A Bayesian Approach to Yield Curve Modelling and Forecasting with Stochastic Volatility for Interest Rate Risk Management

Abstract

This thesis explores how forecasts of Dutch government bond yields can be improved by extending the current Dynamic Nelson-Siegel (DNS) model, used by the Dutch State Treasury Agency (DSTA), with stochastic volatility modeling and a Bayesian approach to parameter estimation and forecasting. The primary goal was to determine if the model extensions together with the Bayesian approach could improve the accuracy of yield forecasts given the highly volatile interest rate environment. In particular, we aimed to improve the "worst-case" forecasts, which we have defined as the upper bound of the 95% credible region with respect to the observed bond yields. To this end, we began with a baseline state-space model, resembling the current model in a state-space framework. Subsequently, we applied the findings from both in-sample and forecasting results as well as the findings from a literature review on volatility modeling to develop different models including two volatility models.

The volatility of the DNS model extensions is modeled as a GARCH process through the observation noise based on findings in the literature. This allowed for computationally efficient state estimation using a modified Kalman filter. Then, employing the Random Walk Metropolis algorithm for parameter estimation allowed us to use Bayesian multiple-step ahead forecasting. In particular, a comparative analysis of various models showed that while the current model performed better than expected, it was significantly outperformed in-sample by the DNS model with AR(1) observation noise (DNS-ARRW) and the DNS model with GARCH(1,1) observation noise volatility (DNS-OV). The Bayesian forecasting method particularly improved capturing the uncertainty of increasing yields in twelve-months ahead forecasts. Moreover, the two volatility models showed promising in-sample performance, but only one (DNS-OV) showed relatively good forecasting performance as well. Furthermore, the DNS-ARRW model consistently showed the best performance both in-sample and in forecasting.

In conclusion, the Bayesian approach to parameter estimation and forecasting proved effective in accounting for more variability in increasing forecast yields and simulating the direction of forecasts slightly better than the current MLE-based method. Moreover, the DNS-ARRW model showed significantly better worst-case forecasting performance, whereas the volatility models had a mixed performance.