Affine Multiple Yield Curve Models

44 Pages Posted: 13 Mar 2019

See all articles by Christa Cuchiero

Christa Cuchiero

University of Vienna - Faculty of Science and Mathematics

Claudio Fontana

Université Paris VII Denis Diderot

Alessandro Gnoatto

University of Verona - Department of Economics

Date Written: April 2019

Abstract

We provide a general and tractable framework under which all multiple yield curve modeling approaches based on affine processes, be it short rate, Libor market, or Heath–Jarrow–Morton modeling, can be consolidated. We model a numéraire process and multiplicative spreads between Libor rates and simply compounded overnight indexed swap rates as functions of an underlying affine process. Besides allowing for ordered spreads and an exact fit to the initially observed term structures, this general framework leads to tractable valuation formulas for caplets and swaptions and embeds all existing multicurve affine models. The proposed approach also gives rise to new developments, such as a short rate type model driven by a Wishart process, for which we derive a closed‐form pricing formula for caplets. The empirical performance of two specifications of our framework is illustrated by calibration to market data.

Keywords: affine processes, forward rate agreement, Libor rate, multiple yield curves, multiplicative spread

JEL Classification: E43, G12

Suggested Citation

Cuchiero, Christa and Fontana, Claudio and Gnoatto, Alessandro, Affine Multiple Yield Curve Models (April 2019). Mathematical Finance, Vol. 29, Issue 2, pp. 568-611, 2019. Available at SSRN: https://ssrn.com/abstract=3352079 or http://dx.doi.org/10.1111/mafi.12183

Christa Cuchiero (Contact Author)

University of Vienna - Faculty of Science and Mathematics ( email )

Vienna
Austria

Claudio Fontana

Université Paris VII Denis Diderot ( email )

2, place Jussieu
Paris, 75005
France

Alessandro Gnoatto

University of Verona - Department of Economics ( email )

Via dell'Artigliere, 8
37129 Verona
Italy

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