finance and Stochastics, Springer, vol. 9(3), pages 327-348, July.
    8. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410.
    9. Tim Dunn & Erik Schlögl & Geoff Barton, 2000. "Simulated Swaption Delta-Hedging in the Lognormal Forward Libor Model," Research Paper Series 40, Quantitative Finance Research Centre, University of Technology, Sydney.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Fred Espen Benth & Paul Kruhner, 2014. "Derivatives pricing in energy markets: an infinite dimensional approach," Papers 1412.7943, arXiv.org.
    2. 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.
    3. Schnurr Alexander & Woerner Jeannette H. C., 2011. "Well-balanced Lévy driven Ornstein–Uhlenbeck processes," Statistics & Risk Modeling, De Gruyter, vol. 28(4), pages 343-357, December.
    4. Pakkanen, Mikko S., 2014. "Limit theorems for power variations of ambit fields driven by white noise," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1942-1973.
    5. Kerstin Gärtner & Mark Podolskij, 2014. "On non-standard limits of Brownian semi-stationary," CREATES Research Papers 2014-50, Department of Economics and Business Economics, Aarhus University.

    More about this item

    Keywords

    Electricity markets; forward prices; random fields; ambit fields; stochastic volatility.;

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • G1 - Financial Economics - - General Financial Markets

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