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 Citationer (Scopus)

85 Downloads (Pure)

Abstract

We introduce a multiple curve framework that combines tractable dynamics and semi-analytic pricing formulas with positive interest rates and basis spreads. Negatives rates and positive spreads can also be accommodated in this framework. 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 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.

Originalsprog	Engelsk
Tidsskrift	SIAM Journal on Financial Mathematics
Vol/bind	6
Udgave nummer	1
Sider (fra-til)	984–1025
Antal sider	42
ISSN	1945-497X
DOI	https://doi.org/10.1137/15M1011731
Status	Udgivet - 2015
Udgivet eksternt	Ja

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q-fin.MF
math.PR
q-fin.PR
91G30, 91G20, 60G44

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10.1137/15M1011731

1405.2450v4

Citationsformater

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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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author = "Zorana Grbac and Antonis Papapantoleon and John Schoenmakers and David Skovmand",

note = "42 pages, 11 figures. Updated version, added section on negative rates and positive spreads",

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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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DO - 10.1137/15M1011731

M3 - Journal article

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

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