The Risk Premium and the Esscher Transform in Power Markets
Fred Espen Benth
University of Oslo
Politecnico di Milano- Dipartimento di Matematica
November 17, 2009
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.
Number of Pages in PDF File: 25
Keywords: Power Market, Derivatives Pricing, Independent Increments Processes, Esscher Transform, Risk Premium
JEL Classification: C00working papers series
Date posted: November 17, 2009 ; Last revised: November 20, 2009
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