Summary
This paper suggests a new approach to model spot prices of electricity. It uses a shot-noise model to capture extreme spikes typically arising in electricity markets. Moreover, the model easily accounts for seasonality and mean reversion. We compute futures prices in closed form and show that the resulting shapes capture a large variety of typically observed term structures. For statistical purposes we show how to use the EM-algorithm. An estimation on spot price data from the European Energy Exchange illustrate the applicability of the model.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
. Altmann T., Schmidt T., Stute, W. (2006) A shot noise model for financialassets. Submitted.
. Benth F. E., Kallsen J., Meyer-Brandis T. (2006) A non-Gaussian Ornstein-Uhlenbeck process for electricity spot price modeling and derivatives pricing.Applied Mathematical Finance: Forthcoming.
Brémaud P. (1981) Point Processes and Queues. Springer Verlag, Berlin Heidelberg New York.
Cartea A., Figueroa, M. G. (2005) Pricing in electricity markets: a mean reverting jump diffusion model with seasonality. Applied Mathematical Finance: 12(4):313–335.
Cox J. C., Ingersoll J. W., Ross, S. A. (1985) A theory of the term structure of interest rates. Econometrica 54:385–407.
Dassios A., Jang J. (2003) Pricing of catastrophe reinsurance & derivatives using the cox process with shot noise intensity. Finance and Stochastics 7(1):73–95.
Eberlein E., Stahl G. (2004) Both sides of the fence: a statistical and regulatory view of electricity risk. Energy & Power Risk Management 8(6):34–38.
Filipović D. (2002) Separable term structures and the maximal degree problem. Mathematical Finance 12(4):341–349.
. Gaspar R. M., Schmidt, T. (2007) Shot-noise quadratic term structure models.Submitted.
Geman H., Roncoroni, A. (2006) Understanding the fine structure of electricity prices. Journal of Business 79(3):1225–1261.
. Hylleberg S. (ed) (1992) Modelling Seasonality. Oxford University Press.
Lucia J. J., Schwartz, E. S. (2002) Electricity prices and power derivatives: evidence from the nordic power exchange. Review of Derivatives Research 5:5–50.
McLachlan J. G., Krishnan, T. (1997) The EM algorithm and extensions, John Wiley & Sons, New York.
Protter P. (2004) Stochastic Integration and Differential Equations, 2nd edn. Springer Verlag, Berlin Heidelberg New York.
. Reiche E., Schmidt, T. (2007) A statistical analysis of models of electricity markets. Working paper.
Schmidt T., Stute W. (2007) General shot-noise processes and the minimal martingale measure. Statistics & Probability Letters 77:1332–1338.
Schmidt W. M. (1997) On a general class of one-factor models for the term structure of interest rates. Finance and Stochastics 1:3–24.
Teichmann J. (2005) A note on nonaffine solutions of term structure equations with applications to power exchanges. Mathematical Finance 15(1):191–201.
Vasiček O. (1977) An equilibrium characterization of the term structure. Journal of Financial Economics 5:177–188.
Weron R. (2005) Heavy tails and electricity prices. The Deutsche Bundesbank’s 2005 Annual Fall Conference (Eltville).
Wu C. F. J. (1983) On the convergence properties of the EM algorithm. The Annals of Statistics 11:95–103.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Schmidt, T. (2008). Modelling Energy Markets with Extreme Spikes. In: Sarychev, A., Shiryaev, A., Guerra, M., Grossinho, M.d.R. (eds) Mathematical Control Theory and Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69532-5_20
Download citation
DOI: https://doi.org/10.1007/978-3-540-69532-5_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69531-8
Online ISBN: 978-3-540-69532-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)