WIAS Preprint No. 1951, (2014)

Affine LIBOR models with multiple curves: Theory, examples and calibration


  • Grbac, Zorana
  • Papapantoleon, Antonis
  • Schoenmakers, John G. M.
    ORCID: 0000-0002-4389-8266
  • Skovmand, David

2010 Mathematics Subject Classification

  • 91G30 91G20 60G44


  • Multiple curve models, LIBOR, OIS, basis spread, affine LIBOR models, caps, swaptions, basis swaptions, calibration


We introduce a multiple curve LIBOR framework that combines tractable dynamics and semi-analytic pricing formulas with positive interest rates and basis spreads. The dynamics of OIS and LIBOR rates are specified following the methodology of the affine LIBOR models and are driven by the wide and flexible class of affine processes. The affine property is preserved under forward measures, which allows to derive Fourier pricing formulas for caps, swaptions and basis swaptions. A model specification with dependent LIBOR rates is developed, that allows for an efficient and accurate calibration to a system of caplet prices.

Appeared in

  • SIAM Journal on Financial Mathematics, 6 (2015), pp. 984--1025

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