[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
IDEAS home Printed from https://ideas.repec.org/a/eee/eneeco/v62y2017icp139-154.html
   My bibliography  Save this article

Joint price and volumetric risk in wind power trading: A copula approach

Author

Listed:
  • Pircalabu, A.
  • Hvolby, T.
  • Jung, J.
  • Høg, E.
Abstract
This paper examines the dependence between wind power production and electricity prices and discusses its implications for the pricing and the risk distributions associated with contracts that are exposed to joint price and volumetric risk. We propose a copula model for the joint behavior of prices and wind power production, which is estimated to data from the Danish power market. We find that the marginal behavior of the individual variables is best described by ARMA–GARCH models with non-Gaussian error distributions, and the preferred copula model is a time-varying Gaussian copula. As an application of our joint model, we consider the case of an energy trading company entering into longer-term agreements with wind power producers, where the fluctuating future wind power production is bought at a predetermined fixed price. We find that assuming independence between prices and wind power production leads to an underestimation of risk, as the profit distribution becomes left-skewed when the negative dependence that we find in the data is accounted for. By performing a simple static hedge in the forward market, we show that the risk can be significantly reduced. Furthermore, an out-of-sample study shows that the choice of copula influences the price of correlation risk, and that time-varying copulas are superior to the constant ones when comparing actual profits generated with different models.

Suggested Citation

  • Pircalabu, A. & Hvolby, T. & Jung, J. & Høg, E., 2017. "Joint price and volumetric risk in wind power trading: A copula approach," Energy Economics, Elsevier, vol. 62(C), pages 139-154.
    • Handle: RePEc:eee:eneeco:v:62:y:2017:i:c:p:139-154
    DOI: 10.1016/j.eneco.2016.11.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0140988316303450
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.eneco.2016.11.023?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Moschini, Giancarlo & Lapan, Harvey, 1995. "The Hedging Role of Options and Futures under Joint Price, Basis, and Production Risk," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 36(4), pages 1025-1049, November.
    2. Markus Burger & Bernhard Klar & Alfred Muller & Gero Schindlmayr, 2004. "A spot market model for pricing derivatives in electricity markets," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 109-122.
    3. Diks, Cees & Panchenko, Valentyn & van Dijk, Dick, 2010. "Out-of-sample comparison of copula specifications in multivariate density forecasts," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1596-1609, September.
    4. Daniel Berg, 2009. "Copula goodness-of-fit testing: an overview and power comparison," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 675-701.
    5. Benth, Fred Espen & Biegler-König, Richard & Kiesel, Rüdiger, 2013. "An empirical study of the information premium on electricity markets," Energy Economics, Elsevier, vol. 36(C), pages 55-77.
    6. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    7. Gelabert, Liliana & Labandeira, Xavier & Linares, Pedro, 2011. "An ex-post analysis of the effect of renewables and cogeneration on Spanish electricity prices," Energy Economics, Elsevier, vol. 33(S1), pages 59-65.
    8. Coulon, Michael & Powell, Warren B. & Sircar, Ronnie, 2013. "A model for hedging load and price risk in the Texas electricity market," Energy Economics, Elsevier, vol. 40(C), pages 976-988.
    9. Avdulaj, Krenar & Barunik, Jozef, 2015. "Are benefits from oil–stocks diversification gone? New evidence from a dynamic copula and high frequency data," Energy Economics, Elsevier, vol. 51(C), pages 31-44.
    10. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    11. Ronald I. McKinnon, 1967. "Futures Markets, Buffer Stocks, and Income Stability for Primary Producers," Journal of Political Economy, University of Chicago Press, vol. 75(6), pages 844-844.
    12. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-235, April.
    13. Kolos, Sergey P. & Ronn, Ehud I., 2008. "Estimating the commodity market price of risk for energy prices," Energy Economics, Elsevier, vol. 30(2), pages 621-641, March.
    14. Wen, Xiaoqian & Wei, Yu & Huang, Dengshi, 2012. "Measuring contagion between energy market and stock market during financial crisis: A copula approach," Energy Economics, Elsevier, vol. 34(5), pages 1435-1446.
    15. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    16. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    17. Andrew Patton & Dimitris Politis & Halbert White, 2009. "Correction to “Automatic Block-Length Selection for the Dependent Bootstrap” by D. Politis and H. White," Econometric Reviews, Taylor & Francis Journals, vol. 28(4), pages 372-375.
    18. Lucia, Julio J. & Schwartz, Eduardo, 2000. "Electricity prices and power derivatives: Evidence from the Nordic Power Exchange," University of California at Los Angeles, Anderson Graduate School of Management qt12w8v7jj, Anderson Graduate School of Management, UCLA.
    19. Elberg, Christina & Hagspiel, Simeon, 2015. "Spatial dependencies of wind power and interrelations with spot price dynamics," European Journal of Operational Research, Elsevier, vol. 241(1), pages 260-272.
    20. De Lira Salvatierra, Irving & Patton, Andrew J., 2015. "Dynamic copula models and high frequency data," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 120-135.
    21. U. Cherubini & E. Luciano, 2002. "Bivariate option pricing with copulas," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(2), pages 69-85.
    22. Dimitris Politis & Halbert White, 2004. "Automatic Block-Length Selection for the Dependent Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 53-70.
    23. Yumi Oum & Shmuel S. Oren, 2010. "Optimal Static Hedging of Volumetric Risk in a Competitive Wholesale Electricity Market," Decision Analysis, INFORMS, vol. 7(1), pages 107-122, March.
    24. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    25. Jónsson, Tryggvi & Pinson, Pierre & Madsen, Henrik, 2010. "On the market impact of wind energy forecasts," Energy Economics, Elsevier, vol. 32(2), pages 313-320, March.
    26. Ulf Schepsmeier & Jakob Stöber, 2014. "Derivatives and Fisher information of bivariate copulas," Statistical Papers, Springer, vol. 55(2), pages 525-542, May.
    27. Fermanian, Jean-David & Wegkamp, Marten H., 2012. "Time-dependent copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 19-29.
    28. Paraschiv, Florentina & Erni, David & Pietsch, Ralf, 2014. "The impact of renewable energies on EEX day-ahead electricity prices," Energy Policy, Elsevier, vol. 73(C), pages 196-210.
    29. Fred Espen Benth & Jūratė Šaltytė Benth, 2012. "Financial markets for weather," World Scientific Book Chapters, in: Modeling and Pricing in Financial Markets for Weather Derivatives, chapter 1, pages 1-13, World Scientific Publishing Co. Pte. Ltd..
    30. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.
    31. G. Elliott & C. Granger & A. Timmermann (ed.), 2013. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 2, number 2.
    32. Carlos Gonz�lez-Pedraz & Manuel Moreno & Juan Ignacio Pe�a, 2015. "Portfolio selection with commodities under conditional copulas and skew preferences," Quantitative Finance, Taylor & Francis Journals, vol. 15(1), pages 151-170, January.
    33. Douglas Rivers & Quang Vuong, 2002. "Model selection tests for nonlinear dynamic models," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 1-39, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sahamkhadam, Maziar & Stephan, Andreas & Östermark, Ralf, 2018. "Portfolio optimization based on GARCH-EVT-Copula forecasting models," International Journal of Forecasting, Elsevier, vol. 34(3), pages 497-506.
    2. Tranberg, Bo & Hansen, Rasmus Thrane & Catania, Leopoldo, 2020. "Managing volumetric risk of long-term power purchase agreements," Energy Economics, Elsevier, vol. 85(C).
    3. Ricardo J. Bessa & Corinna Möhrlen & Vanessa Fundel & Malte Siefert & Jethro Browell & Sebastian Haglund El Gaidi & Bri-Mathias Hodge & Umit Cali & George Kariniotakis, 2017. "Towards Improved Understanding of the Applicability of Uncertainty Forecasts in the Electric Power Industry," Energies, MDPI, vol. 10(9), pages 1-48, September.
    4. Fabrizio Durante & Angelica Gianfreda & Francesco Ravazzolo & Luca Rossini, 2022. "A Multivariate Dependence Analysis for Electricity Prices, Demand and Renewable Energy Sources," Papers 2201.01132, arXiv.org.
    5. Gianfreda, Angelica & Ravazzolo, Francesco & Rossini, Luca, 2020. "Comparing the forecasting performances of linear models for electricity prices with high RES penetration," International Journal of Forecasting, Elsevier, vol. 36(3), pages 974-986.
    6. Apergis, Nicholas & Gozgor, Giray & Lau, Chi Keung Marco & Wang, Shixuan, 2020. "Dependence structure in the Australian electricity markets: New evidence from regular vine copulae," Energy Economics, Elsevier, vol. 90(C).
    7. Johannes Kaufmann & Philipp Artur Kienscherf & Wolfgang Ketter, 2020. "Modeling and Managing Joint Price and Volumetric Risk for Volatile Electricity Portfolios," Energies, MDPI, vol. 13(14), pages 1-19, July.
    8. Yu, L. & Li, Y.P. & Huang, G.H. & Fan, Y.R. & Nie, S., 2018. "A copula-based flexible-stochastic programming method for planning regional energy system under multiple uncertainties: A case study of the urban agglomeration of Beijing and Tianjin," Applied Energy, Elsevier, vol. 210(C), pages 60-74.
    9. Li, Xiafei & Wei, Yu, 2018. "The dependence and risk spillover between crude oil market and China stock market: New evidence from a variational mode decomposition-based copula method," Energy Economics, Elsevier, vol. 74(C), pages 565-581.
    10. Guo, Peng & Chen, Si & Chu, Jingchun & Infield, David, 2020. "Wind direction fluctuation analysis for wind turbines," Renewable Energy, Elsevier, vol. 162(C), pages 1026-1035.
    11. Akhtaruzzaman, Md & Banerjee, Ameet Kumar & Boubaker, Sabri & Moussa, Faten, 2023. "Does green improve portfolio optimisation?," Energy Economics, Elsevier, vol. 124(C).
    12. Zeng, Sheng & Liu, Xinchun & Li, Xiafei & Wei, Qi & Shang, Yue, 2019. "Information dominance among hedging assets: Evidence from return and volatility directional spillovers in time and frequency domains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    13. F. Marta L. Di Lascio & Andrea Menapace & Maurizio Righetti, 2020. "Joint and conditional dependence modelling of peak district heating demand and outdoor temperature: a copula-based approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 373-395, June.
    14. Anne Opschoor & Dewi Peerlings & Luca Rossini & Andre Lucas, 2024. "Density Forecasting for Electricity Prices under Tail Heterogeneity with the t-Riesz Distribution," Tinbergen Institute Discussion Papers 24-049/III, Tinbergen Institute.
    15. Nguyen, Quynh Nga & Bedoui, Rihab & Majdoub, Najemeddine & Guesmi, Khaled & Chevallier, Julien, 2020. "Hedging and safe-haven characteristics of Gold against currencies: An investigation based on multivariate dynamic copula theory," Resources Policy, Elsevier, vol. 68(C).
    16. Fugui Dong & Xiaohui Ding & Lei Shi, 2019. "Wind Power Pricing Game Strategy under the China’s Market Trading Mechanism," Energies, MDPI, vol. 12(18), pages 1-17, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Avdulaj, Krenar & Barunik, Jozef, 2015. "Are benefits from oil–stocks diversification gone? New evidence from a dynamic copula and high frequency data," Energy Economics, Elsevier, vol. 51(C), pages 31-44.
    2. Johannes Kaufmann & Philipp Artur Kienscherf & Wolfgang Ketter, 2020. "Modeling and Managing Joint Price and Volumetric Risk for Volatile Electricity Portfolios," Energies, MDPI, vol. 13(14), pages 1-19, July.
    3. Tranberg, Bo & Hansen, Rasmus Thrane & Catania, Leopoldo, 2020. "Managing volumetric risk of long-term power purchase agreements," Energy Economics, Elsevier, vol. 85(C).
    4. Krenar AVDULAJ & Jozef BARUNIK, 2013. "Can We Still Benefit from International Diversification? The Case of the Czech and German Stock Markets," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 63(5), pages 425-442, November.
    5. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.
    6. Diks, Cees & Panchenko, Valentyn & Sokolinskiy, Oleg & van Dijk, Dick, 2014. "Comparing the accuracy of multivariate density forecasts in selected regions of the copula support," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 79-94.
    7. 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.
    8. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
    9. Wen, Xiaoqian & Cheng, Hua, 2018. "Which is the safe haven for emerging stock markets, gold or the US dollar?," Emerging Markets Review, Elsevier, vol. 35(C), pages 69-90.
    10. De Lira Salvatierra, Irving & Patton, Andrew J., 2015. "Dynamic copula models and high frequency data," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 120-135.
    11. Yang Zhao & Charalampos Stasinakis & Georgios Sermpinis & Filipa Da Silva Fernandes, 2019. "Revisiting Fama–French factors' predictability with Bayesian modelling and copula‐based portfolio optimization," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 24(4), pages 1443-1463, October.
    12. Cees Diks & Valentyn Panchenko & Oleg Sokolinskiy, & Dick van Dijk, 2013. "Comparing the Accuracy of Copula-Based Multivariate Density Forecasts in Selected Regions of Support," Tinbergen Institute Discussion Papers 13-061/III, Tinbergen Institute.
    13. Pircalabu, A. & Benth, F.E., 2017. "A regime-switching copula approach to modeling day-ahead prices in coupled electricity markets," Energy Economics, Elsevier, vol. 68(C), pages 283-302.
    14. Tobias Eckernkemper, 2018. "Modeling Systemic Risk: Time-Varying Tail Dependence When Forecasting Marginal Expected Shortfall," Journal of Financial Econometrics, Oxford University Press, vol. 16(1), pages 63-117.
    15. Fabrizio Durante & Angelica Gianfreda & Francesco Ravazzolo & Luca Rossini, 2022. "A Multivariate Dependence Analysis for Electricity Prices, Demand and Renewable Energy Sources," Papers 2201.01132, arXiv.org.
    16. Yang, Lu & Yang, Lei & Ho, Kung-Cheng & Hamori, Shigeyuki, 2020. "Dependence structures and risk spillover in China’s credit bond market: A copula and CoVaR approach," Journal of Asian Economics, Elsevier, vol. 68(C).
    17. Pedro Antonio Martín Cervantes & Salvador Cruz Rambaud & María del Carmen Valls Martínez, 2020. "An Application of the SRA Copulas Approach to Price-Volume Research," Mathematics, MDPI, vol. 8(11), pages 1-28, October.
    18. Tobias Fissler & Yannick Hoga, 2024. "How to Compare Copula Forecasts?," Papers 2410.04165, arXiv.org.
    19. Ahmed, Osama & Serra, Teresa, 2015. "Evaluate the economic consequences of revenue insurance programs in Spain using copula models. The case of orange and apple," 2015 Conference, August 9-14, 2015, Milan, Italy 212522, International Association of Agricultural Economists.
    20. Warshaw, Evan, 2019. "Extreme dependence and risk spillovers across north american equity markets," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 237-251.

    More about this item

    Keywords

    Volumetric risk; Spot electricity price; Wind power production; Time-varying copula model; Risk management; Correlation risk;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:eneeco:v:62:y:2017:i:c:p:139-154. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eneco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.