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The Normal Inverse Gaussian Distribution And Spot Price Modelling In Energy Markets

Author

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  • FRED ESPEN BENTH

    (Centre of Mathematics for Applications, Department of Mathematics, University of Oslo P.O. Box 1053, Blindern, N–0316 Oslo, Norway;
    Agder University College, Department of Economics and Business Administration, Serviceboks 422, N-4604 Kristiansand, Norway)

  • JŪRATĖ ŠALTYTĖ-BENTH

    (Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N–0316 Oslo, Norway;
    Department of System Research, Klaipėda University, H. Manto 84, LT-5808 Klaipėda, Lithuania)

Abstract

We model spot prices in energy markets with exponential non-Gaussian Ornstein–Uhlenbeck processes. We generalize the classical geometric Brownian motion and Schwartz' mean-reversion model by introducing Lévy processes as the driving noise rather than Brownian motion. Instead of modelling the spot price dynamics as the solution of a stochastic differential equation with jumps, it is advantageous from a statistical point of view to model the price process directly. Imposing the normal inverse Gaussian distribution as the statistical model for the Lévy increments, we obtain a superior fit compared to the Gaussian model when applied to spot price data from the oil and gas markets. We also discuss the problem of pricing forwards and options and outline how to find the market price of risk in an incomplete market.

Suggested Citation

  • Fred Espen Benth & Jūratė Šaltytė-Benth, 2004. "The Normal Inverse Gaussian Distribution And Spot Price Modelling In Energy Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 177-192.
    • Handle: RePEc:wsi:ijtafx:v:07:y:2004:i:02:n:s0219024904002360
    DOI: 10.1142/S0219024904002360
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    Citations

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    Cited by:

    1. Piccirilli, Marco & Schmeck, Maren Diane & Vargiolu, Tiziano, 2021. "Capturing the power options smile by an additive two-factor model for overlapping futures prices," Energy Economics, Elsevier, vol. 95(C).
    2. Deschatre, Thomas & Féron, Olivier & Gruet, Pierre, 2021. "A survey of electricity spot and futures price models for risk management applications," Energy Economics, Elsevier, vol. 102(C).
    3. Dennis Frestad & Fred Espen Benth & Steen Koekebakker, 2010. "Modeling Term Structure Dynamics in the Nordic Electricity Swap Market," The Energy Journal, , vol. 31(2), pages 53-86, April.
    4. Søren Asmussen, 2022. "On the role of skewness and kurtosis in tempered stable (CGMY) Lévy models in finance," Finance and Stochastics, Springer, vol. 26(3), pages 383-416, July.
    5. David Lee, 2022. "Modeling Commodity Price Dynamics," Working Papers hal-03758093, HAL.
    6. Fred Espen Benth & Luca Di Persio & Silvia Lavagnini, 2018. "Stochastic Modeling of Wind Derivatives in Energy Markets," Risks, MDPI, vol. 6(2), pages 1-21, May.
    7. Piergiacomo Sabino, 2021. "Pricing Energy Derivatives in Markets Driven by Tempered Stable and CGMY Processes of Ornstein-Uhlenbeck Type," Papers 2103.13252, arXiv.org.
    8. Takuji Arai & Yuto Imai & Ryo Nakashima, 2018. "Numerical analysis on quadratic hedging strategies for normal inverse Gaussian models," Papers 1801.05597, arXiv.org.
    9. Christensen, Troels Sønderby & Pircalabu, Anca & Høg, Esben, 2019. "A seasonal copula mixture for hedging the clean spark spread with wind power futures," Energy Economics, Elsevier, vol. 78(C), pages 64-80.
    10. Piergiacomo Sabino, 2021. "Normal Tempered Stable Processes and the Pricing of Energy Derivatives," Papers 2105.03071, arXiv.org.
    11. Zdeněk Zmeškal & Dana Dluhošová & Karolina Lisztwanová & Antonín Pončík & Iveta Ratmanová, 2023. "Distribution Prediction of Decomposed Relative EVA Measure with Levy-Driven Mean-Reversion Processes: The Case of an Automotive Sector of a Small Open Economy," Forecasting, MDPI, vol. 5(2), pages 1-19, May.
    12. Fred Espen Benth & Jūratė Šaltytė Benth & Steen Koekebakker, 2008. "Stochastic Modeling of Electricity and Related Markets," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6811, August.
    13. Lee, David, 2022. "Generic Price Model for Commodity Derivatives," MPRA Paper 114283, University Library of Munich, Germany.
    14. Xiao Jiang & Saralees Nadarajah & Thomas Hitchen, 2024. "A Review of Generalized Hyperbolic Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 595-624, July.

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