Abstract
This paper deals with the estimation of continuous time diffusion processes describing the dynamics of electricity spot prices. Different parametric models have been proposed in the literature, each attempting to capture empirical characteristics and stylized facts of the electricity market like the spiky behavior of the spot prices. Although jump-diffusion and regime-switching models perform reasonably well, there is always a trade-off between model parsimony and adequacy. The results in the literature indicate that none of the models seem to consistently outperform its counterparts. This paper avoids making parametric assumption about the drift and the diffusion coefficient functions of the underlying electricity spot prices, and estimates these functions together with the market price of risk in a nonparametric way. The latter allows us to price futures contracts written on electricity spots. Using electricity spot prices and futures data from the regional electricity markets in Australia, we show that besides offering a convenient way of estimating the continuous-time models for electricity spot prices, our nonparametric estimation procedure performs well in- and out-of-sample when dealing with pricing of future contracts.
Acknowledgment
We would like to thank Christian Schlag and Michael Sherris for their valuable comments and helpful suggestions.
References
Ait-Sahalia, Y. 1996a. “Nonparametric Pricing of Interest Rate Derivative Securities.” Econometrica 64: 527–560.10.2307/2171860Search in Google Scholar
Ait-Sahalia, Y. 1996b. “Testing Continuous-Time Models of the Spot Interest Rate.” Review of Financial Studies 9: 385–426.10.1093/rfs/9.2.385Search in Google Scholar
Bessembinder, H., and M. Lemmon. 2002. “Equilibrium Pricing and Optimal Hedging in Electricity Forward Markets.” Journal of Finance 57: 1347–1382.10.1111/1540-6261.00463Search in Google Scholar
Bierbrauer, M., C. Menn, S. Rachev, and S. Trück. 2007. “Spot and Derivative Pricing in the EEX Power Market.” Journal of Banking & Finance 31: 3462–3485.10.1016/j.jbankfin.2007.04.011Search in Google Scholar
Cartea, A., and M. Figueroa. 2005. “Pricing in Electricity Markets: a Mean Reverting Jump Diffusion Model with Seasonality.” Applied Mathematical Finance 12 (4): 313–335.10.1080/13504860500117503Search in Google Scholar
Clewlow, L., and C. Strickland. 2000. Energy Derivatives: Pricing and Risk Management. London: Lacima Publications.Search in Google Scholar
De Jong, C. 2005. “The Nature of Power Spikes: A Regime-Switch Approach.” ERIM Report Series ERS-2005-052-F&A.Search in Google Scholar
Diebold, F., and R. Mariano. 1995. “Comparing Predictive Accuracy.” Journal of Business and Economic Statistics 13: 253–263.Search in Google Scholar
Epanechnikov, V. 1969. “Nonparametric Estimates of Multivariate Probability Density.” Theory of Probability and Applications 14: 153–158.10.1137/1114019Search in Google Scholar
Eydeland, A., and K. Wolyniec. 2003. Energy and Power Risk Management. Hoboken, NJ: Wiley.Search in Google Scholar
Florens-Zmirou, D. 1993. “On Estimating the Diffusion Coeffcient from Discrete Observations.” Journal of Applied Probability 30 (4): 790–804.10.2307/3214513Search in Google Scholar
Geman, H., and A. Roncoroni. 2006. “Understanding the Fine Structure of Electricity Prices.” Journal of Business 79 (3): 1225–1262.10.1086/500675Search in Google Scholar
Gourieroux, C., and J. Jasiak. 2001. Financial Econometrics: Problems, Models, and Methods. Princeton, NJ: Princeton University Press.10.1515/9780691187020Search in Google Scholar
Haldrup, N., and M. Nielsen. 2004. “A Regime Switching Long Memory Model for Electricity Prices.” Working Paper, Department of Economics, University of Aarhus 2.Search in Google Scholar
Haldrup, N., and M. Nielsen. 2006. “A Regime Switching Long Memory Model for Electricity Prices.” Journal of Econometrics 135 (1–2): 349–376.10.1016/j.jeconom.2005.07.021Search in Google Scholar
Härdle, W., M. Müller, S. Sperlich, and A. Werwatz. 2004. Nonparametric and Semiparametric Models. Heidelberg: Springer Verlag.10.1007/978-3-642-17146-8Search in Google Scholar
Higgs, H., and A. Worthington. 2008. “Stochastic Price Modeling of High Volatility, Mean-Reverting, Spike-Prone Commodities: The Australian Wholesale Spot Electricity Market.” Energy Economics 30 (6): 3172–3185.10.1016/j.eneco.2008.04.006Search in Google Scholar
Huisman, R. 2008. “The Influence of Temperature on Spike Probability in Day-Ahead Power Prices.” Energy Economics 30: 2697–2704.10.1016/j.eneco.2008.05.007Search in Google Scholar
Huisman, R., and C. De Jong. 2003. “Option Formulas for Mean-Reverting Power Prices with Spikes.” Energy Power Risk Management 7: 12–16.Search in Google Scholar
Huisman, R., and R. Mahieu. 2003. “Regime Jumps in Electricity Prices.” Energy Economics 25: 425–434.10.1016/S0140-9883(03)00041-0Search in Google Scholar
Jacod, J. 2000. “Non-Parametric Kernel Estimation of the Coeffcient of a Diffusion.” Scandinavian Journal of Statistics 27 (1): 83–96.10.1111/1467-9469.00180Search in Google Scholar
Janczura, J., and R. Weron. 2010. “An Empirical Comparison of Alternate Regime-Switching Models for Electricity Spot Prices.” Energy Economics 32 (5): 1059–1073.10.1016/j.eneco.2010.05.008Search in Google Scholar
Jiang, G., and J. Knight. 1997. “A Nonparametric Approach to the Estimation of Diffusion Processes, with an Application to a Short-Term Interest Rate Model.” Econometric Theory 13 (7): 615–645.10.1017/S0266466600006101Search in Google Scholar
Jones, M. C., J. S. Marron, and S. J. Sheather. 1996. “A Brief Survey of Band-Width Selection for Density Estimation.” Journal of American Statistical Association 91: 401–407.10.1080/01621459.1996.10476701Search in Google Scholar
Kaminski, V. 1999. Managing Energy Price Risk. London: Risk Books.Search in Google Scholar
Kanamura, T., and K. Ohashi. 2008. “On Transition Probabilities of Regime Switching in Electricity Prices.” Energy Economics 30: 1158–1172.10.1016/j.eneco.2007.07.011Search in Google Scholar
Kluge, T., B. Hambly, and S. Howison. 2009. “Modeling Spikes and Pricing Swing Options in Electricity Markets.” Quantitative Finance 9 (8): 937–949.10.1080/14697680802596856Search in Google Scholar
Knittel, C., and M. Roberts. 2001. “An Empirical Examination of Deregulated Electricity Prices.” POWER Working Paper PWP-087.10.2139/ssrn.294382Search in Google Scholar
Kolos, S., and E. Ronn. 2008. “Estimating the Commodity Market Price of Risk for Energy Prices.” Energy Economics 30: 621–641.10.1016/j.eneco.2007.09.005Search in Google Scholar
Kosater, P., and K. Mosler. 2006. “Can Markov Regime-Switching Models Improve Power-Price Forecasts? Evidence from German Daily Power Prices.” Applied Energy, 83, 943–958.Search in Google Scholar
Künsch, H. R. 1989. “The Jackknife and the Bootstrap for General Stationary Observations.” The Annals of Statistics 17: 1217–1241.10.1214/aos/1176347265Search in Google Scholar
Longstaff, F., and A. Wang. 2004. “Electricity Forward Prices: A High-Frequency Empirical Analysis.” Journal of Finance 59: 1877–1900.10.1111/j.1540-6261.2004.00682.xSearch in Google Scholar
Lucia, J., and E. Schwartz. 2002. “Electricity Prices and Power Derivatives: Evidence From the Nordic Power Exchange.” Review of Derivatives Research 5: 5–50.10.1023/A:1013846631785Search in Google Scholar
Merton, R. 1973. “An Intertemporal Capital Asset Pricing Model.” Econometrica 41 (5): 867–887.10.2307/1913811Search in Google Scholar
Mount, T., Y. Ning, and X. Cai. 2006. “Predicting Price Spikes in Electricity Markets Using a Regime-Switching Model with Time-Varying Parameters.” Energy Economics 28: 62–80.10.1016/j.eneco.2005.09.008Search in Google Scholar
Mugele, C., S. T. Rachev, S. Trück. 2002. “Stable Modeling of Different European Power Markets.” Investment Management and Financial Innovations 2 (3), 65–85.Search in Google Scholar
Øksendal, B. 1985. Stochastic Differential Equations: An Introduction with Applications. Berlin-Heidelberg-New-York-Tokyo: Springer Verlag.Search in Google Scholar
Pilipovic, D. 1997. Energy Risk: Valuing and Managing Energy Derivatives. New York: McGraw-Hill.Search in Google Scholar
Pindyck, R. 1999. “The Long-Run Evolution of Energy Prices.” The Energy Journal 20: 1–27.10.5547/ISSN0195-6574-EJ-Vol20-No2-1Search in Google Scholar
Schwartz, E. S. 1997. “The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging.” The Journal of Finance 52: 923–973.10.1111/j.1540-6261.1997.tb02721.xSearch in Google Scholar
Scott, D. 1992. Multivariate Density Estimation: Theory, Practice and Visualization. New York: John Wiley.10.1002/9780470316849Search in Google Scholar
Sheather, S. J., and M. C. Jones. 1991. “A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation.” Journal of the Royal Statistical Society B 53: 683–690.10.1111/j.2517-6161.1991.tb01857.xSearch in Google Scholar
Silverman, B. W. 1986. Density Estimation. London: Chapman and Hall.Search in Google Scholar
Simonsen, I. 2003. “Measuring Anti-Correlations in the Nordic Electricity Spot Market by Wavelets.” Physica A 322: 597–606.10.1016/S0378-4371(02)01938-6Search in Google Scholar
Soulier, P. 1998. “Nonparametric Estimation of the Diffusion Coeffcient of a Diffusion Process.” Stochastic Analysis and Applications 16: 185–200.10.1080/07362999808809525Search in Google Scholar
Stanton, R. 1997. “A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk.” Journal of Finance 52 (5): 1973–2002.10.1111/j.1540-6261.1997.tb02748.xSearch in Google Scholar
Venables, W., and B. D. Ripley. 2002. Modern Applied Statistics with S. New York: Springer-Verlag.10.1007/978-0-387-21706-2Search in Google Scholar
Wand, M. P., and M. C. Jones. 1995. Kernel Smoothing. London: Chapman and Hall.10.1007/978-1-4899-4493-1Search in Google Scholar
Weron, R. 2006. Modeling and Forecasting Loads and Prices in Deregulated Electricity Markets. ARE Agencja Rynku Energii S.A.10.1002/9781118673362Search in Google Scholar
Weron, R., M. Bierbrauer, and S. Trück. 2004a. “Modeling Electricity Prices: Jump Diffusion and Regime Switching.” Physica A 336: 39–48.10.1016/j.physa.2004.01.008Search in Google Scholar
Weron, R., I. Simonsen, and P. Wilman. 2004b. “Modeling Highly Volatile and Seasonal Markets: Evidence from the Nord Pool Electricity Market.” The Application of Econophysics, Proceedings of the Second Nikkei Econophysics Symposium, Yokyp, 182–191.Search in Google Scholar
West, K. 1996. “Asymptotic Inference about Predictive Ability.” Econometrica 64: 1067–1084.10.2307/2171956Search in Google Scholar
©2014 by De Gruyter
Articles in the same Issue
- Frontmatter
- A nonparametric model for spot price dynamics and pricing of futures contracts in electricity markets
- Functional cointegration: definition and nonparametric estimation
- Nonlinearity, heterogeneity and unobserved effects in the carbon dioxide emissions-economic development relation for advanced countries
- A growth model with qualities, varieties, and human capital: stability and transitional dynamics
- Real vs. nominal cycles: a multistate Markov-switching bi-factor approach
Articles in the same Issue
- Frontmatter
- A nonparametric model for spot price dynamics and pricing of futures contracts in electricity markets
- Functional cointegration: definition and nonparametric estimation
- Nonlinearity, heterogeneity and unobserved effects in the carbon dioxide emissions-economic development relation for advanced countries
- A growth model with qualities, varieties, and human capital: stability and transitional dynamics
- Real vs. nominal cycles: a multistate Markov-switching bi-factor approach