Multiple Curve Lévy Forward Price Model Allowing for Negative Interest Rates

26 Pages Posted: 23 May 2018

See all articles by Ernst Eberlein

Ernst Eberlein

University of Freiburg

Christoph Gerhart

University of Freiburg - Institut für Mathematische Stochastik

Zorana Grbac

Université Paris VII Denis Diderot

Multiple version iconThere are 2 versions of this paper

Date Written: May 9, 2018

Abstract

In this paper we develop a framework for discretely compounding interest rates which is based on the forward price process approach. This approach has a number of advantages, in particular in the current market environment. Compared to the classical as well as the Lévy Libor market model, it allows in a natural way for negative interest rates and has superb calibration properties even in the presence of extremely low rates. Moreover, the measure changes along the tenor structure are simplified significantly. These properties make it an excellent base for a post-crisis multiple curve setup. Two variants for multiple curve constructions are discussed. Time-inhomogeneous Lévy processes are used as driving processes. An explicit formula for the valuation of caps is derived using Fourier transform techniques. Based on the valuation formula, we calibrate the two model variants to market data.

Suggested Citation

Eberlein, Ernst and Gerhart, Christoph and Grbac, Zorana, Multiple Curve Lévy Forward Price Model Allowing for Negative Interest Rates (May 9, 2018). Available at SSRN: https://ssrn.com/abstract=3175950 or http://dx.doi.org/10.2139/ssrn.3175950

Ernst Eberlein

University of Freiburg ( email )

Department of Mathematical Stochastics
Eckerstrasse 1
D-79104, Freiburg
Germany
++49 761 203 5660 (Phone)
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Christoph Gerhart

University of Freiburg - Institut für Mathematische Stochastik ( email )

D-79104, Freiburg
Germany

Zorana Grbac (Contact Author)

Université Paris VII Denis Diderot ( email )

2, place Jussieu
Paris, 75005
France

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