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

Zorana Grbac; Antonis Papapantoleon; John Schoenmakers; David Skovmand

doi:10.1137/15M1011731

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

Zorana Grbac, Antonis Papapantoleon, John Schoenmakers, David Skovmand

18 Citations (Scopus)

85 Downloads (Pure)

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 language	English
Journal	SIAM Journal on Financial Mathematics
Volume	6
Issue number	1
Pages (from-to)	984–1025
Number of pages	42
ISSN	1945-497X
DOIs	https://doi.org/10.1137/15M1011731
Publication status	Published - 2015
Externally published	Yes

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10.1137/15M1011731

1405.2450v4

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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.",

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AU - Grbac, Zorana

AU - Papapantoleon, Antonis

AU - Schoenmakers, John

AU - Skovmand, David

N1 - 42 pages, 11 figures. Updated version, added section on negative rates and positive spreads

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

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JO - SIAM Journal on Financial Mathematics

JF - SIAM Journal on Financial Mathematics

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

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