Dynamic Nelson–Siegel model for market risk estimation of bonds: Practical implementation

Abstract

The article is devoted to Value‐at‐Risk estimation of bonds based on Dynamic Nelson–Siegel model (DNS). Instead of dealing with estimation of future interest rates and their volatiles, DNS model forecasts several unobservable shape parameters of the yield curve. We illustrate that for practical purposes one factor model is enough to correctly estimate bond VaR — this factor being long‐term level of interest rates. We recommend to use AR(1)‐GARCH(1,1) model to describe the evolution of interest rates level. Such dynamics specification provides accurate risk estimates while minimizing the number of consecutive VaR violations. We emphasize that the choice of optimization algorithm for estimation of yield curve parameters is crucial for accurate VaR forecasting since it might bring additional model noise into time series of yield curve parameters.