Arbitrage-free Nelson-Siegel Model Research Articles

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

Abstract A closed-form solution for zero-coupon bonds is obtained for a version of the discrete-time arbitrage-free Nelson-Siegel model. An estimation procedure relying on a Kalman filter is provided. The model is shown to produce adequate fit when applied to historical Canadian spot rate data and to improve distributional predictive performance over benchmarks. An adaptation of the mixed fund return model from Augustyniak et al. ((2021). ASTIN Bulletin: The Journal of the IAA, 51(1), 131–159.) is also provided to include the discrete-time arbitrage-free Nelson-Siegel model as one of its building blocks.

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

Capital Structure and the Yield Curve

Abstract We develop a dynamic capital structure model in which interest rates are stochastic and driven by three state variables: level, slope, and curvature of the yield curve in an arbitrage-free Nelson-Siegel model. Our analysis suggests that the yield-curve factors are critical determinants of the capital structure of firms and that an increase in any of the three factors is followed by an increase of the firm’s leverage and a shortening of its debt maturity. We perform a two-stage least squares system of equations that accounts for the joint determination of leverage and debt maturity and confirms our model’s predictions. (JEL E43, G12, G32) Received February 16, 2022; editorial decision: August 13, 2022 by Editor Robert Marquez. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

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

Dynamic Term Structure Models for SOFR Futures

The LIBOR rate is currently scheduled for discontinuation, and the replacement advocated by regulators in the US is the Secured Overnight Financing Rate (SOFR). The change has the potential to disrupt the $200 trillion market of derivatives and debt tied to the LIBOR. The only SOFR linked derivative with any significant liquidity and trading history is the SOFR futures contract, traded at the CME since 2018. We use the historical record of futures prices to construct dynamic arbitrage-free models for the SOFR term structure. The models allow you to construct forward-looking SOFR term rates, imply a SOFR discounting curve and price and risk and risk manage SOFR derivatives, not yet liquidly traded in the market. We find that a standard three-factor Gaussian arbitrage-free Nelson-Siegel model describes term rates very well but a shadow-rate extension is needed to describe the behaviour near the zero-boundary. We also find that the jumps and seasonal effects observed in SOFR, do not need to be specifically accounted for in a model for the futures prices. Finally we study the so-called convexity correction and find that it becomes significant beyond the 2 year maturity. For validation purposes we demonstrate that our model aligns closely with the methodology used by the Federal Reserve to publish indicative SOFR term rates.

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.

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.

Benchmarking Interest Rate Models

Interest rate models are a workhorse for risk and asset managers, in particular for those overseeing long term investments. This paper discusses the suitability of admissible Affine Term Structure Model for risk management applications, and presents some results of two models: A parsimonious specification of the A0(3) model of Dai and Singleton, and the Arbitrage-Free Nelson-Siegel model of Christensen, Diebold and Rudebush. We believe they both have sufficient desirable characteristics to be adopted by risk managers of buy-side institutions, such as insurance companies, as a benchmark for their interest rate models.

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.

Forecasting the yield curve with the arbitrage-free dynamic Nelson–Siegel model: Brazilian evidence

Abstract We assess the extent to which the imposition of a no-arbitrage restriction on the dynamic Nelson–Siegel model helps obtaining more accurate forecasts of the term structure. For that purpose, we provide an empirical application based on a large panel of Brazilian interest rate future contracts and test for differences in forecasting performance among alternative benchmark specifications including the random walk, vector autoregressions, and the dynamic Nelson–Siegel. We show empirically that the arbitrage-free Nelson–Siegel model is able to outperform all other benchmark models when longer forecasting horizons are taken into account.

Forecasting the Term Structure of Interest Rates with Potentially Misspecified Models

This paper assesses the predictive gains of the pooling method in yield curve prediction. We consider three individual yield curve prediction models: the dynamic Nelson-Siegel model (DNS) and the arbitrage-free Nelson-Siegel model in addition to the random walk (RW) model as a benchmark. Despite the popularity of these three frameworks, none of them dominates the others across all maturities and forecast horizons. This fact indicates that those models are potentially misspecified. We investigate whether combining the possibly misspecified models in a linear form helps improve the predictive accuracy. To do this, we evaluate the out-of-sample forecasts of the pooled models in comparison with the individual models. In terms of density prediction, the pooled model of the DNS and RW models consistently outperforms those individual models regardless of maturities and forecast horizons. Our findings strongly suggest that one needs to try the pooling method rather than choosing one of the alternative models.

A Modified Arbitrage-Free Nelson–Siegel Model: An Alternative Affine Term Structure Model of Interest Rates

This paper derives a modified version of the Arbitrage-Free Nelson–Siegel (AFNS) model in which the Gaussian level factor in the AFNS model is replaced by a CIR process. By doing so, the resulting model is a subclass of the $$\mathbb {A}_1 (3)$$ class of affine dynamic term structure models, that tries to maintain the Nelson–Siegel (NS) property. Empirically, we found that for the US treasury data, our model fits better than AFNS, but that is offset by weaker forecasting performance for the very long maturities. For the Japanese Government Bond (JGB) zero-yields data, we found that there is no significant difference between our model and the AFNS model. In addition, for both data sets, our model to some extent, did maintain the NS property. We argued that because of the similarity between our model and the existing AFNS model, for modeling purpose it may be used as an alternative model. To our knowledge, this paper is the first to study the empirical performances and properties of the AFNS model for JGB zero-coupon yields.

An Arbitrage-Free Nelson-Siegel Model with Unspanned Stochastic Volatility for the Pricing of Interest Rate Derivatives

We propose a generalized arbitrage-free Nelson-Siegel model under the HJM framework. It features unspanned stochastic volatility factors while maintaining a Nelson-Siegel factor loading structure. The price of the interest rate derivatives, including European options, Caps and Swaptions are then obtained in semi closed-form. We calibrate the model using an extensive panel data, including the US Libor rates, Swap rates, caps and swaptions. By estimating our model via the extended Kalman filter, we find strong evidence that our model prices interest rates and their derivatives accurately.

A shape-based decomposition of the yield adjustment term in the arbitrage-free Nelson and Siegel (AFNS) model of the yield curve

The appealing feature of the arbitrage-free Nelson-Siegel model of the yield curve is the ability to capture movements in the yield curve through readily interpretable shifts in its level, slope or curvature, all within a dynamic arbitrage-free framework. To ensure that the level, slope and curvature factors evolve so as not to admit arbitrage, the model introduces a yield-adjustment term. This paper shows how the yield-adjustment term can also be decomposed into the familiar level, slope and curvature elements plus some additional readily interpretable shape adjustments. This means that, even in an arbitrage-free setting, it continues to be possible to interpret movements in the yield curve in terms of level, slope and curvature influences.

A generalised arbitrage-free Nelson–Siegel model: The impact of unspanned stochastic volatility

Although statistical term structure models provide exceptional in-sample fitting and out-of-sample forecasting of interest rates, the lack of theoretical background is criticized by academics and practitioners, such as the absent of arbitrage free. In this paper we develop a general Arbitrage-Free Nelson–Siegel model under the HJM framework. It features unspanned stochastic volatility factors while maintaining a Nelson–Siegel factor loading structure. This paper also exploits the potential to jointly model the interest rates and their derivatives.