State-space dynamic functional regression for multicurve fixed income spread analysis and stress testing

We propose a smooth shadow-rate version of the dynamic Nelson-Siegel (DNS) model to analyze the term structure of interest rates during a zero lower bound (ZLB) period. By relaxing the no-arbitrage restriction, our shadow-rate model becomes highly tractable with a closed-form yield curve expression. This permits the implementation of readily available DNS extensions such as allowing for time-varying parameters and the integration of macroeconomic variables. Using U.S. Treasury data, we provide clear evidence of a smooth transition of the yields entering and leaving the ZLB state. Moreover, we show that the smooth shadow-rate DNS model dominates the baseline DNS model and (shadow-rate) affine term structure models in terms of fitting and forecasting the yield curve, while it also produces plausible policy insights at the ZLB.

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.

The predictive density simulation of the yield curve with a zero lower bound

At the zero lower bound, the dynamic Nelson–Siegel (DNS) model and even the Svensson generalization of the model have trouble in fitting the short maturity yields and fail to grasp the characteristics of the Japanese government bonds (JGBs) yield curve. During the zero interest rate policy regime, the short end of the yield curve is flat and yields corresponding to various maturities have asymmetric movements. Therefore, closely related generalized versions of Nelson–Siegel model—with and without no-arbitrage restriction (GAFNS and GDNS)—that have two slopes and curvatures factors are considered and compared empirically in terms of in-sample fit as well as out-of-sample forecasts with the standard Nelson–Siegel model—with and without no-arbitrage restriction (AFNS and DNS). The affine-based models provide a more attractive fit of the yield curve than their counterpart DNS-based models. Both extended models are capable to restrict the estimated rates from becoming negative at the short end of the curve and distill the JGBs term structure of interest rate quite well. The affine-based extended model leads to a better in-sample fit than the simple GDNS model. In terms of out-of-sample accuracy, both non-affine models outperform the affine models at least for 1- and 6-month horizons. The out-of-sample predictability of the GDNS for the 1- and 6-month-ahead forecasts is superior to the GAFNS for all maturities, and for longer horizons, i.e., 12-month-ahead, the former is still compatible to the latter, particularly for short- and medium-term maturities.

In this paper we survey a number of recent empirical findings regarding the usefulness of including diffusion indexes in dynamic Nelson-Siegel (DNS) type models used to predict the term structure of interest rates (see e.g., Diebold and Li (2007) and Diebold and Rudebusch (2013)). We also survey various empirical methods used in the construction of DNS models, and used to specify and estimate diffusion index augmented DNS models. In particular, we review (sparse) principal component analysis, factor augmented autoregression, and various dimension reduction, variable selection, machine learning, and shrinkage methods, such as the least absolute shrinkage operator (lasso), the elastic net, and independent component analysis, among others. Finally, we discuss the importance of using real-time data in contexts where datasets are subject to revision; and we compare and contrast the use of targeted versus un-targeted specification methods when including diffusion indexes in DNS type prediction models. Interestingly, as noted in Swanson and Xiong (2018a, 2018b), the usefulness of diffusion indexes is crucially dependent upon whether real-time data are used or not. Specifically, when real-time data are used to estimate the weights in di usion indexes, it is found that relatively few “data rich” models that use big data are preferred to simpler DNS models, post 2010. Instead, pure DNS models that rely only on historical interest rate data deliver mean square error “best” forecasts. However, when data are not real-time, diffusion indexes always have marginal predictive content for interest rates. Moreover, it is clear that in more volatile interest rate regimes, such as prior to 2010, machine learning and related methods have much to offer, regardless of the type of dataset used in their construction.

Forecasting the Term Structure of Government Bond Yields Using Credit Spreads and Structural Breaks

Accurate modelling and precise estimation of the term structure of interest rate are of crucial importance in many areas of finance and macroeconomics as it is the most important factor in the capital market and probably the economy. This study compares the in‐sample fit and out‐of‐sample forecast accuracy of the Cox–Ingersoll–Ross (CIR) and Nelson–Siegel models. For the in‐sample fit, there is a significant lack of information on the short‐term CIR model. The CIR model should also be considered too poor to describe the term structure in a simulation‐based context. It generates a downward slope average yield curve. Contrary to CIR model, Nelson–Siegel model is not only compatible to fit attractively the yield curve but also accurately forecast the future yield for various maturities. Furthermore, the non‐linear version of the Nelson–Siegel model outperforms the linearised one. In a simulation‐based context, the Nelson–Siegel model is capable to replicate most of the stylised facts of the Japanese market yield curve. Therefore, it turns out that the Nelson–Siegel model (non‐linear version) could be a good candidate among various alternatives to study the evolution of the yield curve in Japanese market.

Investigating United Kingdom's monetary policy with Macro-Factor Augmented Dynamic Nelson–Siegel models

This paper examines the theoretical restrictions on alternative term structure models in assessing sovereign borrowing strategies. Our approach draws upon Hahm & Kim’s (2003) cost–risk analytic model of sovereign debt management within a mean–variance framework. To explore the effects of different interest rate modeling strategies on government debt portfolio selection, two models are considered; namely, the time series‐based dynamic Nelson–Siegel (DNS) model proposed by Diebold & Li (2006) and the DNS model with arbitrage‐free restrictions proposed by Christensen et al. (2008a) . Using monthly spot rates for 12 maturities of nominal Korea Treasury Bonds (KTB) from September 2000 to November 2008, the present paper finds that a more generic term structure model, such as the DNS model, performs better in terms of smaller out‐of‐sample root mean squared errors at different forecast horizons. However, looking at the goodness‐of‐fit, the size of pricing errors and the magnitude of the root mean squared errors suggests that both models are reasonable representations of KTB spot curves. For the actual KTB position as of December 2007, the present paper shows that the 95% cost‐at‐risk level might be able to trim as much as 5–6% by rebalancing the portfolio. Furthermore, DNS models, both with and without no‐arbitrage restrictions, produce a consistent assessment of different strategies. This paper also shows that introducing new short‐term domestic debt instruments, such as 1‐year zero coupon KTB, would benefit government in terms of lowering both the average debt‐service cost and the 95% cost‐at‐risk. However, it is found that such benefits might dissipate if the issuance weights for such instruments exceed a certain level, which is approximately 4% of the position in the case of Korea.

Using a dynamic semiparametric factor model (DSFM) we investigate the term structure of interest rates. The proposed methodology is applied to monthly interest rates for four southern European countries: Greece, Italy, Portugal and Spain from the introduction of the Euro to the recent European sovereign-debt crisis. Analyzing this extraordinary period, we compare our approach with the standard market method – dynamic Nelson–Siegel model. Our findings show that two nonparametric factors capture the spatial structure of the yield curve for each of the bond markets separately. We attributed both factors to the slope of the yield curve. For panel term structure data, three nonparametric factors are necessary to explain 95% variation. The estimated factor loadings are unit root processes and reveal high persistency. In comparison with the benchmark model, the DSFM technique shows superior short-term forecasting in times of financial distress.

This study extends the affine Nelson–Siegel model by introducing the time-varying volatility component in the observation equation of yield curve, modeled as a standard EGARCH process. The model is illustrated in state-space framework and empirically compared to the standard affine and dynamic Nelson–Siegel model in terms of in-sample fit and out-of-sample forecast accuracy. The affine based extended model that accounts for time-varying volatility outpaces the other models for fitting the yield curve and produces relatively more accurate 6- and 12-month ahead forecasts, while the standard affine model comes with more precise forecasts for the very short forecast horizons. The study concludes that the standard and affine Nelson–Siegel models have higher forecasting capability than their counterpart EGARCH based models for the short forecast horizons, i.e., 1 month. The EGARCH based extended models have excellent performance for the medium and longer forecast horizons.

Insurance companies and pension funds have liabilities far into the future and typically well beyond the longest maturity bonds trading in fixed-income markets. Such long-lived liabilities still need to be discounted, and yield curve extrapolations based on the information in observed yields can be used. We use dynamic Nelson-Siegel (DNS) yield curve models to extrapolate risk-free yield curves for Switzerland and several countries. We find slight biases in extrapolated long bond yields of just a few basis points. In addition, the DNS model allows the generation of useful financial risk metrics, such as ranges of possible yield outcomes over projection horizons commonly used for stress-testing purposes. Therefore, we recommend using DNS models as a simple tool for generating extrapolated yields for long-term interest rate risk management. This paper was accepted by Kay Giesecke, finance. Supplemental Material: The data files and online appendices are available at https://doi.org/10.1287/mnsc.2021.4215 .

Insurance companies and pension funds have liabilities far into the future and typically well beyond the longest maturity bonds trading in fixed-income markets. Such long-lived liabilities still need to be discounted, and yield curve extrapolations based on the information in observed yields can be used. We use dynamic Nelson-Siegel (DNS) yield curve models for extrapolating risk-free yield curves for Switzerland, Canada, France, and the U.S. We find slight biases in extrapolated long bond yields of a few basis points. In addition, the DNS model allows the generation of useful financial risk metrics, such as ranges of possible yield outcomes over projection horizons commonly used for stress-testing purposes. Therefore, we recommend using DNS models as a simple tool for generating extrapolated yields for long-term interest rate risk management. [The first version of this paper was July 6, 2018.]

In this article we introduce time-varying parameters in the dynamic Nelson–Siegel yield curve model for the simultaneous analysis and forecasting of interest rates of different maturities. The Nelson–Siegel model has been recently reformulated as a dynamic factor model with vector autoregressive factors. We extend this framework in two directions. First, the factor loadings in the Nelson–Siegel yield model depend on a single loading parameter that we treat as the fourth latent factor. Second, we specify the overall volatility as a generalized autoregressive conditional heteroscedasticity (GARCH) process. We present empirical evidence of considerable increases in within-sample goodness of fit for these advances in the dynamic Nelson–Siegel model.

Since China's economic reform in 1978, the country's economic system has foreseen rapid evolvements, particularly in issuing debt securities by the Chinese central government to financing its drastic economic growth (Loo & Lqbal, 2019). This research study examines the zero-coupon bond yield curve's predictive power on China's GDP growth rate by adopting the Nelson-Siegel (1987) dynamic yield curve model. This research study adopts various approaches to refining the Nelson-Siegel (1987) model to enhance its predictive power on future economic activities, drawing upon the modifications undertaken by Diebold & Li's (2006) study to examining the constructed yield curve in accordance with the three latent factors of level, slope and curvature of the entire yield curve. A 67 period of zero-coupon bond yields is gathered between Q3 2002 and Q1 2019 quarterly from zero-coupon bond maturities of 1, 3, 5, 10, 20, and 30 years, finding that all types of zero-coupon bond maturities to exhibit similar yield curve movements across short, intermediary and long term durations. A multiple regression model was used to examine the correlation coefficient between the three latent factors and China's GDP, finding a significant relationship in the slope factor. A relationship was also found between the level and slope factors with a significance of 0.854, whereby the average rates between the two variables were calculated under the augmented Dicky Fuller test to ensure all factors are at stationary states to enhance the accuracy of future testing. The researcher also performed a least-squares equation (OLS) test to addressing the identified multicollinearity problem aforementioned, finding the R-squared value of 29.6%. Which suggested the level and curvature factors of the constructed yield curve would accurately explain 29.6% of China's GDP growth rates. To further examine the predictive power of the constructed yield curve in accordance to Nelson-Siegel's (1987) dynamic model, an out-of-sample forecasting method is employed with the out-of-sample size of 40 periods between Q3 2002 and Q2 2012 against 27 periods between Q3 and Q1 2019. The out-of-sample regression test founded an R squared value of 11.4,% suggesting that in sample forecasts contained higher predictive power to China's GDP growth based on the constructed yield curve. Furthermore, the out-of-sample forecast results show no significant relationship between the level and curvature factors, further reaffirming the argument that the yield curve in sample forecasts would better predict future economic activities. The research findings were consistent with findings from other studies conducted by Diebold & Li (2006); Hvozdenska (2015), and Campbell & Thompson (2008), whereby the spread of the yield curve constructed by the Nelson-Siegel (1987) dynamic model showed a strong relationship between China's GDP growth and the produced yield curve, representing strong predictive power and offers valuable insights to addressing the identified research gap where minimal research studies have explored the predictive power of China's zero-coupon bond yields in relation to the macroeconomic outlook. Keywords: Nelson-Siegel model, Yield curve, Zero-coupon bond, Maturity, Regression, Dynamic model. DOI: 10.7176/JEP/11-24-02 Publication date: December 31 st 2020