Multivariate continuous-time modeling of wind indexes and hedging of wind risk

Abstract

With the introduction of the exchange-traded German wind power futures, opportunities for German wind power producers to hedge their volumetric risk are present. We propose two continuous-time multivariate models for wind power utilization at different wind sites, and discuss the properties and estimation procedures for the models. Applying the models to wind index data for wind sites in Germany and the underlying wind index of exchange-traded wind power futures contracts, the estimation results of both models suggest that they capture key statistical features of the data. We show how these models can be used to find optimal hedging strategies using exchange-traded wind power futures for the owner of a portfolio of so-called tailor-made wind power futures. Both in-sample and out-of-sample hedging scenarios are considered, and, in both cases, significant variance reductions are achieved. Additionally, the risk premium of the German wind power futures is analysed, leading to an indication of the risk premium of tailor-made wind power futures.

Keywords:

• Multivariate Ornstein-Uhlenbeck process
• Wind power futures
• Hedging
• risk premium

JEL Classification:

• C3
• G1
• Q4

Acknowledgment

We are grateful for the careful reading and comments from two referees.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The locations are approximate due to confidentially issues.

2 Since the same quantities for the site wind indexes are not relevant in the remaining part of the paper, we have chosen to omit them.

3 Despite the fact that $RP(t_0,S,T)$ still depends on $t_0$ thorugh ${\overline{P}}_n(t_0,S,T)$, the assumption of stationarity is to some degree confirmed by the constant pattern of ${\overline{P}}_n(t_0,S,T)$ observed in figures 11 and 12(a).

Additional information

Funding

Troels Sønderby Christensen is supported by the Innovation Fund Denmark under Grant 5189-00117B. Victor Rohde is supported by the Danish Council for Independent Research under Grant DFF-4002-00003.