Bayesian Inference in a Stochastic Volatility Nelson-Siegel Model

Abstract

In this paper, we develop and apply Bayesian inference for an extended Nelson-Siegel (1987) term structure model capturing interest rate risk. The so-called Stochastic Volatility Nelson-Siegel (SVNS) model allows for stochastic volatility in the underlying yield factors. We propose a Markov chain Monte Carlo (MCMC) algorithm to efficiently estimate the SVNS model using simulation-based inference. Applying the SVNS model to monthly U.S. zero-coupon yields, we find significant evidence for time-varying volatility in the yield factors. This is mostly true for the level and slope volatility revealing also the highest persistence. It turns out that the inclusion of stochastic volatility improves the model's goodness-of-fit and clearly reduces the forecasting uncertainty particularly in low-volatility periods. The proposed approach is shown to work efficiently and is easily adapted to alternative specifications of dynamic factor models revealing (multivariate) stochastic volatility.