Estimating the Interest Rate Term Structures of Treasury and Corporate Debt with Bayesian Penalized Splines
Volume 3, Issue 3 (2005), pp. 223–240
Pub. online: 19 July 2021 Type: Research Article Open Access
19 July 2021
19 July 2021
Abstract: This paper provides a Bayesian approach to estimating the interest rate term structures of Treasury and corporate debt with a penalized spline model. Although the literature on term structure modeling is vast, to the best of our knowledge, all methods developed so far belong to the frequentist school. In this paper, we develop a two-step estimation procedure from a Bayesian perspective. The Treasury term structure is first estimated with a Bayesian penalized spline model. The smoothing parameter is naturally embedded in the model as a ratio of posterior variances and does not need to be selected as in the frequentist approach. The corporate term structure is then estimated by adding a credit spread to the estimated Treasury term structure, incorporating knowledge of the positive credit spread into the Bayesian model as an informative prior. In contrast to the frequentist method, the small sample size of the corporate debt poses no particular difficulty to the proposed Bayesian approach.