A General HJM Framework for Multiple Yield Curve Modeling

40 Pages Posted: 17 Jun 2014 Last revised: 8 May 2015

See all articles by Christa Cuchiero

Christa Cuchiero

Independent

Claudio Fontana

Université Paris VII Denis Diderot

Alessandro Gnoatto

University of Verona - Department of Economics

Date Written: June 17, 2014

Abstract

We propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between (normalized) FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to construct models such that multiplicative spreads are greater than one and ordered with respect to the tenor’s length. When the driving semimartingale is specified as an affine process, we obtain a flexible Markovian structure which allows for tractable valuation formulas for most interest rate derivatives. Finally, we show that the proposed framework allows to unify and extend several recent approaches to multiple yield curve modeling.

Keywords: Multi-Curve Framework, HJM Framework, Interest Rate Derivatives, Basis Swaps, Discounting Curve, Affine Processes

JEL Classification: G13

Suggested Citation

Cuchiero, Christa and Fontana, Claudio and Gnoatto, Alessandro, A General HJM Framework for Multiple Yield Curve Modeling (June 17, 2014). Available at SSRN: https://ssrn.com/abstract=2454003 or http://dx.doi.org/10.2139/ssrn.2454003

Christa Cuchiero

Independent ( email )

No Address Available

Claudio Fontana

Université Paris VII Denis Diderot ( email )

avenue de France
Paris, 75205
France

Alessandro Gnoatto (Contact Author)

University of Verona - Department of Economics ( email )

Via dell'Artigliere, 8
37129 Verona
Italy

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