Forward Curve Modelling by Ambit Fields

  • Ole E. Barndorff-Nielsen
  • Fred Espen Benth
  • Almut E. D. Veraart
Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 88)


The final chapter of the book is devoted to forward pricing. We apply ambit fields in order to extend the so-called Heath-Jarrow-Morton approach to forward price modelling. Indeed, we state general ambit field models with drift, where the spatial dimension is the delivery time of the forward contract. The ambit sets will have a simple form in our setting, and we derive explicit no-arbitrage conditions for the drift in both arithmetic and geometric (i.e., exponentiated) ambit specifications. Basic properties such as the temporal and spatial correlation are studied, as well as the implied spot price dynamics. The chapter ends with a detailed study of spread option pricing, where we show that in the Gaussian case we recover a general version of the classical Margrabe formula, while in the Lévy case we can provide a Fourier-based expression for the price.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Ole E. Barndorff-Nielsen
    • 1
  • Fred Espen Benth
    • 2
  • Almut E. D. Veraart
    • 3
  1. 1.Department of MathematicsUniversity of AarhusAarhusDenmark
  2. 2.Department of MathematicsUniversity of OsloOsloNorway
  3. 3.Department of MathematicsImperial College LondonLondonUK

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