Affine multiple yield curve models

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 simpl...

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Bibliographic Details
Published in:Mathematical finance 2019-04, Vol.29 (2), p.568-611
Main Authors: Cuchiero, Christa, Fontana, Claudio, Gnoatto, Alessandro
Format: Article
Language:English
Subjects:
affine processes
E43
forward rate agreement
G12
Libor rate
Markets
Mathematics
Modelling
multiple yield curves
multiplicative spread
Probability
Valuation
Yield curve
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Summary: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.
ISSN:0960-1627
1467-9965
DOI:10.1111/mafi.12183