Affine multiple yield curve models. (17th August 2018)

• Record Type: Journal Article
• Authors: Cuchiero, Christa; Fontana, Claudio; Gnoatto, Alessandro
• Is Part Of: Mathematical finance. Volume 29:Number 2(2019)
• Page Start: 568
• Page End: 611
• Publication Date: 2018-08-17
• Subjects: affine processes -- forward rate agreement -- Libor rate -- multiple yield curves -- multiplicative spread -- E43 -- G12; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12183
• Languages: English
• ISSNs: 0960-1627

Abstract

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.