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A general HJM framework for multiple yield curve modelling

Author

Listed:
  • Christa Cuchiero

    (University of Vienna)

  • Claudio Fontana

    (Université Paris Diderot)

  • Alessandro Gnoatto

    (Ludwig-Maximilians-Universität München)

Abstract

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.

Suggested Citation

  • Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2016. "A general HJM framework for multiple yield curve modelling," Finance and Stochastics, Springer, vol. 20(2), pages 267-320, April.
    • Handle: RePEc:spr:finsto:v:20:y:2016:i:2:d:10.1007_s00780-016-0291-5
    DOI: 10.1007/s00780-016-0291-5
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    More about this item

    Keywords

    Multiple yield curves; HJM model; Semimartingale; Forward rate agreement; Libor rate; Affine processes; Multiplicative spreads;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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