Nelson-Siegel Model Research Articles

Research on RMB exchange rate forecast based on the neural network model and the Nelson–Siegel model

This paper expands the neural network model to predict exchange rate based on the factors extracted from the Nelson–Siegel model. Based on the theory about exchange rate forecasting, interest could be used to predict the movement of exchange rate. Therefore, this paper analyzes the interest rate term structure factors based on the US and China yield curves data, then uses the Nelson–Siegel model to extract the factors of the interest rate term structure. Finally, the factors of yield curves are used as input data to of the neural network model. And the mean forecasting squared errors, mean absolute errors, mean absolute percentage errors of neural network model, Nelson–Siegel regression model, and ARIMA model are compared. The results show that the neural network model has a superior ability to explain the exchange rate fluctuations of the CNY and USD, and the prediction ability is better than the exchange rate prediction ability of the Nelson–Siegel regression model and ARIMA model.

Predicting Interest Rates Using Shrinkage Methods, Real-Time Diffusion Indexes, and Model Combinations

In the context of predicting the term structure of interest rates, we explore the marginal predictive content of real-time diffusion indexes extracted from a “data rich” real-time dataset, when used in dynamic Nelson-Siegel (NS) models of the variety discussed in Diebold and Li (DNS: 2007) and Svensson (NSS: 1994). We find that the indexes have significant predictive content for sample periods ranging from 2001 through 2010. Additionally, DNS and NSS type models that include these indexes are the mean square forecast error (MSFE) “best” performers, when compared with various other econometric specifications, for the same period. In our top ranked models, diffusion indexes are sometimes optimally constructed used un-targeted principal component analysis (PCA), and sometimes using targeted PCA in conjunction with elastic net and least absolute shrinkage operators. The news is not all good for models utilizing indexes constructed from real-time datasets, however. In particular, after 2010 relatively few “data-rich” prediction models “beat” a random walk benchmark. Also, forecast combinations that utilize models that exclude real-time diffusion indexes yield the lowest overall MSFEs, dominating all other combination and individual models, across all sample periods, forecast horizons and bond maturities. Two key conclusions from our analysis are the following. First, fully revised data may have an important confounding effect upon results obtained when instead carrying out real-time prediction experiments. Second, real-time diffusion indexes matter when comparing the predictive performance of individual models, indicating the presence of unspanned macroeconomic risks in the term structure of interest rates. However, there appear to be two different ways to “capture” these unspanned risks. One is to use data rich real-time diffusion indexes, and another is to simply combine predictions from many non-data rich models.

Natural Yield Curve: The Case of Indonesia

The purpose of this study is to estimate the natural yield curve for an emerging economy, with Indonesia as a case study. The estimation is done by a two-stage approach, namely, the decomposition of the yield curve component through a dynamic Nelson-Siegel model, the results of which are then used to estimate a natural yield curve. Both steps are estimated through state space modeling with a Kalman filter. In addition, the study also analyzes the principal components of the real yields of Indonesia to prove that the use of the Nelson-Siegel model is relevant and sufficient. The main contribution of this research is the estimation of the natural yield curve for an emerging economy. The findings provide some evidence that a policy mix is needed for emerging economies to maintain macroeconomic stability. Some other findings are as follows: first, almost all yield curve variations can be explained by the first three principal components that moved similarly to level, slope, and curvature. Second, Indonesia's natural yield curve always has a positive slope over time. Third, across maturities, medium-term yields have the largest impact on the output gap. Fourth, the estimated natural yield curve can provide a gauge of the monetary policy stance, or external pressure.

Forecasting the Term Structure in Emerging Markets using Extensions of the Dynamic Nelson-Siegel Model

The dynamic Nelson-Siegel model and its extensions are used by many central banks to forecast the term structure. Their forecasting performance has been studied for many countries, but a little can be said about their accuracy for emerging market economies (EMEs). In this work we test the traditional dynamic Nelson-Siegel models, their extensions without the “curvature” factor and with inflation for six EMEs. Other extensions are model selection via BIC minimization and the Bayesian estimation with the conjugate Normal-inverse Wishart prior, which are novel in the field. The results indicate that inflation data and the Bayesian approach improve the forecasting performance relative to the traditional models. We also conclude that the multivariate dynamic Nelson-Siegel models often outperform univariate ones, while the “curvature” factor is rarely helpful for forecasting at a long horizon.

The sovereign yield curve and credit ratings in GIIPS

AbstractThis paper studies the impact of sovereign credit rating and outlook changes on the shape of the sovereign yield curve using data for five European countries, namely, Greece, Ireland, Italy, Portugal, and Spain, known as the GIIPS for the period of 2001–2016. We use the dynamic Nelson–Siegel model to estimate the level, slope, and curvature of the yield curve. Subsequently, we employ the vector autoregressive model to estimate the effect of sovereign rating and outlook changes on the sovereign yield curve. We find a significant effect of rating downgrades and an insignificant effect of rating upgrades in all five countries; however, the results for the effect of changes in outlook status are mixed. Our results remain robust to various sensitivity tests.

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

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.

Term Structure of CDS Spreads and Risk-Based Capital of the Protection Seller: An Extension of the Dynamic Nelson–Siegel Model with the Business Cycle

This article proposes an extended Diebold-Li dynamic Nelson-Siegel model with factors following AR-GARCH processes to fit the term structure of CDS spreads. The proposed model is used to estimate the risk-based capital of a protection seller of CDS contracts. Using CDX North American Investment Grade Index and CDX North American High Yield Index data, we find the AR-GARCH process with the business cycle to outperform all the other models. The risk-based capital for a protection seller increases with the duration of the holding period. Moreover, the protection seller of CDS contracts on high-yield reference entity needs capital-at-risk at least twice the amount that is needed for similar CDS on the investment-grade reference entity. The observed high level of capital-at-risk is driven mainly by the high volatility period identified in our sample, because the low volatility period is characterized by low realized defaults and persistent decline in CDS spreads. TOPICS:Factor-based models, credit default swaps Key Findings • This paper proposes an extended version of the Diebold-Li dynamic Nelson-Siegel (DNS) model to fit the term structure of CDS spreads; with a family of AR-GARCH process with business cycle to capture the dynamics of the conditional mean and the conditional volatility of CDS spreads. • Using data on the CDX North American Investment Grade index (CDXIG) and the CDX North American High Yield index (CDXHY), the proposed model is used to determine the risk-based capital of a protection seller of CDS contracts. • Overall, the proposed AR-GARCH process with the business cycle outperforms all the other processes (AR, AR-GARCH, AR-EGARCH, and AR-GJR), which highlights the importance of the business cycle to better forecast CDS spreads.

Application of improved adaptive Kalman filter in China’s interest rate market

With the increasing number of data in China’s interest rate market, the model is increasingly complex. For most interest rate models at this stage, its parameter estimation has become the focus of many scholars in recent years. At present, for the parameter estimation of the interest rate model, there is often a problem that the parameter estimation accuracy is not high and the algorithm stability is poor. Therefore, this research work investigates the parameter estimation method of the no-arbitrage Nelson–Siegel model for the classical interest rate model and points out the shortcomings of the estimation method. In the iterative process, the mean error and the estimated error covariance will expand continuously. The phenomenon eventually leads to the consequences of poor estimation. In this study, an improved adaptive Kalman filtering method is proposed. In the process of algorithm updating, an exponential decay factor is added to improve the accuracy of parameter estimation and the stability of the algorithm. Finally, based on China’s national debt data, the simulation experiment is carried out.

Comparing different methods for the estimation of interbank intraday yield curves

AbstractIn this study, we compare three different models, namely, the Nelson–Siegel model (NSM), the Svensson model (SVM), and the Diebold–Li model (DLM), for the estimation of an intraday yield curve on the Italian interbank credit market e‐MID. Using a sample, which spans from October 2005 until March 2010, the first important finding is that all three models are highly suitable for the estimation of an intraday yield curve providing superior empirical results when compared with similar works on e‐MID. The second important finding is that, based on different in‐sample statistics, the SVM dominates the other two models before, during, and after the financial crisis from 2007. Moreover, the NSM seems to dominate the DLM although these differences in goodness‐of‐fit between these two models may not be statistically significant. Our findings are of high practical importance from different perspectives regarding interbank credit markets, including the better understanding of trading processes, the optimization of banks' trading strategies, and monetary policy implications. Finally, our findings can be seen as the starting point for further analyses in this research area.

Cohort and value-based multi-country longevity risk management

ABSTRACT Multi-country risk management of longevity risk provides new opportunities to hedge mortality and interest rate risks in guaranteed lifetime income streams. This requires consideration of both interest rate and mortality risks in multiple countries. For this purpose, we develop value-based longevity indexes for multiple cohorts in two different countries that take into account the major sources of risks impacting life insurance portfolios, mortality and interest rates. To construct the indexes we propose a cohort-based affine model for multi-country mortality and use an arbitrage-free multi-country Nelson–Siegel model for the dynamics of interest rates. Index-based longevity hedging strategies have the advantages of efficiency, liquidity and lower cost but introduce basis risk. Graphical risk metrics are a way to effectively capture the relationship between an insurer's portfolio and hedging strategies. We illustrate the effectiveness of using a value-based index for longevity risk management between two countries using graphical basis risk metrics. To show the impact of both interest rate and mortality risk we use Australia and the UK as domestic and foreign countries, and, to show the impact of mortality only, we use the male populations of the Netherlands and France with common interest rates and basis risk arising only from differences in mortality risks.

Analyzing China’s Term Structure of Interest Rates Using VAR and Nelson-Siegel Model

China’s bonds market has developed rapidly in recent years. A further study of interest rate term structure is essential. Nelson-Siegel model is widely used to fit interest rate term structure around the world. In this essay, we try to find out whether Nelson-Siegel model is efficiency in China, and which model is most efficient among some typical variants of Nelson-Siegel model. After brief theoretical introduction, we conduct empirical analysis, which contains two sections. In the first session, we focus on fitting Chinese interest rate term structure using Nelson-Siegel model, and fitting efficiency turns out to be pretty good. In the second section, we establish a VAR model with macroeconomic variables to predict parameters in Nelson-Siegel model, and use the combination of VAR and NS model to predict interest rate term structure in 2019 and 2020 respectively. Also, in terms of prediction efficiency, VAR (Macro)-NS model performs better than both VAR-NS model without macroeconomic variables and simple NS model.

A Comparative Analysis of Parsimonious Yield Curve Models with Focus on the Nelson-Siegel, Svensson and Bliss Models

We shed light on computational challenges when fitting the Nelson-Siegel, Bliss and Svensson parsimonious yield curve models to observed US Treasury securities with maturities up to 30 years. As model parameters have a specific financial meaning, the stability of their estimated values over time becomes relevant when their dynamic behavior is interpreted in risk-return models. Our study is the first in the literature that compares the stability of estimated model parameters among different parsimonious models and for different approaches for predefining initial parameter values. We find that the Nelson-Siegel parameter estimates are more stable and conserve their intrinsic economical interpretation. Results reveal in addition the patterns of confounding effects in the Svensson model. To obtain the most stable and intuitive parameter estimates over time, we recommend the use of the Nelson-Siegel model by taking initial parameter values derived from the observed yields. The implications of excluding Treasury bills, constraining parameters and reducing clusters across time to maturity are also investigated.

Forecasting the yield of Chinese corporate bonds

In this paper we focus on predicting the yield that is the centrepiece of bond markets. The dynamic Nelson-Siegel model is used to predict the yield of the Chinese corporate bonds with a class of AA, AA+ and AAA ratings. Our empirical results show that this model not only provides good in-sample fit, but also indicates the long-term, medium-term and short-term dynamic features of the yield curve of the corporate bonds with different credit ratings. Finally, we employ AR(1) model to forecast the three factors of the yield curve. Overall, the outcomes are very encouraging for the development of better forecasting systems for fixed income markets.

Forecasting the yield of Chinese corporate bonds

In this paper we focus on predicting the yield that is the centrepiece of bond markets. The dynamic Nelson-Siegel model is used to predict the yield of the Chinese corporate bonds with a class of AA, AA+ and AAA ratings. Our empirical results show that this model not only provides good in-sample fit, but also indicates the long-term, medium-term and short-term dynamic features of the yield curve of the corporate bonds with different credit ratings. Finally, we employ AR(1) model to forecast the three factors of the yield curve. Overall, the outcomes are very encouraging for the development of better forecasting systems for fixed income markets.

The effects of conventional and unconventional monetary policy on forecasting the yield curve

We investigate how conventional and unconventional monetary policies affect the dynamics of the yield curve by assessing the performance of individual yield curve models and their mixtures. Out-of-sample forecasts for U.S. bond yields show that the arbitrage-free Nelson–Siegel model and its mixtures with other models perform well in the period of conventional monetary policy, whereas the random walk model outperforms all the other models in the period of unconventional monetary policy. The diminished role of the no-arbitrage restriction in forecasting the yield curve since 2009 can be attributed to unconventional monetary policy, which resulted in low correlations between short- and long-term bond yields and little variation in the short-term rates. During the period of the maturity extension program in 2011–2012, the superiority of the random walk forecasts is more pronounced, reinforcing our finding that the monetary policy framework affects yield curve forecast accuracy.

Modeling the density of US yield curve using Bayesian semiparametric dynamic Nelson-Siegel model

This paper proposes the Bayesian semiparametric dynamic Nelson-Siegel model for estimating the density of bond yields. Specifically, we model the distribution of the yield curve factors according to an infinite Markov mixture (iMM). The model allows for time variation in the mean and covariance matrix of factors in a discrete manner, as opposed to continuous changes in these parameters such as the Time Varying Parameter (TVP) models. Estimating the number of regimes using the iMM structure endogenously leads to an adaptive process that can generate newly emerging regimes over time in response to changing economic conditions in addition to existing regimes. The potential of the proposed framework is examined using US bond yields data. The semiparametric structure of the factors can handle various forms of non-normalities including fat tails and nonlinear dependence between factors using a unified approach by generating new clusters capturing these specific characteristics. We document that modeling parameter changes in a discrete manner increases the model fit as well as forecasting performance at both short and long horizons relative to models with fixed parameters as well as the TVP model with continuous parameter changes. This is mainly due to fact that the discrete changes in parameters suit the typical low frequency monthly bond yields data characteristics better.

Arbitrage-free relative Nelson–Siegel model

This paper introduces a model of the difference between home and foreign country interest rates based on the arbitrage-free pricing theory, called the “Arbitrage-free relative Nelson–Siegel model” (AFRNS). This model implies that the relative volatility effect of the model appreciates future exchange rate changes. The effect increases as the future period lengthens.

Analyzing Commodity Futures Using Factor State-Space Models with Wishart Stochastic Volatility

We propose a factor state-space approach with stochastic volatility to model and forecast the term structure of future contracts on commodities. Our approach builds upon the dynamic 3-factor Nelson-Siegel model and its 4-factor Svensson extension and assumes for the latent level, slope and curvature factors a Gaussian vector autoregression with a multivariate Wishart stochastic volatility process. Exploiting the conjugacy of the Wishart and the Gaussian distribution, we develop a computationally fast and easy to implement MCMC algorithm for the Bayesian posterior analysis. An empirical application to daily prices for contracts on crude oil with stipulated delivery dates ranging from one to 24 months ahead show that the estimated 4-factor Svensson model with two curvature factors provides a good parsimonious representation of the serial correlation in the individual prices and their volatility. It also shows that this model has a good out-of-sample forecast performance.

Forecasting and trading monetary policy effects on the riskless yield curve with regime switching Nelson–Siegel models

We use 1982–2014 data on the US riskless yield curve to show that regime switching dynamics in Nelson-Siegel factor models extended to encompass variables that summarize the state of monetary policy lead to superior predictive accuracy. Such spread in forecasting power turns out to be statistically significant even controlling for parameter uncertainty and sample variation. Exploiting regimes, we obtain evidence that the increase in predictive accuracy is stronger during the Great Financial Crisis, when monetary policy underwent a significant, sudden shift. Although more caution applies in comparisons to a naïve random walk benchmark over a few sub-samples and when transaction costs are accounted for, we report that the increase in predictive power owed to the combination of regimes and of variables that capture the stance of unconventional monetary policies is tradeable. We devise and test butterfly strategies that exploit the forecasts from the models and obtain evidence of risk-adjusted profits both per se and in comparisons to simpler models.

A dynamic Nelson–Siegel model with forward-looking macroeconomic factors for the yield curve in the US

This paper employs a factor-augmented dynamic Nelson–Siegel (FADNS) model to predict the yield curve in the US that relies on a large data set of mostly forward-looking macroeconomic variables. FADNS models significantly improve interest rate forecasts relative to many extant models in the literature. For longer horizons, it outperforms autoregressive alternatives, with reductions in mean absolute forecast error of up to 18% using quarterly data and of up to 40% at higher frequencies. For shorter horizons, it is still competitive against autoregressive forecasts, outclassing them for 7- and 10-year yields. The out-of-sample analysis reveals that the forward-looking nature of the indicators we employ is crucial for improving forecasting performance. Including them indeed reduces the mean absolute error with respect to specifications based on backward-looking macroeconomic indicators for any model we consider.