Testing Term Structure Estimation Methods: Evidence from the UK STRIPS Market

Prices and yields of UK government zero‐coupon bonds are used to test alternative yield curve estimation models. Zero‐coupon bonds permit a more pure comparison, as the models are providing only the interpolation service and also not making estimation feasible. It is found that better yield curves estimates are obtained by fitting to the yield curve directly rather than fitting first to the discount function. A simple procedure to set the smoothness of the fitted curves is developed, and a positive relationship between over‐smoothness and the fitting error is identified. A cubic spline function fitted directly to the yield curve provides the best overall balance of fitting error and smoothness, both along the yield curve and within local maturity regions.     

MODELING THE TERM STRUCTURE FROM THE ON‐THE‐RUN TREASURY YIELD CURVE

We propose a new model to estimate the term structure of interest rates using observed on‐the‐run Treasury yields. The new model is an improvement over models that require a priori knowledge of the shape of the yield curve to estimate the term structure. The general form of the model is an exponential function that depends on the estimation of four parameters fit by nonlinear least squares and has straightforward interpretations. In comparing the proposed model with current yield‐curve‐smoothing models, we find that, for the data used, the proposed model does best overall in terms of pricing accuracy both in sample and out of sample. JEL classification: E43, G12     

Fitting the term structure of interest rates for Taiwanese government bonds

The term structure of interest rates provides a basis for pricing fixed-income securities and interest rate derivative securities as well as other capital assets. Unfortunately, the term structure is not always directly observable because most of the substitutes for default-free bonds are not pure discount bonds. We use curve fitting techniques with the observed government coupon bond prices to estimate the term structure. In this paper, the B-spline approximation is used to estimate the Taiwanese Government Bond (TGB) term structure. We apply the B-spline functions to approximate the discount function, spot yield curve, and forward yield curve respectively. Among the three approaches, the discount fitting approach and the spot fitting approach are reasonable and reliable, but the spot fitting approach achieves the most suitable fit. Using this methodology, we can investigate term structure fitting problems, identify coupon effects, and analyze factors which drive term structure fluctuations in the TGB market.     

A Two-Factor Model for Low Interest Rate Regimes

This paper derives a two-factor model for the term structure of interest rates that segments the yield curve in a natural way. The first factor involves modelling a non-negative short rate process that primarily determines the early part of the yield curve and is obtained as a truncated Gaussian short rate. The second factor mainly influences the later part of the yield curve via the market index. The market index proxies the growth optimal portfolio (GOP) and is modelled as a squared Bessel process of dimension four. Although this setup can be applied to any interest rate environment, this study focuses on the difficult but important case where the short rate stays close to zero for a prolonged period of time. For the proposed model, an equivalent risk neutral martingale measure is neither possible nor required. Hence we use the benchmark approach where the GOP is chosen as numeraire. Fair derivative prices are then calculated via conditional expectations under the real world probability measure. Using this methodology we derive pricing functions for zero coupon bonds and options on zero coupon bonds. The proposed model naturally generates yield curve shapes commonly observed in the market. More importantly, the model replicates the key features of the interest rate cap market for economies with low interest rate regimes. In particular, the implied volatility term structure displays a consistent downward slope from extremely high levels of volatility together with a distinct negative skew. 1991 Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: G10, G13     

An Unobserved Components Model of the Yield Curve

We develop an unobserved component model in which the short‐term interest rate is composed of a stochastic trend and a stationary cycle. Using the Nelson–Siegel model of the yield curve as inspiration, we estimate an extremely parsimonious state‐space model of interest rates across time and maturity. The time‐series process suggests a specific functional form for the yield curve. We use the Kalman filter to estimate the time‐series process jointly with observed yield curves, greatly improving empirical identification. Our stochastic process generates a three‐factor model for the term structure. At the estimated parameters, trend and slope factors matter while the third factor is empirically unimportant. Our baseline model fits the yield curve well. Model generated estimates of uncertainty are positively correlated with estimated term premia. An extension of the model with regime switching identifies a high‐variance regime and a low‐variance regime, where the high‐variance regime occurs rarely after the mid‐1980s. The term premium is higher, and more so for yields of short maturities, in the high‐variance regime than in the low‐variance regime. The estimation results support our model as a simple and yet reliable framework for modeling the term structure.     

No-dynamic-arbitrage and market impact

Starting from a no-dynamic-arbitrage principle that imposes that trading costs should be non-negative on average and a simple model for the evolution of market prices, we demonstrate a relationship between the shape of the market impact function describing the average response of the market price to traded quantity and the function that describes the decay of market impact. In particular, we show that the widely assumed exponential decay of market impact is compatible only with linear market impact. We derive various inequalities relating the typical shape of the observed market impact function to the decay of market impact, noting that, empirically, these inequalities are typically close to being equalities.     

Price Discovery in the U.S. Treasury Market: The Impact of Orderflow and Liquidity on the Yield Curve

We examine the role of price discovery in the U.S. Treasury market through the empirical relationship between orderflow, liquidity, and the yield curve. We find that orderflow imbalances (excess buying or selling pressure) account for up to 26% of the day‐to‐day variation in yields on days without major macroeconomic announcements. The effect of orderflow on yields is permanent and strongest when liquidity is low. All of the evidence points toward an important role of price discovery in understanding the behavior of the yield curve.     

公开市场操作与利率期限结构行为——基于混频数据信息的研究视角

在混频数据信息环境中,精准识别公开市场操作(央行政策利率)和国债收益率曲线(基准利率体系)之间的关联机制至关重要,其影响了货币政策期限结构传导的有效性。本文在混频Nelson-Siegel(N-S)利率期限结构模型框架下,引入央行政策利率,揭示公开市场操作与利率期限结构(水平、斜率、曲度)因子之间的作用机制。实证结果表明:混频数据信息条件下,引入的公开市场操作信息显著改进国债收益率曲线的拟合效果;斜率因子冲击对公开市场操作具有显著的正向影响,而利率期限结构因子对政策调控的反应不敏感。进一步研究表明,2015年以来,公开市场操作对斜率因子的影响逐渐扩大,政策利率向国债收益率曲线的传导效率得到显著提高,我国现代货币政策框架日益健全。     

A general HJM framework for multiple yield curve modelling

We propose a general framework for modelling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to construct models such that multiplicative spreads are greater than one and ordered with respect to the tenor’s length. When the driving semimartingale is an affine process, we obtain a flexible and tractable Markovian structure. Finally, we show that the proposed framework allows unifying and extending several recent approaches to multiple yield curve modelling.     

Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models

We propose using model‐free yield quadratic variation measures computed from intraday data as a tool for specification testing and selection of dynamic term structure models. We find that the yield curve fails to span realized yield volatility in the U.S. Treasury market, as the systematic volatility factors are largely unrelated to the cross‐section of yields. We conclude that a broad class of affine diffusive, quadratic Gaussian, and affine jump‐diffusive models cannot accommodate the observed yield volatility dynamics. Hence, the Treasury market per se is incomplete, as yield volatility risk cannot be hedged solely through Treasury securities.     

The Effect of Monetary Unification on German Bond Markets

We develop a benchmark against which the effects of ECB monetary policy on the German bond market can be evaluated. We first estimate an affine term structure model for the pre‐EMU period linking the German yield curve with the Bundesbank monetary policy. The German monetary policy and its implied yield curve are then reprojected onto the EMU period. The reprojected yield curve differs significantly from the observed one. Short‐term interest rates during the EMU period are significantly lower than they would have been in case the Bundesbank were still in charge of monetary policy. Furthermore, yield spreads increased substantially during the EMU period.     

Bayesian approach to yield curve modelling with application to the simulation of EMU environments: generating scenarios by modelling yield curve movements

A Bayesian approach to yield curve modelling is developed where information on the current and recent yield curves is used to generate yield curve scenarios, and a model is proposed that generates return distribution for bonds. The predictive power of the model is developed by comparing out-of-sample lagged realized yields with forecast yields, and it is demonstrated that the returns generated by this scenario approach and those generated using the standard time series approach are consistent. The model is applied to pre-EMU and post-EMU environments. This paper assesses the implications of different assumptions on the early post-EMU environment for international bond portfolio selection, as well as the immediate short-term effect of EMU on risk and return.     

How arbitrage-free is the Nelson-Siegel model?

We test whether the Nelson and Siegel (1987) yield curve model is arbitrage-free. Theoretically, the Nelson-Siegel model does not ensure the absence of arbitrage opportunities, as shown by Bjork and Christensen (1999) and Filipovic (1999). Still, central banks and wealth managers rely heavily on it. Using zero-coupon yield curve data from the US market, we find that the no-arbitrage parameters are not statistically different from those obtained from the Nelson-Siegel model. We therefore conclude that the Nelson-Siegel yield curve model is compatible with the no-arbitrage constraints on the US market. To corroborate this result, we also show that the Nelson-Siegel model performs as well as its no-arbitrage counterpart in an out-of-sample forecasting experiment.     

Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks

This paper quantifies how variation in economic activity and inflation in the United States influences the market prices of level, slope, and curvature risks in Treasury markets. We develop a novel arbitrage‐free dynamic term structure model in which bond investment decisions are influenced by output and inflation risks that are unspanned by (imperfectly correlated with) information about the shape of the yield curve. Our model reveals that, between 1985 and 2007, these risks accounted for a large portion of the variation in forward terms premiums, and there was pronounced cyclical variation in the market prices of level and slope risks.     

Term premium dynamics in an emerging market: Risk,liquidity, and behavioral factors

This paper contributes to the fixed income research by identifying determinants of term premium in an emerging market’s treasury bond yields with particular attention on ambiguity. We use Nelson–Siegel yield curves generated from daily bond price quotes as input to construct a three-factor affine term structure model which decomposes observed yields into risk-neutral and term premium components. We also construct an ambiguity index using intraday FX return data following Brenner and Izhakian (2018). Our analyses suggest that a combination of factors representing market risk, credit risk, liquidity, ambiguity, and investor sentiments can explain majority of the variation in term premia. Explanatory power of credit risk measures are found to increase while those of volatility, ambiguity, and sentiment measures diminish with the maturity horizon. The results imply that ambiguity aversion of bond investors is a major determinant of the shape of the yield curve as it drives the premia for short end of the yield curve lower in line with the expectation of flight-to-safety behavior.     

基准利率和基准收益率曲线的内涵及关系探讨

我国相继推出基准利率SHIBOR和银行间国债收益率曲线、央行票据收益率曲线与政策性金融债收益率曲线等三条基准收益率曲线,备受瞩目。那么,基准利率和基准收益率曲线的内涵有什么不同?二者之间是怎样的关系?搞清楚这些问题,对引导我国基准利率的选择和培育及完善基准收益率曲线的构建,提高货币当局宏观调控效率和促进我国金融市场的发展,具有重要的理论意义和现实意义。本文对这些问题进行了深入探讨。     

Bond pricing with a surface of zero coupon yields

We present a new method for consistent cross‐sectional pricing of all traded bonds in the fixed income market. By applying thin plate regression splines ( Wood, 2003 ) to bootstrapped zero coupon bond yields ( Hagan and West, 2006 ), the method decomposes traded yields into a risk‐free component plus premia for credit and liquidity risks, where the decomposition is consistent with the market valuations and underlying cash flows of the bonds. We apply the framework to end of quarter yield data from 2008 to 2011 on Australian dollar denominated semi‐government, supranational and agency (SSA) bonds, and find that the surface provides an excellent fit to the underlying zero coupon yield curves. Further, the decomposition of selected yield time series and cross‐sections demonstrates how credit premia increased for Australian SSA bonds through the Global Financial Crisis (GFC), but were counterbalanced by liquidity discounts as investors sought safe haven securities.     

The forecasting efficiency of the dynamic Nelson Siegel model on credit default swaps

This paper extends the Diebold–Li dynamic Nelson Siegel model to a new asset class, credit default swaps (CDSs). The similarities between the term structure of CDSs and the term structure of interest rates allow CDS curves to be modelled successfully using a parsimonious three factor model as first proposed by Nelson and Siegel (1987). CDSs and yield curves are modelled using the Diebold and Li (2006) dynamic interpretation of the Nelson Siegel model where the three factors are representative of the level, slope and curvature of the curve. Our results show that the CDS curve fits the data well and allows for the various shapes exhibited by the CDS data including steep, inverted and downward sloping curves. In addition to in sample fit of the modelled curve we explore the out of sample forecasting abilities of the model and using a univariate autoregressive model we forecast 1, 5 and 10 days ahead. Our results show that although the one day ahead forecast under performs the random walk, the 5 and 10 day forecast consistently outperforms the random walk for both yields and CDSs. This study reaffirms the ability of the Diebold–Li (2006) methodology to forecast yields and provides new evidence that this methodology is efficacious when applied to CDS spreads.     

The changing relation between the Canadian and U.S. yield curves

The term structures of Canada and of the United States, two countries with historically interdependent economic ties, have been closely linked. We investigate the link between Canadian and U.S. yield curves and show previously strong correlations between yield curve components dissipate after Canadian monetary policy reforms in the early 1990s. We attribute the separated ties to the adoption of explicit inflation targets in 1991 and the maintenance of credibility in price stability as a central policy goal by the Bank of Canada. The effect is particularly evident in the diminished cross-country correlations of the short term bond yields. Additionally, there exists strong evidence of cointegration before the reforms, evidence which weakens after the policy change date. Lastly, the results on the term structure are shown using a vector autoregression with an endogenously determined break date for Canadian and U.S. estimates of the three-factor Nelson and Siegel (1987) yield curve model.     

A new measure of cross-sectional risk and its empirical implications for portfolio risk management

Litterman et al. [Litterman, R., Scheinkman, J., Weiss, L., 1991. Volatility and the yield curve. Journal of Fixed Income 1 (June), 49–53] and Engle and Ng [Engle, R.F., Ng, V.K., 1993. Time-varying volatility and the dynamic behavior of the term structure. Journal of Money, Credit and Banking 25(3), 336–349] provide empirical evidence of a relation between yield curve shape and volatility. This study offers theoretical support for that finding in the general context of cross-sectional time series. We introduce a new risk measure quantifying the link between cross-sectional shape and market risk. A simple econometric procedure allows us to represent the risk experienced by cross-sections over a time period in terms of independent factors reproducing possible cross-sectional deformations. We compare our risk measure to the traditional cross-yield covariance according to their relative performance. Empirical investigation in the US interest rate market shows that (1) cross-shape risk factors outperform cross-yield risk factors (i.e., yield curve level, slope, and convexity) in explaining the market risk of yield curve dynamics; (2) hedging multiple liabilities against cross-shape risk delivers superior trading strategies compared to those stemming from cross-yield risk management.