Affine LIBOR Models with Multiple Curves: Theory, Examples and Calibration

Zorana Grbac, Antonis Papapantoleon, John Schoenmakers, David Skovmand

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Abstract

We introduce a multiple curve framework that combines tractable dynamics and semianalytic pricing formulas with positive interest rates and basis spreads. Negative rates and positive spreads can also be accommodated in this framework. The dynamics of overnight indexed swap 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 us 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.
Original languageEnglish
JournalSIAM Journal on Financial Mathematics
Volume6
Issue number1
Pages (from-to)984–1025
Number of pages42
ISSN1945-497X
DOIs
Publication statusPublished - 2015

Keywords

  • Multiple curve models
  • LIBOR
  • OIS
  • Basis spread
  • Affine LIBOR models
  • Caps
  • Swaptions
  • Basis swaptions
  • Calibration

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