Recovering Yield Curves from Dynamic Term Structure Models with Time-Varying Factors

Hiroyuki Kawakatsu

doi:10.3390/stats3030020

Abstract

A dynamic version of the Nelson-Siegel-Svensson term structure model with time-varying factors is considered for predicting out-of-sample maturity yields. Simple linear interpolation cannot be applied to recover yields at the very short- and long- end of the term structure where data are often missing. This motivates the use of dynamic parametric term structure models that exploit both time series and cross-sectional variation in yield data to predict missing data at the extreme ends of the term structure. Although the dynamic Nelson–Siegel–Svensson model is weakly identified when the two decay factors become close to each other, their predictions may be more accurate than those from more restricted models depending on data and maturity.

Highlights

Yield curves need to be estimated, since bonds with different maturities are not directly comparable due to different coupon payments
Given the black box nature of yield curve data construction, the main objective of this paper is to examine whether parametric dynamic term structure models can recover the yield curve data provided by central banks
This research was motivated by the need to recover missing yield data at the extreme ends, very short- and long- maturities, of the term structure

Summary

Introduction

Yield curves need to be estimated, since bonds with different maturities are not directly comparable due to different coupon payments. Many central banks provide estimated yields from government bonds. The two common methods used to construct such estimates are those based on splines (smooth curve fitting) and those that are based on parametric models. Most central banks make the estimated yield curve data publicly available, the exact methodology used to construct such estimates are usually not disclosed. //www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/yieldmethod.aspx (last revised 14 October 2018; accessed on 14 July 2019)). “Treasury reserves the option to make changes to the yield curve as appropriate and in its sole discretion. Such changes may include, but are not necessarily limited to, adding, removing, or modifying inputs, and making changes to the methodology for deriving the yield curve.”

Objectives

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Conclusion