Affine LIBOR models with multiple curves: theory, examples and calibration.

Zorana Grbac (1) , Antonis Papapantoleon (2) , John Schoenmakers , David Skovmand

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 TU - Technical University of Berlin / Technische Universität Berlin

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.

Domaines: Probabilités [math.PR]

Zorana Grbac, Antonis Papapantoleon, John Schoenmakers, David Skovmand. Affine LIBOR models with multiple curves: theory, examples and calibration.. SIAM Journal on Financial Mathematics, 2015, 6, pp.984-1025. ⟨hal-01485693⟩