Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications

43 Pages Posted: 24 Jun 2003

See all articles by Markus Junker

Markus Junker

Center of Advanced European Studies and Research, Germany (CAESAR) - Financial Engineering Group

Alexander Szimayer

University of Hamburg - Faculty of Economics and Business Administration

Niklas Wagner

Passau University

Date Written: July 2003

Abstract

This paper documents nonlinear cross-sectional dependence in the term structure of U.S. Treasury yields and points out risk management implications. The analysis is based on a Kalman filter estimation of a two-factor affine model which specifies the yield curve dynamics. We then apply a broad class of copula functions for modeling dependence in factors spanning the yield curve. Our sample of monthly yields in the 1982 to 2001 period provides evidence of upper tail dependence in yield innovations; i.e., large positive interest rate shocks tend to occur under increased dependence. In contrast, the best fitting copula model coincides with zero lower tail dependence. This asymmetry has substantial risk management implications. We give an example in estimating bond portfolio loss quantiles and report the biases which result form an application of the normal dependence model.

Keywords: affine term structure models, nonlinear dependence, copula functions, tail dependence, value-at-risk

JEL Classification: C13, C16, G10, G21

Suggested Citation

Junker, Markus and Szimayer, Alexander and Wagner, Niklas F., Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications (July 2003). Available at SSRN: https://ssrn.com/abstract=407240 or http://dx.doi.org/10.2139/ssrn.407240

Markus Junker

Center of Advanced European Studies and Research, Germany (CAESAR) - Financial Engineering Group ( email )

53175 Bonn
Germany

Alexander Szimayer

University of Hamburg - Faculty of Economics and Business Administration ( email )

Von-Melle-Park 5
Hamburg, 20146
Germany

Niklas F. Wagner (Contact Author)

Passau University ( email )

Innstrasse 27
Passau, 94030
Germany

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