×

zbMATH — the first resource for mathematics

A non-Gaussian Ornstein-Uhlenbeck process for electricity spot price modeling and derivatives pricing. (English) Zbl 1160.91337
Summary: A mean-reverting model is proposed for the spot price dynamics of electricity which includes seasonality of the prices and spikes. The dynamics is a sum of non-Gaussian Ornstein-Uhlenbeck processes with jump processes giving the normal variations and spike behaviour of the prices. The amplitude and frequency of jumps may be seasonally dependent. The proposed dynamics ensures that spot prices are positive, and that the dynamics is simple enough to allow for analytical pricing of electricity forward and futures contracts. Electricity forward and futures contracts have the distinctive feature of delivery over a period rather than at a fixed point in time, which leads to quite complicated expressions when using the more traditional multiplicative models for spot price dynamics. In a simulation example it is demonstrated that the model seems to be sufficiently flexible to capture the observed dynamics of electricity spot prices. The pricing of European call and put options written on electricity forward contracts is also discussed.

MSC:
91G20 Derivative securities (option pricing, hedging, etc.)
60J60 Diffusion processes
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1109/78.978374 · doi:10.1109/78.978374
[2] DOI: 10.1111/1467-9868.00282 · Zbl 0983.60028 · doi:10.1111/1467-9868.00282
[3] Benth, F. E. and Koekebakker, S. 2005. Stochastic modeling of forward and futures contracts in electricity markets. E-print, No. 24, Dept. Mathematics, University of Oslo
[4] Bjerksund, P. 2000. Valuation and risk management in the Nordic electricity market. Working paper, Institute of finance and management sciences, Norwegian School of Economics and Business Administration
[5] Carr M., Journal Computational Finance 2 pp 61– (1999)
[6] Geman H., Journal Business 79 (2006)
[7] DOI: 10.2307/1912775 · Zbl 0502.62098 · doi:10.2307/1912775
[8] DOI: 10.1007/s001860000048 · Zbl 1054.91038 · doi:10.1007/s001860000048
[9] DOI: 10.1023/A:1013846631785 · Zbl 1064.91508 · doi:10.1023/A:1013846631785
[10] Marcus M. B., Mem American Mathematical Society 368 (1987)
[11] Rosinski J., Stable Processes and Related Topics pp 27– (1991)
[12] DOI: 10.1111/1368-423X.00042 · Zbl 0998.62071 · doi:10.1111/1368-423X.00042
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.