Abstract
In this paper we derive power futures prices from a two-factor spot model being a generalization of the classical Schwartz–Smith commodity dynamics. We include non-Gaussian effects by introducing Lévy processes as the stochastic drivers, and estimate the model to data observed at the European Electricity Exchange in Germany. The spot and futures price models are fitted jointly, including the market price of risk parameterized from an Esscher transform. We apply this model to price call and put options on power futures. It is argued theoretically that the pricing measure for options may be different to the pricing measure of futures from spot in power markets due to the non-storability of the electricity spot. Empirical evidence pointing to this fact is found from option prices observed at the European Electricity Exchange.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Some markets have both forwards and futures traded. We shall not make a distinction between these two asset classes here, but stick to the notion of futures.
References
Barndorff-Nielsen OE (1998) Processes of normal inverse Gaussian type. Finance Stoch 2(1):41–68
Barndorff-Nielsen OE, Benth FE, Veraat AED (2013) Modelling energy spot prices by volatility modulated Lévy-driven Volterra processes. Bernoulli 19(3):803–845
Benth FE, Šaltytė-Benth J, Koekebakker S (2008) Stochastic modelling of electricity and related markets. World Scientific, Singapore
Benth FE, Klüppelberg C, Müller G, Vos L (2011) Futures pricing in electricity markets based on stable CARMA spot models (Preprint)
Benth FE, Šaltytė-Benth J (2004) The normal inverse Gaussian distribution and spot price modelling in energy markets. Int J Theor Appl Finance 7(2):177–192
Benth FE, Sgarra C (2012) The risk premium and the Esscher transform in power markets. Stoch Anal Appl 30:20–43
Black F (1976) The pricing of commodity contracts. J Financial Econ 3:169–179
Börger R, Cartea A, Kiesel R, Schindlmayer G (2009) A multivariate commodity analysis and applications to risk management. J Futures Mark 29(3):197–217
Cont R, Tankov P (2004) Financial modelling with jump processes. Chapman & Hall/CRC, Boca Raton
Duffie D (1992) Dynamic asset pricing theory. Princeton University Press, Princeton
Lucia JJ, Schwartz ES (2002) Electricity prices and power derivatives: evidence from the Nordic power exchange. Rev Deriv Res 5(1):5–50
Rouge R, El Karoui N (2000) Pricing via utility maximization and entropy. Math Finance 10:259–276
Samuelson P (1965) Proof that properly anticipated prices fluctuate randomly. Ind Manag Rev 6:41–44
Shiryaev AN (1999) Essentials of stochastic finance. World Scientific, Singapore
Schwartz E, Smith JE (2000) Short-term variations and long-term dynamics in commodity prices. Manag Sci 46(7):893–911
Acknowledgments
Fred Espen Benth acknowledges the financial support from the project “Energy markets: modelling, optimization and simulation” (EMMOS), funded by the Norwegian Research Council under grant evita 205328/v30.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Benth, F.E., Schmeck, M.D. (2014). Pricing Futures and Options in Electricity Markets. In: Ramos, S., Veiga, H. (eds) The Interrelationship Between Financial and Energy Markets. Lecture Notes in Energy, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55382-0_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-55382-0_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-55381-3
Online ISBN: 978-3-642-55382-0
eBook Packages: EnergyEnergy (R0)