Publication: Long-term swings and seasonality in energy markets
Loading...
Files
Official URL
Full text at PDC
Publication Date
2019
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Fac. de Ciencias Económicas y Empresariales. Instituto Complutense de Análisis Económico (ICAE)
Citations
Exportar
Abstract
This paper introduces a two-factor continuous-time model for commodity pricing under the assump- tion 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 si- multaneously 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 the 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.
Description
UCM subjects
Unesco subjects
Keywords
Citation
Aiube, F., T. Baidya, and E. Tito (2008). Analysis of Commodity Prices with the Particle Filter. Energy Economics. 30, 2, 597-605.
Almansour, A. (2016). Convenience Yield in Commodity Price Modeling: A Regime Switching Approach. Energy Economics, 53, 238-247.
Arismendi, J.C., J. Back, M. Propkopczuk, R. Paschke, and M. Rudolf (2016). Seasonal Stochas- tic Volatility: Implication for the Pricing of Commodity Options. Journal of Banking and Fi- nance, 66, 53-65.
Back, J., M. Propkopczuk, and M. Rudolf. (2013). Seasonality and the Valuation of Commodity Options. Journal of Banking and Finance, 37, 2, 273-290.
Borovkova, S. and H. Geman (2007) Seasonal and Stochastic Effects in Commodity Forward Curves. Review of Derivatives Research, 9, 2, 167-186.
Burger, M., B. Graeber, and G. Schindlmayr (2007). Managing Energy Risk: An Integrated View on Power and Other Energy Markets. Finance. Wiley.
Carmona, R. and M. Coulon (2013). A Survey of Commodity Markets and Structural Models for Electricity Prices. Proceedings from the special thematic year at the Wolfgang Pauli Institute, Vienna, Editors: F.E. Benth, V. Kholodnyi, P. Laurence.
Cartea, A. and M.G. Figueroa (2005). Pricing in Electricity Markets: a Mean Reverting Jump Diffusion Model with Seasonality, Applied Mathematical Finance, 12, 4, 313-335.
Cartea, A. and P. Villaplana (2008). Spot Price Modeling and the Valuation of Electricity Forward Contracts: The Role of Demand and Capacity, Journal of Banking and Finance, 32, 12, 2502-2519.
Cartea, A. and T. Williams (2008). UK Gas Markets: The Market Price of Risk and Applications to Multiple Interruptible Supply Contracts, Energy Economics, 30, 3, 829-846.
Cartea, A. and C. González-Pedraz (2012). How Much Should We Pay for Interconnecting Electricity Markets? A Real Options Approach, Energy Economics, 34, 1, 14-30.
Casassus, J., P. Collin-Dufresne, and B.R. Routledge (2005). Equilibrium Commodity Prices with Irreversible Investment and Non-linear Technology. Working Paper 11864. National Bureau of Economic Research.
Chiu, M.C., H.Y. Wong, and J. Zhao (2015). Commodity Derivatives Pricing with Cointegration and Stochastic Covariances. European Journal of Operational Research, 246, 2, 476-486.
Chkili, W., S. Hammoudeh, and D.K. Nguyen (2014). Volatility Forecasting and Risk Man- agement for Commodity Markets in the Presence of Asymmetry and Long Memory, Energy Economics, 41, 1-18.
Deng, S. (2001). Stochastic Models of Energy Commodity Prices and their Applications: Mean- reversion with Jumps and Spikes. Journal of Regulatory Economics, 19, 3, 239?270.
Escribano, A., J.I. Peña, and P. Villaplana (2011). Modelling Electricity Prices: International Evidence. Oxford Bulletin of Economics and Statistics, 73, 5, 622-650.
Ewald, C.O., A. Zhang, and Z. Zong (2018). On the Calibration of the Schwartz Two-factor Model to WTI Crude Oil Options and the Extended Kalman Filter. Annals of Operations Research, January, available at https://doi.org/10.1007/s10479-018-2770-x.
Forsythe, P. (2007). A Semi-Lagrangian Approach for Natural Gas Valuation and Optimal Operation. SIAM Journal on Scientific Computing, 30, 1, 339-368.
Fouquau, J. and P. Six (2015). A Comparison of the Convenience Yield and Interest-adjusted Basis. Finance Research Letters, 14, 142-149.
Furió, D. and H. Chuliá (2012). Price and Volatility Dynamics between Electricity and Fuel Costs: Some Evidence for Spain. Energy Economics, 34, 6, 2058-2065.
Geman, H. (2005). Commodities and Commodity Derivatives: Modeling and Pricing of Agri- culturals, Metals and Energy. Finance. Wiley.
Geman H. and V.N. Nguyen (2005). Soybean Inventory and Forward Curve Dynamics. Man- agement Science, 51, 7, 1076-1091.
Gibson, R. and E.S. Schwartz (1990). Stochastic Convenience Yield and the Pricing of Oil Contingent Claims. Journal of Finance, 45, 3, 959-976.
Gómez-Valle, L., Z. Habibilashkary, and J. Martínez-Rodríguez (2017). A New Technique to Estimate the Risk-neutral Processes in Jump?Diffusion Commodity Futures Models. Journal of Computational and Applied Mathematics, 309, 435-441.
Gómez-Valle, L., Z. Habibilashkary, and J. Martínez-Rodríguez (2018). A Multiplicative Sea- sonal Component in Commodity Derivative Pricing. Journal of Computational and Applied Mathematics, 330, 835-847.
Gould P.G., A.B. Koehler, J.K. Ord, R.D. Snyder, R.J. Hyndman, and F. Vahid-Araghi (2008). Forecasting Time-series with Multiple Seasonal Patterns. European Journal of Operational Re- search, 191, 1, 207-222.
Hambly, B., S, Howison, and T. Kluge (2009). Modelling Spikes and Pricing Swing Options in Electricity Markets. Quantitative Finance, 9, 8, 937-949.
Harvey, A, C. (1997). Trends, Cycles and Autoregression. Economic Journal, 107, 440, 192-201.
Hilliard, J.E. and J. Hilliard (2015). Estimating Early Exercise Premiums on Gold and Copper Options using a Multifactor Model and Density Matched Lattice. Financial Review, 50, 1, 27-56.
Hilliard, J.E. and J. Reis. (1998) Valuation of Commodity Futures and Options under Stochastic Convenience Yields, Interest Rates, and Jump Diffusion in the Spot. Journal of Financial and Quantitative Analysis, 33, 1, 61-86.
Hodrick, R.J. and E.C. Prescott (1980). Postwar U.S. Business Cycles: an Empirical Investiga- tion. Carnegie-Mellon University, Discussion Papers 451, Northwestern University.
Islyaev, S. and P. Date (2015). Electricity Futures Price Models: Calibration and Forecasting. European Journal of Operational Research, 247, 1, 144-154.
Janczura, J. (2014). Pricing Electricity Derivatives within a Markov Regime-switching Model: a Risk Premium Approach. Mathematical Methods of Operations Research, 79, 1, 1-30.
Kamat, R. and S.S. Oren (2002). Exotic Options for Interruptible Electricity Supply Contracts. Operations Research, 50, 5, 835-850.
Kyriakou, I., N.K. Nomikos, N.C. Papastolou, and P.K. Poliasis (2016). Affine-Structure Models and the Pricing of Energy Commodity Derivatives. European Financial Management, 22, 5, 853- 881.
Lai, A.N. and C. Mellios (2016). Valuation of Commodity Derivatives with an Unobservable Convenience Yield. Computers and Operations Research, 66, 402-414.
Li, L. and V. Linetsky (2013). Optimal Stopping and Early Exercise: an Eigenfunction Expan- sion Approach. Operations Research, 61, 3, 625-646.
Li, L. and R. Mendoza Arriaga (2013). Ornstein-Uhlenbeck Processes Time Changed with Additive Subordinators and Their Applications in Commodity Derivative Models. Operations Research Letters, 41, 5, 521-525.
Li, L., R. Mendoza-Arriaga, Z. Mo, and D. Mitchell (2016). Modelling Electricity Prices: A Time Change Approach. Quantitative Finance, 16, 7, 1089-1109.
Liu, P. and K. Tang (2011). The Stochastic Behavior of Commodity Prices with Heteroskedas- ticity in the Convenience Yield. Journal of Empirical Finance, 18, 2, 211-224.
Lucía, J. and E.S. Schwartz (2002). Electricity Prices and Power Derivatives: Evidence from the Nordic Power Exchange. Review of Derivatives Research, 5, 1, 5-50.
Manoliu, M., and S. Tompaidis (2002). Energy Futures Prices: Term Structure Models with Kalman Filter Estimation. Applied Mathematical Finance, 9, 1, 21-43.
Mayer, K., Th. Schmid, and F. Weber (2011). Modeling Electricity Spot Prices - Combining Mean-reversion, Spikes and Stochastic Volatility, CEFS working paper series, No. 2011-02.
Mirantes, A.G., J. Población, and G. Serna (2012). The Stochastic Seasonal Behaviour of Nat- ural Gas Prices. European Financial Management, 18, 3, 410-443.
Mirantes, A.G., J. Población, and G. Serna (2015). Commodity Derivative Valuation under a Factor Model with Time-varying Market Prices of Risk. Review of Derivatives Research, 18, 75-93.
Moreno, M. and F. Platania (2015). A Cyclical Square-Root Model for the Term Structure of Interest Rates. European Journal of Operational Research, 241, 1, 109-121.
Mu, X. and H. Ye (2015). Small Trends and Big Cycles in Crude Oil Prices. Energy Journal, 36, 1, 49-72.
Pellegrino, T. and P. Sabino (2014). Pricing and Hedging Multiasset Spread Options using a Three-Dimensional Fourier Cosine Series Expansion Method. Journal of Energy Markets, 7, 2, 71-92.
Sbuelz, A. (2015). The Schwartz and Smith (2000) Model with State-dependent Risk Premia. Mathematical Finance Letters, 7, 1-7.
Schmitz, A., Z. Wang, and J.H. Kimn (2014). A Jump Diffusion Model for Agricultural Com- modities with Bayesian Analysis. Journal of Futures Markets, 34, 3, 235-260.
Schwartz, E.S. (1997). The Stochastic Behaviour of Commodity Prices: Implications for Valu- ation and Hedging. Journal of Finance, 52, 3, 923-973.
Schwartz, E.S. and J. Smith (2000). Short-Term Variations and Long-Term Dynamics in Com- modity Prices. Management Science, 46, 7, 893-911.
Sévi, B. (2015). Explaining the Convenience Yield in the WTI Crude Oil Market Using Realized Volatility and Jumps. Economic Modelling, 44, 243-251.
Sφrensen, C. (2002). Modeling Seasonality in Agricultural Commodity Futures. Journal of Futures Markets, 22, 5, 393-426.
Taylor, J.W. (2010). Triple Seasonal Methods for Short-term Electricity Demand Forecasting. European Journal of Operational Research, 204, 1, 139-152
Vasicek, O. (1977). An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, 5, 2, 177-188.
Weron, R. (2007). Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach. Finance. Wiley.
Wong, H.Y. and Lo, Y.W. (2009). Option Pricing with Mean Reversion and Stochastic Volatility. European Journal of Operational Research, 197, 1, 179-187.
Yan, X. (2002). Valuation of Commodity Derivatives in a New Multi-factor Model. Review of Derivatives Research, 5, 3, 251-271.
Young, P.C., D.J. Pedregal, and W. Tych (1999). Dynamic Harmonic Regression. Journal of Forecasting, 18, 6, 369-394.