Interpolating the Yield Curve

Abstract

This article proposes an interpolation (and an extrapolation to the short rate) of the yield curve between a given number of observed yields on benchmark bonds that is compatible with an arbitrage-free model of the term structure of interest rates. The model is a multivariate time-homogeneous Gaussian yield factor model. It is shown that the interpolation that minimizes the integral of the yield variance, called the maximum stability interpolation, corresponds to the case that all eigenvalues of the mean-reversion matrix of the benchmark yields are equal. Explicit equations for calculation of the maximum stability interpolation are given.

TOPICS: Factor-based models, derivatives

Key Findings

• • Explicit equations are given for interpolation of the yield curve.

• • The equations are based on an equilibrium multifactor term structure model.

• • A criterion for maximum stability of the interpolation is introduced.