Multiple Curve Lévy Forward Price Model Allowing for Negative Interest Rates

29 Pages Posted: 29 May 2020

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: January 2020

Abstract

In this paper, we develop a framework for discretely compounding interest rates that 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 significantly simplified. These properties make it an excellent base for a postcrisis multiple curve setup. Two variants for multiple curve constructions based on the multiplicative spreads 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. Relying on the valuation formula, we calibrate the two model variants to market data.

Keywords: multiple yield curves, forward price model, negative interest rates, time‐inhomogeneous Lévy processes, Libor‐OIS spread

Suggested Citation

Eberlein, Ernst and Gerhart, Christoph and Grbac, Zorana, Multiple Curve Lévy Forward Price Model Allowing for Negative Interest Rates (January 2020). Mathematical Finance, Vol. 30, Issue 1, pp. 167-195, 2020, Available at SSRN: https://ssrn.com/abstract=3613900 or http://dx.doi.org/10.1111/mafi.12210

Ernst Eberlein (Contact Author)

University of Freiburg ( email )

Department of Mathematical Stochastics
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D-79104, Freiburg
Germany
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Christoph Gerhart

University of Freiburg - Institut für Mathematische Stochastik ( email )

D-79104, Freiburg
Germany

Zorana Grbac

Université Paris VII Denis Diderot ( email )

2, place Jussieu
Paris, 75005
France

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