Pricing forward contracts in power markets by the certainty equivalence principle: Explaining the sign of the market risk premium

Abstract

In this paper we provide a framework that explains how the market risk premium, defined as the difference between forward prices and spot forecasts, depends on the risk preferences of market players and the interaction between buyers and sellers. In commodities markets this premium is an important indicator of the behavior of buyers and sellers and their views on the market spanning between short-term and long-term horizons. We show that under certain assumptions it is possible to derive explicit solutions that link levels of risk aversion and market power with market prices of risk and the market risk premium. We apply our model to the German electricity market and show that the market risk premium exhibits a term structure which can be explained by the combination of two factors. Firstly, the levels of risk aversion of buyers and sellers, and secondly, how the market power of producers, relative to that of buyers, affects forward prices with different delivery periods.

A non-parametric structural hybrid modeling approach for electricity prices

“…Then to project the electricity forward curve for maturities beyond what is currently available in the market and to leverage long fuel forward curves, a common practitioners' approach is to extrapolate the computed market risk premiums m T1 , · · · , m TN e , see, e.g., Benth et al (2008). Being able to discover the pattern of risk premia for different maturities allows us to better estimate the forward curve beyond liquidly tradable maturities, a procedure which can be very valuable for accurately valuing or hedging very long maturity contracts or assets such as physical power plants.…”

Pricing electricity derivatives within a Markov regime-switching model: a risk premium approach

“…The risk premium defined in such a way is called in the literature (see e.g. Lucia and Torro 2008;Benth et al 2008b;Karakatsani and Bunn 2005) the ex-ante risk premium. On the other hand, the risk premium is also often defined using the ex-post (historical) approach and calculated as the difference between the forward price and the realized spot price at the time of the forward contract delivery (see e.g.…”

“…In the following we will assume that the measure Q λ is the probability measure under which the drift of the base regime process is parametrized by a function λ(T ) chosen so that E λ (P T |F 0 ) yields the market forward price f T 0 . The function λ(T ) is called the market price of risk, which can be seen as a drift adjustment in the dynamics of an asset to reflect how investors are compensated for bearing risk when holding the asset (Benth et al 2008b). …”

“…It should be noted that there are also different attempts to explain signs of the risk premium in the literature. Benth and MeyerBrandis (2009) use an information-based approach, while Benth et al (2008b) give an interpretation of the risk premium on the basis of the certainty equivalent principle and jumps in the spot price dynamics.…”

“…Lucia and Schwartz 2002;Miltersen 2003;Benth et al 2003;Bierbrauer and Menn 2007) and then modeling a link between the forward and spot markets. Usually, a convenience yield or risk premium notion is used (Benth et al 2008a;Geman 2005;Weron 2006;Benth and Sgarra 2012;Haerdle and LopezCabrera 2012;Longstaff and Wang 2004;Lucia and Torro 2008;Benth et al 2008b;Benth and Meyer-Brandis 2009). Using such an approach allows to price derivatives written both on the spot and the forward price.…”