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Modelling energy spot prices by volatility modulated L\'{e}vy-driven Volterra processes

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  • Ole E. Barndorff-Nielsen
  • Fred Espen Benth
  • Almut E. D. Veraart

Abstract

This paper introduces the class of volatility modulated L\'{e}vy-driven Volterra (VMLV) processes and their important subclass of L\'{e}vy semistationary (LSS) processes as a new framework for modelling energy spot prices. The main modelling idea consists of four principles: First, deseasonalised spot prices can be modelled directly in stationarity. Second, stochastic volatility is regarded as a key factor for modelling energy spot prices. Third, the model allows for the possibility of jumps and extreme spikes and, lastly, it features great flexibility in terms of modelling the autocorrelation structure and the Samuelson effect. We provide a detailed analysis of the probabilistic properties of VMLV processes and show how they can capture many stylised facts of energy markets. Further, we derive forward prices based on our new spot price models and discuss option pricing. An empirical example based on electricity spot prices from the European Energy Exchange confirms the practical relevance of our new modelling framework.

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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1307.6332.

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Date of creation: Jul 2013
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Publication status: Published in Bernoulli 2013, Vol. 19, No. 3, 803-845
Handle: RePEc:arx:papers:1307.6332

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Web page: http://arxiv.org/

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References

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  1. Fred Espen Benth & Jan Kallsen & Thilo Meyer-Brandis, 2007. "A Non-Gaussian Ornstein-Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 14(2), pages 153-169.
  2. Ole E. Barndorff–Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2010. "Modelling electricity forward markets by ambit fields," CREATES Research Papers 2010-41, School of Economics and Management, University of Aarhus.
  3. Koopman, Siem Jan & Ooms, Marius & Carnero, M. Angeles, 2007. "Periodic Seasonal Reg-ARFIMAGARCH Models for Daily Electricity Spot Prices," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 102, pages 16-27, March.
  4. Ole E. Barndorff–Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2010. "Ambit processes and stochastic partial differential equations," CREATES Research Papers 2010-17, School of Economics and Management, University of Aarhus.
  5. Fred Benth & Wolfgang Karl Härdle & Brenda López Cabrera, 2009. "Pricing of Asian temperature risk," SFB 649 Discussion Papers SFB649DP2009-046, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  6. P. Brockwell, 2001. "Lévy-Driven Carma Processes," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 53(1), pages 113-124, March.
  7. Almut E. D. Veraart & Luitgard A. M. Veraart, 2012. "Modelling electricity day–ahead prices by multivariate Lévy semistationary processes," CREATES Research Papers 2012-13, School of Economics and Management, University of Aarhus.
  8. Alvaro Cartea & Marcelo Gustavo Figueroa, 2005. "Pricing in Electricity Markets: a Mean Reverting Jump Diffusion Model with Seasonality," Birkbeck Working Papers in Economics and Finance, Birkbeck, Department of Economics, Mathematics & Statistics 0507, Birkbeck, Department of Economics, Mathematics & Statistics.
  9. Samuel Hikspoors & Sebastian Jaimungal, 2008. "Asymptotic Pricing of Commodity Derivatives using Stochastic Volatility Spot Models," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 15(5-6), pages 449-477.
  10. Ole E. Barndorff-Nielsen & Almut E. D. Veraart, 2012. "Stochastic Volatility of Volatility and Variance Risk Premia," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 11(1), pages 1-46, December.
  11. Paolo Guasoni & Mikl\'os R\'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
  12. Schwartz, Eduardo S, 1997. " The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, American Finance Association, vol. 52(3), pages 923-73, July.
  13. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501.
  14. Mikko S. Pakkanen, 2011. "Brownian Semistationary Processes And Conditional Full Support," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 579-586.
  15. Anders B. Trolle & Eduardo S. Schwartz, 2009. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 22(11), pages 4423-4461, November.
  16. Claudia Kluppelberg & Thilo Meyer-Brandis & Andrea Schmidt, 2010. "Electricity spot price modelling with a view towards extreme spike risk," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 10(9), pages 963-974.
  17. Benth, Fred Espen & Saltyte Benth, Jurate, 2009. "Dynamic pricing of wind futures," Energy Economics, Elsevier, Elsevier, vol. 31(1), pages 16-24, January.
  18. Basse, Andreas & Pedersen, Jan, 2009. "Lévy driven moving averages and semimartingales," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 119(9), pages 2970-2991, September.
  19. Wolfgang Härdle & Brenda López Cabrera, 2009. "Implied Market Price of Weather Risk," SFB 649 Discussion Papers SFB649DP2009-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  20. Brockwell, Peter J. & Davis, Richard A. & Yang, Yu, 2011. "Estimation for Non-Negative Lévy-Driven CARMA Processes," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 29(2), pages 250-259.
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Citations

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Cited by:
  1. Fred Espen Benth & Salvador Ortiz-Latorre, 2013. "A pricing measure to explain the risk premium in power markets," Papers 1308.3378, arXiv.org.
  2. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2014. "Discretization of Lévy semistationary processes with application to estimation," CREATES Research Papers 2014-21, School of Economics and Management, University of Aarhus.
  3. Almut E. D. Veraart & Luitgard A. M. Veraart, 2013. "Risk premia in energy markets," CREATES Research Papers 2013-02, School of Economics and Management, University of Aarhus.
  4. Barndorff-Nielsen, Ole E. & Benth, Fred Espen & Pedersen, Jan & Veraart, Almut E.D., 2014. "On stochastic integration for volatility modulated Lévy-driven Volterra processes," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 124(1), pages 812-847.
  5. Benth, Fred Espen & Taib, Che Mohd Imran Che, 2013. "On the speed towards the mean for continuous time autoregressive moving average processes with applications to energy markets," Energy Economics, Elsevier, Elsevier, vol. 40(C), pages 259-268.
  6. Ole E. Barndorff-Nielsen & Mikko S. Pakkanen & Jürgen Schmiegel, 2013. "Assessing Relative Volatility/Intermittency/Energy Dissipation," CREATES Research Papers 2013-15, School of Economics and Management, University of Aarhus.
  7. 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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