Derivatives pricing in energy markets: an infinite dimensional approach

Based on forward curves modelled as Hilbert-space valued processes, we analyse the pricing of various options relevant in energy markets. In particular, we connect empirical evidence about energy forward prices known from the literature to propose stochastic models. Forward prices can be represented as linear functions on a Hilbert space, and options can thus be viewed as derivatives on the whole curve. The value of these options are computed under various specifications, in addition to their deltas. In a second part, cross-commodity models are investigated, leading to a study of square integrable random variables with values in a "two-dimensional" Hilbert space. We analyse the covariance operator and representations of such variables, as well as presenting applications to pricing of spread and energy quanto options

Market coupling and the organization of counter-trading: separating energy and transmission again?

The horizontal integration of the energy market and the organization of transmission services remain two open issues in the restructured European electricity sector. The coupling of the French, Belgian and Dutch electricity markets (the trilateral market) in November 2006 was a real success that the inclusion of Germany to the trilateral market should soon prolong. But the extension of market coupling whether in Central Western Europe or in other European regions encounters several difficulties and the future remains far from clear. The highly meshed grid of continental Europe complicates things and it is now sometimes recognized that the penetration of wind will further exacerbate these difficulties. The nodal system could go a long way towards solving these problems, but its implementation is not yet foreseen in the EU. This paper analyzes versions of market coupling that differ by the organization of counter- trading. While underplayed in current discussions, counter-trading will become a key element of market coupling as its geographic coverage expands and wind penetration develops. We consider a stylized six node example found in the literature and simulate market coupling for different assumptions of zonal decomposition and coordination of TSOs. We show that these assumptions matter: market coupling can be quite vulnerable to the particular situation on hand; counter-trading can work well or completely fail depending on the case and it is not clear beforehand what will prevail. Our analysis relies on standard economic notions such as social welfare, Nash and Generalized Nash equilibrium. But the use of these notions is probably novel. We also simplify matters by assuming away strategic behaviour. The nodal organization is the reference first best scenario: different zonal decompositions and degrees of coordinations are then studied with respect to this first best solution.D52, D58, Q40