The Affine LIBOR Models

32 Pages Posted: 6 Aug 2013

See all articles by Martin Keller‐Ressel

Martin Keller‐Ressel

Technische Universität Berlin (TU Berlin)

Antonis Papapantoleon

Technische Universität Berlin (TU Berlin)

Josef Teichmann

ETH Zurich; Swiss Finance Institute

Date Written: October 2013

Abstract

We provide a general and flexible approach to LIBOR modeling based on the class of affine factor processes. Our approach respects the basic economic requirement that LIBOR rates are nonnegative, and the basic requirement from mathematical finance that LIBOR rates are analytically tractable martingales with respect to their own forward measure. Additionally, and most importantly, our approach also leads to analytically tractable expressions of multi‐LIBOR payoffs. This approach unifies therefore the advantages of well‐known forward price models with those of classical LIBOR rate models. Several examples are added and prototypical volatility smiles are shown. We believe that the CIR process‐based LIBOR model might be of particular interest for applications, since closed form valuation formulas for caps and swaptions are derived.

Keywords: LIBOR rate models, forward price models, affine processes, analytically tractable models

Suggested Citation

Keller‐Ressel, Martin and Papapantoleon, Antonis and Teichmann, Josef, The Affine LIBOR Models (October 2013). Mathematical Finance, Vol. 23, Issue 4, pp. 627-658, 2013, Available at SSRN: https://ssrn.com/abstract=2306443 or http://dx.doi.org/10.1111/j.1467-9965.2012.00531.x

Martin Keller‐Ressel (Contact Author)

Technische Universität Berlin (TU Berlin)

Straße des 17
Juni 135
Berlin, 10623
Germany

Antonis Papapantoleon

Technische Universität Berlin (TU Berlin)

Straße des 17
Juni 135
Berlin, 10623
Germany

Josef Teichmann

ETH Zurich ( email )

Rämistrasse 101
ZUE F7
Zürich, 8092
Switzerland

HOME PAGE: http://www.math.ethz.ch/~jteichma

Swiss Finance Institute ( email )

c/o University of Geneva
40 Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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