Forecasting the Term Structure of Interest Rates with Dynamic Constrained Smoothing B-Splines

Eduardo Mineo,Airlane Pereira Alencar,Marcelo Moura,Antonio Elias Fabris

doi:10.3390/jrfm13040065

Abstract

The Nelson–Siegel framework published by Diebold and Li created an important benchmark and originated several works in the literature of forecasting the term structure of interest rates. However, these frameworks were built on the top of a parametric curve model that may lead to poor fitting for sensible term structure shapes affecting forecast results. We propose DCOBS with no-arbitrage restrictions, a dynamic constrained smoothing B-splines yield curve model. Even though DCOBS may provide more volatile forward curves than parametric models, they are still more accurate than those from Nelson–Siegel frameworks. DCOBS has been evaluated for ten years of US Daily Treasury Yield Curve Rates, and it is consistent with stylized facts of yield curves. DCOBS has great predictability power, especially in short and middle-term forecast, and has shown greater stability and lower root mean square errors than an Arbitrage-Free Nelson–Siegel model.

Highlights

Forecast methods applied to a term structure of interest rates are important tools for banks and financial firms, or governments and policy makers, but for society itself, helping to understand the movements of markets and flows of money
This paper presents a dynamic version of the constrained smoothing B-splines model to forecast the yield curve with no-arbitrage restrictions
They keep the desired economic properties of the three-factors model of the original structure of Dynamic Nelson–Siegel (DNS). They ensure lack of arbitrage opportunities with a more simple structure compared to those affine arbitrage-free models published previously by Duffie and Kan (1996) and Duffee (2002). This is achieved by adding a yield-adjustment term to the Nelson–Siegel yield curve model described as an ordinary differential system of equations to ensure no-arbitrage

Summary

Introduction

Forecast methods applied to a term structure of interest rates are important tools for banks and financial firms, or governments and policy makers, but for society itself, helping to understand the movements of markets and flows of money. This paper presents a dynamic version of the constrained smoothing B-splines model to forecast the yield curve with no-arbitrage restrictions. In order to challenge this idea, Diebold and Li proposed the DNS model using a Nelson–Siegel yield curve fitting to forecast its dynamics This model became very popular among financial market users and even central banks around the world. They ensure lack of arbitrage opportunities with a more simple structure compared to those affine arbitrage-free models published previously by Duffie and Kan (1996) and Duffee (2002) This is achieved by adding a yield-adjustment term to the Nelson–Siegel yield curve model described as an ordinary differential system of equations to ensure no-arbitrage. Our present work proposes DCOBS, a dynamic constrained smoothing B-splines model to forecast the term structure of interest rates.

Term Structure of Interest Rates

Arbitrage-Free Nelson–Siegel

Dynamic Constrained Smoothing B-Splines

Descriptive Analysis

Results

Conclusions