Paul Krühner: On infinite dimensional modelling in electricity finance

Abstract: The most traded securities in electricity markets are future contracts for various delivery periods. They are usually modelled by a curve-valued process where the value of the curve at some time denotes the value of the future contract with delivery point. This is very similar to bond markets where the Heath-Jarrow-Morton framework is well established and used for modelling the whole family of bonds by modelling the term structure curve. Unlike bond markets, future markets for electricity cannot be explained by a small number of stochastic factors. Consequently, it seems reasonable to model the whole future curve with infinite dimensional processes. However, a reasonable assumption is that only finitely many components can be observed or, put otherwise, a finite dimensional projection can be observed. Utilising smooth Hilbert-spaces as in [1] we show that finite dimensional projections of infinite dimensional Lévy driven processes can often be realised as finite dimensional Lévy driven processes and analyse some implications for modelling in electricity markets.

[1] D. Filipović, Consistency problems for heath-jarrow-morton interest rate models, Lecture Notes in Mathematics, vol. 1760, Springer, Berlin, 2001.