The forward dynamics in energy markets – infinite-dimensional modelling and simulation

Abstract

In this paper an infinite-dimensional approach to model energy forward markets is introduced. Similar to the Heath–Jarrow–Morton framework in interest-rate modelling, a first-order hyperbolic stochastic partial differential equation models the dynamics of the forward price curves. These equations are analysed, and in particular regularity and no-arbitrage conditions in the general situation of stochastic partial differential equations driven by an infinite-dimensional martingale process are studied. Both arithmetic and geometric forward price dynamics are studied, as well as accounting for the delivery period of electricity forward contracts. A stable and convergent numerical approximation in the form of a finite element method for hyperbolic stochastic partial differential equations is introduced and applied to some examples with relevance to energy markets.

Keywords::

• energy markets
• forward price
• random fields
• infinite-dimensional analysis
• stochastic partial differential equation

Acknowledgements

It is a pleasure to thank Claude J. Gittelson, Annika Lang, Santiago Moreno Bromberg, Jürgen Potthoff and Oleg Reichmann for all the fruitful discussions and helpful comments. We are grateful for the comments and critics of two anonymous referees.

Notes

^1. Email: [email protected]; http://folk.uio.no/fredb/

^2. This parameter is usually denoted in the NIG distribution, but that notation was not available to us.

Additional information

Funding

Fred Espen Benth acknowledges financial support from the Norwegian Research Council under the eVita project 205328 ‘Energy markets: modeling, optimization and simulation’ (Emmos).