A mixed C-vine copula model for hedging price and volumetric risk in wind power trading

Abstract

When energy trading companies enter into long-term agreements with wind power producers, where a fixed price is paid for the fluctuating production, they are facing a joint price and volumetric risk. Since the pay-off of such agreements is non-linear, a hedging portfolio would ideally consist of not only forwards, but also a basket of e.g. call and put options. Illiquidity and an almost non-existent market for options challenge however the optimal hedging of joint price and volumetric risk in many market places. Here, we consider the case of the Danish power market, and exploit its strong positive correlation with the much more liquid German market to construct a proxy hedge. We propose a three-dimensional mixed vine copula to model the evolution of the Danish and German spot electricity prices and the Danish wind power production. We construct a realistic hedging portfolio by identifying various instruments available in the market, such as real options in the form of the right to transfer electricity across the border and the right to convert electricity to heat. Using the proposed vine copula to determine optimal hedging decisions, we show that significant benefits are to be drawn by extending the hedging portfolio with the proposed instruments.

Keywords:

• Spot electricity prices
• Wind power production
• Mathematical finance
• Copula vines
• Energy derivatives
• Hedging

JEL Classification:

• C22
• C51
• G13

Acknowledgements

The authors would like to thank Esben Høg, Thomas Aalund Fredholm, Christian Sønderup and Jakob Vive Munk for providing valuable ideas and comments. The authors also thank two anonymous referees for providing constructive criticism and suggestions that enhanced the quality of this paper.

Notes

No potential conflict of interest was reported by the authors.

1 For the wind data, the skew t distribution converges towards the skew normal distribution since we obtain an estimate for the degrees of freedom above 300. Therefore, we replace the skew t with the skew normal distribution in this case.

2 We note that our product description of wind index futures is based on Nasdaq (2015) and EEX (2014).

3 Due to lower demand for heat during summer, CHP plants have a lower capacity. Moreover, high wind / low price scenarios are less likely.

4 Sampling from a copula vine is based on a recursive procedure and using the inverse of the h-functions, cf. equation 6(6) . We refer to Aas et al. (2009) for a detailed description of the procedure.

Additional information

Funding

Anca Pircalabu acknowledges support from Innovation Fund Denmark.