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Long-term swings and seasonality in energy markets

Author

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  • Moreno, Manuel
  • Novales, Alfonso
  • Platania, Federico
Abstract
This paper introduces a two-factor continuous-time model for commodity pricing under the assumption that prices revert to a stochastic mean level, which shows smooth, periodic fluctuations over long periods of time. We represent the mean reversion price by a Fourier series with a stochastic component. We also consider a seasonal component in the price level, an essential characteristic of many commodity prices, which we represent again by a Fourier series. We obtain analytical pricing expressions for futures contracts. Using futures price data on Natural Gas, we provide evidence on the presence of long-term fluctuations and show how to estimate the long-term component simultaneously with a seasonal component using the Kalman filter. We analyse the in-sample and out-of-sample empirical performance of our pricing model with and without a seasonal component and compare it with Schwartz and Smith (2000) model. Our findings show the in-sample and out-of-sample superiority of our model with seasonal fluctuations, thereby providing a simple and powerful tool for portfolio management, risk management, and derivative pricing.

Suggested Citation

  • Moreno, Manuel & Novales, Alfonso & Platania, Federico, 2019. "Long-term swings and seasonality in energy markets," European Journal of Operational Research, Elsevier, vol. 279(3), pages 1011-1023.
    • Handle: RePEc:eee:ejores:v:279:y:2019:i:3:p:1011-1023
    DOI: 10.1016/j.ejor.2019.05.042
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    as
    1. Xiaoyi Mu and Haichun Ye, 2015. "Small Trends and Big Cycles in Crude Oil Prices," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1).
    2. Andrés Mirantes & Javier Población & Gregorio Serna, 2015. "Commodity derivative valuation under a factor model with time-varying market prices of risk," Review of Derivatives Research, Springer, vol. 18(1), pages 75-93, April.
    3. Adam Schmitz & Zhiguang Wang & Jung‐Han Kimn, 2014. "A Jump Diffusion Model for Agricultural Commodities with Bayesian Analysis," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(3), pages 235-260, March.
    4. Cartea, Álvaro & Williams, Thomas, 2008. "UK gas markets: The market price of risk and applications to multiple interruptible supply contracts," Energy Economics, Elsevier, vol. 30(3), pages 829-846, May.
    5. Anh Ngoc Lai & Constantin Mellios, 2016. "Valuation of commodity derivatives with an unobservable convenience yield," Post-Print hal-03708996, HAL.
    6. Aiube, Fernando Antonio Lucena & Baidya, Tara Keshar Nanda & Tito, Edison Americo Huarsaya, 2008. "Analysis of commodity prices with the particle filter," Energy Economics, Elsevier, vol. 30(2), pages 597-605, March.
    7. Back, Janis & Prokopczuk, Marcel & Rudolf, Markus, 2013. "Seasonality and the valuation of commodity options," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 273-290.
    8. Eduardo Schwartz & James E. Smith, 2000. "Short-Term Variations and Long-Term Dynamics in Commodity Prices," Management Science, INFORMS, vol. 46(7), pages 893-911, July.
    9. Ioannis Kyriakou & Nikos K. Nomikos & Nikos C. Papapostolou & Panos K. Pouliasis, 2016. "Affine†Structure Models and the Pricing of Energy Commodity Derivatives," European Financial Management, European Financial Management Association, vol. 22(5), pages 853-881, November.
    10. Cartea, Álvaro & Villaplana, Pablo, 2008. "Spot price modeling and the valuation of electricity forward contracts: The role of demand and capacity," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2502-2519, December.
    11. Jaime Casassus & Pierre Collin-Dufresne & Bryan R. Routledge, 2005. "Equilibrium Commodity Prices with Irreversible Investment and Non-Linear Technology," NBER Working Papers 11864, National Bureau of Economic Research, Inc.
    12. Lingfei Li & Vadim Linetsky, 2013. "Optimal Stopping and Early Exercise: An Eigenfunction Expansion Approach," Operations Research, INFORMS, vol. 61(3), pages 625-643, June.
    13. Lingfei Li & Rafael Mendoza-Arriaga & Zhiyu Mo & Daniel Mitchell, 2016. "Modelling electricity prices: a time change approach," Quantitative Finance, Taylor & Francis Journals, vol. 16(7), pages 1089-1109, July.
    14. Moreno, Manuel & Platania, Federico, 2015. "A cyclical square-root model for the term structure of interest rates," European Journal of Operational Research, Elsevier, vol. 241(1), pages 109-121.
    15. Cartea, Álvaro & González-Pedraz, Carlos, 2012. "How much should we pay for interconnecting electricity markets? A real options approach," Energy Economics, Elsevier, vol. 34(1), pages 14-30.
    16. Gould, Phillip G. & Koehler, Anne B. & Ord, J. Keith & Snyder, Ralph D. & Hyndman, Rob J. & Vahid-Araghi, Farshid, 2008. "Forecasting time series with multiple seasonal patterns," European Journal of Operational Research, Elsevier, vol. 191(1), pages 207-222, November.
    17. Taylor, James W., 2010. "Triple seasonal methods for short-term electricity demand forecasting," European Journal of Operational Research, Elsevier, vol. 204(1), pages 139-152, July.
    18. Andrés García Mirantes & Javier Población & Gregorio Serna, 2012. "The Stochastic Seasonal Behaviour of Natural Gas Prices," European Financial Management, European Financial Management Association, vol. 18(3), pages 410-443, June.
    19. Arismendi, Juan C. & Back, Janis & Prokopczuk, Marcel & Paschke, Raphael & Rudolf, Markus, 2016. "Seasonal Stochastic Volatility: Implications for the pricing of commodity options," Journal of Banking & Finance, Elsevier, vol. 66(C), pages 53-65.
    20. Alvaro Cartea & Marcelo Figueroa, 2005. "Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 313-335.
    21. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    22. Xuemin Yan, 2002. "Valuation of commodity derivatives in a new multi-factor model," Review of Derivatives Research, Springer, vol. 5(3), pages 251-271, October.
    23. Gibson, Rajna & Schwartz, Eduardo S, 1990. "Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-976, July.
    24. Jimmy E. Hilliard & Jitka Hilliard, 2015. "Estimating Early Exercise Premiums on Gold and Copper Options Using a Multifactor Model and Density Matched Lattices," The Financial Review, Eastern Finance Association, vol. 50(1), pages 27-56, January.
    25. Moreno, Manuel & Novales, Alfonso & Platania, Federico, 2018. "A term structure model under cyclical fluctuations in interest rates," Economic Modelling, Elsevier, vol. 72(C), pages 140-150.
    26. Anh Ngoc Lai & Constantin Mellios, 2016. "Valuation of commodity derivatives with an unobservable convenience yield," Post-Print halshs-01183166, HAL.
    27. Chkili, Walid & Hammoudeh, Shawkat & Nguyen, Duc Khuong, 2014. "Volatility forecasting and risk management for commodity markets in the presence of asymmetry and long memory," Energy Economics, Elsevier, vol. 41(C), pages 1-18.
    28. Sévi, Benoît, 2015. "Explaining the convenience yield in the WTI crude oil market using realized volatility and jumps," Economic Modelling, Elsevier, vol. 44(C), pages 243-251.
    29. Wong, Hoi Ying & Lo, Yu Wai, 2009. "Option pricing with mean reversion and stochastic volatility," European Journal of Operational Research, Elsevier, vol. 197(1), pages 179-187, August.
    30. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    31. Ben Hambly & Sam Howison & Tino Kluge, 2009. "Modelling spikes and pricing swing options in electricity markets," Quantitative Finance, Taylor & Francis Journals, vol. 9(8), pages 937-949.
    32. Helyette Geman & V. Nguyen, 2005. "Soybeans Inventory and Forward Curve Dynamics," Post-Print halshs-00144292, HAL.
    33. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    34. Mayer, Klaus & Schmid, Thomas & Weber, Florian, 2011. "Modeling electricity spot prices - Combining mean-reversion, spikes and stochastic volatility," CEFS Working Paper Series 2011-02, Technische Universität München (TUM), Center for Entrepreneurial and Financial Studies (CEFS).
    35. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    36. Liu, Peng & Tang, Ke, 2011. "The stochastic behavior of commodity prices with heteroskedasticity in the convenience yield," Journal of Empirical Finance, Elsevier, vol. 18(2), pages 211-224, March.
    37. Hélyette Geman & Vu-Nhat Nguyen, 2005. "Soybean Inventory and Forward Curve Dynamics," Management Science, INFORMS, vol. 51(7), pages 1076-1091, July.
    38. Rajnish Kamat & Shmuel S. Oren, 2002. "Exotic Options for Interruptible Electricity Supply Contracts," Operations Research, INFORMS, vol. 50(5), pages 835-850, October.
    39. repec:dau:papers:123456789/1937 is not listed on IDEAS
    40. Islyaev, Suren & Date, Paresh, 2015. "Electricity futures price models: Calibration and forecasting," European Journal of Operational Research, Elsevier, vol. 247(1), pages 144-154.
    41. Furió, Dolores & Chuliá, Helena, 2012. "Price and volatility dynamics between electricity and fuel costs: Some evidence for Spain," Energy Economics, Elsevier, vol. 34(6), pages 2058-2065.
    42. Chiu, Mei Choi & Wong, Hoi Ying & Zhao, Jing, 2015. "Commodity derivatives pricing with cointegration and stochastic covariances," European Journal of Operational Research, Elsevier, vol. 246(2), pages 476-486.
    43. Mihaela Manoliu & Stathis Tompaidis, 2002. "Energy futures prices: term structure models with Kalman filter estimation," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(1), pages 21-43.
    44. Harvey, Andrew, 1997. "Trends, Cycles and Autoregressions," Economic Journal, Royal Economic Society, vol. 107(440), pages 192-201, January.
    45. Alvaro Escribano & J. Ignacio Peña & Pablo Villaplana, 2011. "Modelling Electricity Prices: International Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(5), pages 622-650, October.
    46. Hilliard, Jimmy E. & Reis, Jorge, 1998. "Valuation of Commodity Futures and Options under Stochastic Convenience Yields, Interest Rates, and Jump Diffusions in the Spot," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(1), pages 61-86, March.
    47. Fouquau, Julien & Six, Pierre, 2015. "A comparison of the convenience yield and interest-adjusted basis," Finance Research Letters, Elsevier, vol. 14(C), pages 142-149.
    48. Almansour, Abdullah, 2016. "Convenience yield in commodity price modeling: A regime switching approach," Energy Economics, Elsevier, vol. 53(C), pages 238-247.
    49. Joanna Janczura, 2014. "Pricing electricity derivatives within a Markov regime-switching model: a risk premium approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(1), pages 1-30, February.
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