Dynamic copula models for the spark spread

Abstract

We propose a non-symmetric copula to model the evolution of electricity and gas prices by a bivariate non-Gaussian autoregressive process. We identify the marginal dynamics as driven by normal inverse Gaussian processes, estimating them from a series of observed UK electricity and gas spot data. We estimate the copula by modeling the difference between the empirical copula and the independent copula. We then simulate the joint process and price options written on the spark spread. We find that option prices are significantly influenced by the copula and the marginal distributions, along with the seasonality of the underlying prices.

Keywords:

• Mathematical finance
• Copulas
• Derivative pricing models
• Asymmetry
• Empirical time series analysis
• Energy derivatives
• Levy process
• Numerical simulation

Acknowledgements

The authors wish to thank Jūratė Šaltytė-Benth for providing the estimates, Jan Kallsen for valuable discussions, and Heren Energy, Ltd., for the provision of the data used in this study. Two anonymous referees are thanked for their constructive criticism which led to a significant improvement of the presentation of this paper.

Notes

†We take these views to keep the origin on the left in each case.

†From the observed innovations, we estimated the mean and standard deviation for the electricity data to be −0.0025 and 0.17, whereas the corresponding estimates for gas were 0.0014 and 0.10. The correlation coefficient is 0.27.