The Joint Estimation of Term Structures and Credit Spreads

Abstract

We present a new framework for the joint estimation of the default-free term structure of interest rates and corporate credit spread curves. It specifies the discount curve of a specific credit rating class as the sum of the government discount function and a discount spread function. Both functions are modelled using splines so that we can jointly estimate the default-free government term structure and corporate credit spread curves with least squares. We construct confidence intervals around the estimated term structures and credit spreads and use them to determine the number of knots and the order of the involved spline functions. By using a high-quality data set of German mark denominated bonds, we show that the new framework yields more realistic spreads than conventionally obtained spread curves that result from subtracting independently estimated government and corporate term structures. The estimated spread curves are now smooth functions of time to maturity, as opposed to the twisting curves one gets from the traditional method, and are less sensitive to model specifications. Moreover, the implied corporate term structures have tighter confidence bands. The credit spreads and term structures that result from the framework are therefore more suited to be used as input to, e.g., models that asses the credit risk in derivatives, pricing models for credit derivatives and corporate bonds, risk management procedures, and time series analyses of credit spreads.