Modeling Nelson-Siegel Yield Curve using Bayesian Approach

TL;DR

This paper applies Bayesian statistical methods to model the Nelson-Siegel yield curve, enabling better parameter estimation and bond valuation insights through Monte Carlo simulations and HMC sampling.

Contribution

It introduces a hierarchical Bayesian model for Nelson-Siegel parameters and demonstrates its application using US Treasury data with advanced sampling techniques.

Findings

Strong negative correlation between bond price and long-term yield effect

Weak positive correlation between short-term interest rate and bond value

Bayesian approach improves yield curve modeling and bond valuation accuracy

Abstract

Yield curve modeling is an essential problem in finance. In this work, we explore the use of Bayesian statistical methods in conjunction with Nelson-Siegel model. We present the hierarchical Bayesian model for the parameters of the Nelson-Siegel yield function. We implement the MAP estimates via BFGS algorithm in rstan. The Bayesian analysis relies on the Monte Carlo simulation method. We perform the Hamiltonian Monte Carlo (HMC), using the rstan package. As a by-product of the HMC, we can simulate the Monte Carlo price of a Bond, and it helps us to identify if the bond is over-valued or under-valued. We demonstrate the process with an experiment and US Treasury's yield curve data. One of the interesting observation of the experiment is that there is a strong negative correlation between the price and long-term effect of yield. However, the relationship between the short-term interest rate effect and the value of the bond is weakly positive. This is because posterior analysis shows that the short-term effect and the long-term effect are negatively correlated.