A Simple Measure for Examining the Proxy Problem of the Short-Rate

The behavior of a finite-maturity yield used as a proxy for the short-rate can deviate substantially from that of the short-rate, which causes estimation biases of model parameters and pricing errors of interest-rate claims. This study proposes a simple measure that visualizes this deviation based on an analytical approximation of the term structure of interest rates. The computation of the measure is almost as easy as that of an affine model, so the adequacy of proxy can be readily checked even for short-rate models that do not admit closed-forms of bond prices.