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A general HJM framework for multiple yield curve modelling

Authors :: Alessandro Gnoatto
Christa Cuchiero
Claudio Fontana
Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
Laboratoire de Mathématiques et Modélisation d'Evry (LaMME)
Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS)
Fontana, Claudio
Laboratoire de Mathématiques et Modélisation d'Evry
Institut National de la Recherche Agronomique (INRA)-Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Centre National de la Recherche Scientifique (CNRS)
Benassù, Serena
Source :: Finance and Stochastics, Finance and Stochastics, 2016, 20 (2), pp.267-320, Finance and Stochastics, Springer Verlag (Germany), 2016, 20 (2), pp.267-320
Publication Year :: 2016
Publisher :: Springer Verlag, 2016.
Abstract: We propose a general framework for modeling 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 specified as an affine process, we obtain a flexible Markovian structure. Finally, we show that the proposed framework allows to unify and extend several recent approaches to multiple yield curve modeling.<br />Comment: (40 pages, 4 figures)