Finance and Stochastics

, Volume 22, Issue 2, pp 327–366 | Cite as

Approximation of forward curve models in commodity markets with arbitrage-free finite-dimensional models

  • Fred Espen Benth
  • Paul Krühner


In this paper, we show how to approximate Heath–Jarrow–Morton dynamics for the forward prices in commodity markets with arbitrage-free models which have a finite-dimensional state space. Moreover, we recover a closed-form representation of the forward price dynamics in the approximation models and derive the rate of convergence to the true dynamics uniformly over an interval of time to maturity under certain additional smoothness conditions. In the Markovian case, we can strengthen the convergence to be uniform over time as well. Our results are based on the construction of a convenient Riesz basis on the state space of the term structure dynamics.


Energy markets Heath–Jarrow–Morton modelling Nonharmonic Fourier analysis Arbitrage-free approximations 

Mathematics Subject Classification (2010)

60H15 91B24 91G20 

JEL Classification

C02 C63 G13 



An anonymous referee and the Associate Editor are thanked for their constructive criticisms.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OsloOsloNorway
  2. 2.Institute for Financial and Actuarial MathematicsThe University of LiverpoolLiverpoolUK

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