The Risk Premium and the Esscher Transform in Power Markets

25 Pages Posted: 17 Nov 2009 Last revised: 20 Nov 2009

See all articles by Fred Espen Benth

Fred Espen Benth

University of Oslo

Carlo Sgarra

Politecnico di Milano- Dipartimento di Matematica

Date Written: November 17, 2009

Abstract

In power markets one frequently encounters a risk premium being positive in the short end of the forward curve, and negative in the long end. Economically it has been argued that the positive premium is reflecting retailers aversion for spike risk, wheras in the long end of the forward curve the hedging pressure kicks in as in other commodity markets. Mathematically, forward prices are expressed as risk-neutral expectations of the spot at delivery. We apply the Esscher transform on power spot models based on mean-reverting processes driven by independent increment (time-inhomogeneous Lévy) processes. It is shown that the Esscher transform is yielding a change of mean-reversion level. Moreover, we show that an Esscher transform together with jumps occuring seasonally may explain the occurence of a positive risk premium in the short end. This is demonstrated both mathematically and by a numerical example for a two-factor spot model being relevant for electricity markets. Our results indicate that the seasonally occuring spikes may explain why the market in periods experience short term risk premia being positive.

Keywords: Power Market, Derivatives Pricing, Independent Increments Processes, Esscher Transform, Risk Premium

JEL Classification: C00

Suggested Citation

Benth, Fred Espen and Sgarra, Carlo, The Risk Premium and the Esscher Transform in Power Markets (November 17, 2009). Available at SSRN: https://ssrn.com/abstract=1507627 or http://dx.doi.org/10.2139/ssrn.1507627

Fred Espen Benth

University of Oslo ( email )

Center of Mathematics for Applications
Oslo, N-0317
Norway

Carlo Sgarra (Contact Author)

Politecnico di Milano- Dipartimento di Matematica ( email )

Piazza Leonardo da Vinci
Milan, Milano 20100
Italy

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