Siegel Model Research Articles

Zero coupon yield curve dynamics in the Russian sovereign bond market

Yield curve is a graphical representation of a relationship between interest rates and maturity. Shape of yield curve often attracts attention of analysts, because it represents market implied expectation of future interest rate path. However, the analysis of the yield curve shape often lacks theoretical foundation. It is based either on review of term spreads or on a simple visual investigation. In this article we formally define the shape of the yield curve in terms of function invariants. We use Nelson–Siegel model as a backbone for our classification and show that there exists only six possible shapes of yield curve. They are: a normal upward slopping yield curve, inverted yield curve, humped upward slopping, dipped upward slopping, humped inverted and dipped inverted. We analyze dynamics of zero coupon yield curve in Russian market based on real historical data. We show that transition from an upward slopping curve to an inverted one was always preceded by a hump at mid-tem maturities, while the transition back was always done through the dip. This highlights the importance of mid-term rates in reshapening the curve. We explain this behavior by short end of the curve being linked to the key rate and thus being more sticky. The contribution of the paper is twofold. First, it provides a formal framework to analyze the shape of the yield curve. Second, it describes the patterns in dynamic of the ruble yield curve that can be useful for bond investors in the Russian market.

Yield curve extrapolation with machine learning

Abstract Yield curve extrapolation to unobservable tenors is a key technique for the market-consistent valuation of actuarial liabilities required by Solvency II and forthcoming similar regulations. Since the regulatory method, the Smith–Wilson method, is inconsistent with observable yield curve dynamics, parsimonious parametric models, the Nelson–Siegel model and its extensions, are often used for yield curve extrapolation in risk management. However, it is difficult for the parsimonious parametric models to extrapolate yield curves without excessive volatility because of their limited ability to represent observed yield curves with a limited number of parameters. To extend the representational capabilities, we propose a novel yield curve extrapolation method using machine learning. Using the long short-term memory architecture, we achieve purely data-driven yield curve extrapolation with better generalization performance, stability, and consistency with observed yield curve dynamics than the previous parsimonious parametric models on US and Japanese yield curve data. In addition, our method has model interpretability using the backpropagation algorithm. The findings of this study prove that neural networks, which have recently received considerable attention in mortality forecasting, are useful for yield curve extrapolation, where they have not been used before.

Sovereign CDS Spread and Term Structure Forecasting Based on Neural Network

The article aims to forecast credit risk for BRICS countries using daily credit default swaps (CDS) spreads obtained from Datastream data base from 2018 to 2023. Our approach consists, first, of forecasting the CDS spread in order to estimate the forecasted CDS term structure. The general regression neural network (GRNN) is used to predict the CDS spread. By checking the accuracy of the prediction, the results show that the GRNN model can be recommended as an effective forecasting tool for CDS spread. Second, the predicted spreads are used to estimate the forecasted CDS term structure using the Nelson–Siegel model. The results show that for Russia, overall, the CDS spreads in the long term are less than those in the short term, which implies that the future outlook is more optimistic, given the events that occurred during the study period, but it still retains the highest level of credit risk compared to other countries. Unlike Brazil, India and South Africa, the future outlook is more pessimistic. For China, the term structure is unstable; in the short term, there is a tendency to reduce the risk, but for longer horizons, the risk will increase. Thus, BRICS countries have different risk profiles depending on investment horizons. The study’s findings help policymakers in developing tailored risk management strategies for BRICS countries and guide investors in making informed credit investment decisions. The use of advanced forecasting tools like GRNN and Nelson–Siegel models emphasizes the importance of sophisticated techniques in enhancing financial market resilience.

Forecasting the yield curve: the role of additional and time‐varying decay parameters, conditional heteroscedasticity, and macro‐economic factors

In this article, we analyse the forecasting performance of several parametric extensions of the popular Dynamic Nelson–Siegel (DNS) model for the yield curve. Our focus is on the role of additional and time‐varying decay parameters, conditional heteroscedasticity, and macroeconomic variables. We also consider the role of several popular restrictions on the dynamics of the factors. Using a novel dataset of end‐of‐month continuously compounded Treasury yields on US zero‐coupon bonds and frequentist estimation based on the extended Kalman filter, we show that a second decay parameter does not contribute to better forecasts. In concordance with the preferred habitat theory, we also show that the best forecasting model depends on the maturity. For short maturities, the best performance is obtained in a heteroscedastic model with a time‐varying decay parameter. However, for long maturities, neither the time‐varying decay nor the heteroscedasticity plays any role, and the best forecasts are obtained in the basic DNS model with the shape of the yield curve depending on macroeconomic activity. Finally, we find that assuming non‐stationary factors is helpful in forecasting at long horizons.

Monetary Policy Effectiveness under the Ultra‐Low Interest Rate Environment: Evidence from Yield Curve Dynamics in Japan

I examine the effectiveness of monetary policy under the ultra‐low interest rate environment in Japan through the lens of yield curve dynamics. To that end, I employ the dynamic Nelson–Siegel model with time‐varying parameters, thereby computing indicators for tracing monetary easing effects. I show that the estimation performance of the yield curve models is sufficiently improved even under the ultra‐low interest rate environment by extending the dynamic Nelson–Siegel model to allow a loading parameter to vary over time, in addition to three factors of yield curve dynamics: level, slope, and curvature. However, I also demonstrate that the identification of the level and loading parameters is critical in assessing monetary policy effects. I reveal that monetary easing effects under the Quantitative and Qualitative Monetary Easing (QQE) are produced by flattening the yield curve in the ultra‐long‐term maturity zone over 10 years, while monetary easing effects from maturities shorter than ten years remain almost unchanged. Monetary policy fails to produce sufficient monetary easing effects within the time frame of the standard macroeconomic stabilization policy, even with the full‐fledged implementation of unconventional monetary policy measures under the ultra‐low interest rate environment in Japan.

Yield curve trading strategies exploiting sentiment data

This paper builds upon previous research findings that show macro sentiment data-augmented models are better at predicting the yield curve. We extend the dynamic Nelson–Siegel model with macro sentiment data from either Twitter or RavenPack. Vector autogressive (VAR) models and Markov-switching VAR models are used to predict changes in the shape of the yield curve. We build bond butterfly trading strategies that exploit our yield curve shape change predictions. We find that the economic returns from our trading strategies based upon models exploiting macro sentiment data do not statistically significantly differ from those which do not rely on it.

Sovereign Credit Risk in Saudi Arabia, Morocco and Egypt

The purpose of this paper is to assess and predict sovereign credit risk for Egypt, Morroco and Saudi Arabia using credit default swap (CDS) spreads obtained from the DataStream database for the period from 2009 to 2022. Our approach consists of generating the implied default probability and the corresponding credit rating in order to estimate the term structure of the implied default probability using the Nelson–Siegel model. In order to validate the prediction from the probability term structure, we calculate the transition matrices based on the implied rating using the homogeneous Markov model. The main results show that, overall, the probabilities of defaulting in the long term are higher than those in the short term, which implies that the future outlook is more pessimistic given the events that occurred during the study period. Egypt seems to be the country with the most fragile economy, especially after 2009, likely because of the political events that marked the country at that time. The economies of Morocco and Saudi Arabia are more resilient in terms of both default probability and credit rating. These findings can help policymakers develop targeted strategies to mitigate economic risks and enhance stability, and they provide investors with valuable insights for managing long-term investment risks in these countries.

Foreign trade and China’s yield curve during the COVID-19 pandemic: An analysis based on an extended arbitrage-free Nelson–Siegel model

We propose a general extension of the arbitrage-free Nelson–Siegel (AFNS) model by incorporating exogenous factors into the unspanned AFNS model. Regarding the number of people newly diagnosed with COVID-19 as an exogenous shock and net foreign purchases of treasury bonds of different maturities as unspanned factors, we study the impacts of the COVID-19 pandemic and the trading behavior of foreign investors on the yield curve in China. Our empirical results show that the COVID-19 pandemic significantly increases net foreign purchases of short-to-medium-term treasury bonds while significantly reducing the long-term treasury yield. Net foreign purchases of treasury bonds of different maturities cause large shifts with different shapes in the yield curve and have different effects on the excess returns of bonds of different maturities. This paper provides an important reference for risk management, investment decision-making and risk assessment of China’s financial opening policy for its treasury bond market.

Pricing swaptions and zero-coupon futures options under the discrete-time arbitrage-free Nelson–Siegel model

Pricing swaptions and zero-coupon futures options under the discrete-time arbitrage-free Nelson–Siegel model

Forecasting term structure of the Japanese bond yields in the presence of a liquidity trap

AbstractThe Nelson–Siegel (NS) model is widely used in practice to fit the term structure of interest rates largely due to its high efficacy in the in‐sample fit and out‐of‐sample forecasting of bond yields. In this paper, we compare forecasting performances of estimated yields from the Nelson–Siegel‐based models and some simpler time series models, using the daily, weekly, and monthly data during a prolong period of liquidity trap in Japan. We find that the out‐of‐sample expanding window forecasts by NS‐based models in general perform less satisfactory than the competitor models. However, the NS‐based models can be useful in forecasting yields over longer horizons and can work well with GARCH‐type structures in modeling the conditional volatility.

Динамическая модель Нельсона–Зигеля для оценки рыночного риска облигаций: практические аспекты имплементации

The article is devoted to Value‐at‐Risk estimation of bonds based on Dynamic Nelson–Siegel model (DNS). Instead of dealing with estimation of future interest rates and their volatiles, DNS model forecasts several unobservable shape parameters of the yield curve. We illustrate that for practical purposes one factor model is enough to correctly estimate bond VaR — this factor being long‐term level of interest rates. We recommend to use AR(1)‐GARCH(1,1) model to describe the evolution of interest rates level. Such dynamics specification provides accurate risk estimates while minimizing the number of consecutive VaR violations. We emphasize that the choice of optimization algorithm for estimation of yield curve parameters is crucial for accurate VaR forecasting since it might bring additional model noise into time series of yield curve parameters.

Learning Forecast-Efficient Yield Curve Factor Decompositions with Neural Networks

Most factor-based forecasting models for the term structure of interest rates depend on a fixed number of factor loading functions that have to be specified in advance. In this study, we relax this assumption by building a yield curve forecasting model that learns new factor decompositions directly from data for an arbitrary number of factors, combining a Gaussian linear state-space model with a neural network that generates smooth yield curve factor loadings. In order to control the model complexity, we define prior distributions with a shrinkage effect over the model parameters, and we present how to obtain computationally efficient maximum a posteriori numerical estimates using the Kalman filter and automatic differentiation. An evaluation of the model’s performance on 14 years of historical data of the Brazilian yield curve shows that the proposed technique was able to obtain better overall out-of-sample forecasts than traditional approaches, such as the dynamic Nelson and Siegel model and its extensions.

How arbitrage-free is the Nelson–Siegel model under stochastic volatility?

This study examines the effect of no-arbitrage on the Nelson–Siegel (NS) model under stochastic interest-rate volatility. Unlike under constant volatility, in which only a constant (convexity-adjustment) term of a yield function differs with and without no-arbitrage, factor loadings also differ when the volatility is spanned by interest-rate factors. After controlling for the drift, we find that spanned volatility does not magnify the effect of no-arbitrage relative to constant volatility. The finding implies that enriching the NS model with stochastic volatility is of significant benefit as this better describes interest-rate data without increasing the cost of allowing arbitrage opportunities.

The discrete-time arbitrage-free Nelson–Siegel model: a closed-form solution and applications to mixed funds representation

The discrete-time arbitrage-free Nelson–Siegel model: a closed-form solution and applications to mixed funds representation

Does ESG Disclosure Affect Corporate-Bond Credit Spreads? Evidence from China

With the exponential development of an ecological and sustainable economy and society, the concept and practice of environmental, social, and governance (ESG) investments are being popularized in the capital market of China. ESG disclosure is an important supplement to financial disclosure and plays an increasingly significant role in asset pricing. In this paper, we selected corporate bond data in China’s secondary bond market from 2015 to 2020, and introduced the Nelson–Siegel model to study the influence of ESG disclosure on corporate bond credit spreads in the secondary market. This model passed robustness tests when we used alternative data fitted by the modified Nelson–Siegel model. Results show that ESG disclosure significantly reduces credit spreads on corporate bonds in the secondary market. State ownership and industry play significant roles in moderating the impact of ESG disclosure on corporate bond credit spreads. Specifically, the ESG disclosure of non-state-owned companies and companies in non-high-pollution and -energy-consumption industries has a greater impact on reducing corporate bond credit spreads. Therefore, we urge regulatory departments to establish a sound ESG disclosure evaluation system, and the issue companies to improve the quality of their ESG disclosure, especially non-state-owned companies, and those in non-high-pollution and -energy-consumption industries. Corporate bond investors would benefit from integrating ESG information into their investment decision-making process.

Dynamic term structure models for SOFR futures

AbstractThe London InterBank Offered Rate is scheduled for discontinuation, and the replacement advocated by US regulators is the Secured Overnight Financing Rate (SOFR). The only SOFR‐linked derivative with significant liquidity and trading history is the SOFR futures contract, traded at the Chicago Mercantile Exchange. We use the historical record of futures prices to construct dynamic arbitrage‐free models for the SOFR term structure. We find that a Gaussian arbitrage‐free Nelson–Siegel model describes term structure well without accounting for jumps and seasonal effects observed in SOFR. However, a shadow‐rate extension is needed to describe volatility near the zero‐boundary impacting the futures convexity adjustment and option pricing.

The impact of the Covid-19 related media coverage upon the five major developing markets.

This paper analyses the influence of the Covid-19 coverage by the social media upon the shape of the sovereign yield curves of the five major developing countries, namely Federative Republic of B razil, Russian Federation, Republic of India, People’s Republic of China, and the Republic of South Africa (BRICS). The coherenc e between the level, slope, and the curvature of the sovereign yield term structures and the Covid-19 medi a coverage is found to vary between low and high ranges, depending on the phases of the pandemic. The empirical estimations of the yield-curve factors a re performed by means of the Diebold–Li modified version of the Nelson–Siegel model. The intervals of low coherence reveal the capacity of the two latent factors, level and slope, to be used for creating cross-factor diversification strategies, workable under crisis conditions, as evidenced on the example of the ongoing pandemic. Diverse coherence patterns are reported on a per-country basis, highlighting a promising potential of sovereign debt investments for designing cross-country and cross-factor fixed-income strategies, capable of hedging downside risks.

Scenario-based measurement of interest rate risks

PurposeThis paper aims to propose a scenario-based approach for measuring interest rate risks. Many regulatory capital standards in banking and insurance make use of similar approaches. The authors provide a theoretical justification and extensive backtesting of our approach.Design/methodology/approachThe authors theoretically derive a scenario-based value-at-risk for interest rate risks based on a principal component analysis. The authors calibrate their approach based on the Nelson–Siegel model, which is modified to account for lower bounds for interest rates. The authors backtest the model outcomes against historical yield curve changes for a large number of generated asset–liability portfolios. In addition, the authors backtest the scenario-based value-at-risk against the stochastic model.FindingsThe backtesting results of the adjusted Nelson–Siegel model (accounting for a lower bound) are similar to those of the traditional Nelson–Siegel model. The suitability of the scenario-based value-at-risk can be substantially improved by allowing for correlation parameters in the aggregation of the scenario outcomes. Implementing those parameters is straightforward with the replacement of Pearson correlations by value-at-risk-implied tail correlations in situations where risk factors are not elliptically distributed.Research limitations/implicationsThe paper assumes deterministic cash flow patterns. The authors discuss the applicability of their approach, e.g. for insurance companies.Practical implicationsThe authors’ approach can be used to better communicate interest rate risks using scenarios. Discussing risk measurement results with decision makers can help to backtest stochastic-term structure models.Originality/valueThe authors’ adjustment of the Nelson–Siegel model to account for lower bounds makes the model more useful in the current low-yield environment when unjustifiably high negative interest rates need to be avoided. The proposed scenario-based value-at-risk allows for a pragmatic measurement of interest rate risks, which nevertheless closely approximates the value-at-risk according to the stochastic model.

The predictive power of Nelson–Siegel factor loadings for the real economy

Abstract We generalize the arbitrage-free Nelson–Siegel (AFNS) model to allow λ t to vary over time. We find that the time-varying λ t , which determines the relative factor loadings, typically reaches its local peak before starting to decline right before a recession. Through conducting extensive in-sample and out-of-sample forecast exercises, we show that the information in the time-varying λ t factor has strong predictive power for business cycles and real economic activity. In particular, λ t contains additional useful information beyond those in conventional yield curve predictors, such as the yield spread. We argue and also document empirical evidence that the information in λ t is related to the market perception of the economic risk and uncertainty.

The impact of oil price shocks on Turkish sovereign yield curve

PurposeThis paper aims to investigate the impact of oil price shocks on the Turkish sovereign yield curve factors.Design/methodology/approachTo extract the latent factors (level, slope and curvature) of the Turkish sovereign yield curve, we estimate conventional Nelson and Siegel (1987) model with nonlinear least squares. Then, we decompose oil price shocks into supply, demand and risk shocks using structural VAR (structural VAR) models. After this separation, we apply Engle (2002) dynamic conditional correlation GARCH (DCC-GARCH (1,1)) method to investigate time-varying co-movements between yield curve factors and oil price shocks. Finally, using the LP (local projections) proposed by Jorda (2005), we estimate the impulse-response functions to examine the impact of different oil price shocks on yield curve factors.FindingsOur results demonstrate that the various oil price shocks influence the yield curve factors quite differently. A supply shock leads to a statistically significant increase in the level factor. This result shows that elevated oil prices due to supply disruptions are interpreted as a signal of a surge in inflation expectations since the cost channel prevails. Besides, unanticipated demand shocks have a positive impact on the slope factor as a result of the central bank policy response for offsetting the elevated inflation expectations. Finally, a risk shock is associated with a decrease in the curvature factor indicating that risk shocks influence the medium-term bonds due to the deflationary pressure resulting from depressed economic conditions.Practical implicationsOur results provide new insights to understand the driving forces of yield curve movements induced by various oil shocks to formulate appropriate policy responses.Originality/valueThe study contributes to the literature by two main dimensions. First, the recent oil shock identification scheme of Ready (2018) is modified using the “geopolitical oil price risk index” to capture the changes in the risk perceptions of oil markets driven by geopolitical tensions such as terrorism and conflicts and sanctions. The modified identification scheme attributes more power to demand shocks in explaining the variation of the oil price compared to that of the baseline scheme. Second, it provides recent evidence that distinguishes the impact of oil demand and supply shocks on Turkey's yield curve.