Modelling Energy Spot Prices by Volatility Modulated Lévy-Driven Volterra Processes

38 Pages Posted: 24 Feb 2013

See all articles by Ole E. Barndorff-Nielsen

Ole E. Barndorff-Nielsen

University of Aarhus - Thiele Centre, Department of Mathematical Sciences

Fred Espen Benth

University of Oslo

Almut Veraart

Imperial College London; CREATES

Date Written: October 26, 2012

Abstract

This paper introduces the class of volatility modulated Lévy-driven Volterra (VMLV) processes and their important subclass of Lévy semistationary (LSS) processes as a new framework for modelling energy spot prices. The main modelling idea consists of four principles: First, deseasonalised spot prices can be modelled directly in stationarity. Second, stochastic volatility is regarded as a key factor for modelling energy spot prices. Third, the model allows for the possibility of jumps and extreme spikes and, lastly, it features great flexibility in terms of modelling the autocorrelation structure and the Samuelson effect. We provide a detailed analysis of the probabilistic properties of VMLV processes and show how they can capture many stylised facts of energy markets. Further, we derive forward prices based on our new spot price models and discuss option pricing. An empirical example based on electricity spot prices from the European Energy Exchange confirms the practical relevance of our new modelling framework.

Keywords: energy markets, forward price, generalised hyperbolic distribution, Lévy semistationary process, volatility modulated Lévy-driven Volterra process, stochastic integration, stochastic volatility, Samuelson effect, spot price

JEL Classification: C0, C1, C5, G1

Suggested Citation

Barndorff-Nielsen, Ole E. and Benth, Fred Espen and Veraart, Almut, Modelling Energy Spot Prices by Volatility Modulated Lévy-Driven Volterra Processes (October 26, 2012). Available at SSRN: https://ssrn.com/abstract=2223610 or http://dx.doi.org/10.2139/ssrn.2223610

Ole E. Barndorff-Nielsen

University of Aarhus - Thiele Centre, Department of Mathematical Sciences ( email )

Ny Munkegade
Aarhus, DK 8000
Denmark

Fred Espen Benth

University of Oslo ( email )

Center of Mathematics for Applications
Oslo, N-0317
Norway

Almut Veraart (Contact Author)

Imperial College London ( email )

Department of Mathematics
180 Queen's Gate
London, SW7 2AZ

CREATES ( email )

Aarhus University
DK-8000 Aarhus C
Denmark

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