Finance and Stochastics

, Volume 20, Issue 2, pp 267–320 | Cite as

A general HJM framework for multiple yield curve modelling

  • Christa Cuchiero
  • Claudio Fontana
  • Alessandro Gnoatto


We propose a general framework for modelling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to construct models such that multiplicative spreads are greater than one and ordered with respect to the tenor’s length. When the driving semimartingale is an affine process, we obtain a flexible and tractable Markovian structure. Finally, we show that the proposed framework allows unifying and extending several recent approaches to multiple yield curve modelling.


Multiple yield curves HJM model Semimartingale Forward rate agreement Libor rate Affine processes Multiplicative spreads 

Mathematics Subject Classification (2010)

91G30 91B24 91B70 

JEL Classification

E43 G12 



The research of the second author was partly supported by a Marie Curie Intra European Fellowship within the 7th European Community Framework Programme under grant agreement PIEF-GA-2012-332345.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Christa Cuchiero
    • 1
  • Claudio Fontana
    • 2
  • Alessandro Gnoatto
    • 3
  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria
  2. 2.Laboratoire de Probabilités et Modèles AléatoiresUniversité Paris DiderotParisFrance
  3. 3.Department of MathematicsLudwig-Maximilians-Universität MünchenMunichGermany

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