Multivariate Continuous-Time Modeling of Wind Indexes and Hedging of Wind Risk

34 Pages Posted: 31 Dec 2019

See all articles by Fred Espen Benth

Fred Espen Benth

University of Oslo

Troels Sønderby Christensen

Aalborg University - Department of Mathematical Sciences; Centrica Energy Trading

Victor Rohde

Aarhus University

Date Written: December 9, 2019


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 the wind power utilization at different wind sites, and discuss the properties and estimation procedures for the models. Employing 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 argue 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

Suggested Citation

Benth, Fred Espen and Christensen, Troels Sønderby and Rohde, Victor, Multivariate Continuous-Time Modeling of Wind Indexes and Hedging of Wind Risk (December 9, 2019). Available at SSRN: or

Fred Espen Benth

University of Oslo ( email )

Center of Mathematics for Applications
Oslo, N-0317

Troels Sønderby Christensen (Contact Author)

Aalborg University - Department of Mathematical Sciences ( email )

Fredrik Bajers Vej 7E

Centrica Energy Trading ( email )

Skelagervej 1
Aalborg, 9000

Victor Rohde

Aarhus University ( email )

Nordre Ringgade 1
DK-8000 Aarhus C, 8000

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