A MEAN-FIELD EXTENSION OF THE LIBOR MARKET MODEL

Author:

DESMETTRE SASCHA1,HOCHGERNER SIMON2,OMEROVIC SANELA3,THONHAUSER STEFAN3

Affiliation:

1. Institute of Financial Mathematics and Applied Number Theory, Johannes Kepler University Linz, Altenbergerstrasse 69, 4040 Linz, Austria

2. Austrian Financial Market Authority, Otto-Wagner-Platz 5, 1090 Wien, Austria

3. Institute of Statistics, Graz University of Technology, Kopernikusgasse 24/III, 8010 Graz Austria

Abstract

In this paper, we introduce a mean-field extension of the LIBOR market model (LMM) which preserves the basic features of the original model. Among others, these features are the martingale property, a directly implementable calibration and an economically reasonable parametrization of the classical LMM. At the same time, the mean-field LIBOR market model (MF-LMM) is designed to reduce the probability of exploding scenarios, arising in particular in the market-consistent valuation of long-term guarantees. To this end, we prove existence and uniqueness of the corresponding MF-LMM and investigate its practical aspects, including Black’s formula. Moreover, we present an extensive numerical analysis of the MF-LMM. The corresponding Monte Carlo method is based on a suitable interacting particle system which approximates the underlying mean-field equation.

Funder

Austrian Science Fund

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Economics, Econometrics and Finance,Finance

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