Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications
43 Pages Posted: 24 Jun 2003
Date Written: July 2003
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: Suggested Citation