A Classification of Two-Factor Affine Diffusion Term Structure Models

Dai and Singleton (2000) introduced a typology of affine diffusionmodels when the domain of admissible values of the factors isan intersection of half planes and under some additional constraintson the parameters. This condition on the domain and the additionalsufficient constraints are restrictive and can considerablydiminish the practical interest of affine models. In this articlewe successfully address the research agenda sketched by Duffie,Filipovic, Schachermayer (2003, section 12.2, p. 1042). A systematicinvestigation is performed and our article provides a completetypology in the two-factor case, without prior restrictionson the domain and on the parameters.     

最优多因子仿射利率期限结构模型选择

在利用NS模型估计出市场即期利率的基础上,采用卡尔曼滤波方法对多因子Vasieck和CIR模型进行参数估计,最后运用蒙特卡罗模拟方法对交易所国债价格进行模拟,并与实际价格进行比较,进而确定了符合我们国债市场的最优多因子仿射利率期限结构模型。研究结果表明：多因子CIR模型对数据的拟合效果及对国债价格模拟效果要明显优于多因子Vasicek模型;对于多因子CIR模型而言,因子个数增加并没有提高模型的价格模拟效果;两因子CIR模型具有最优的国债价格模拟效果。     

Valuing Fixed-Income Options and Mortgage-Backed Securities with Alternative Term Structure Models

To value mortgage-backed securities and options on fixed-income securities, it is necessary to make assumptions regarding the term structure of interest rates. We assume that the multi-factor fixed parameter term structure model accurately represents the actual term structure of interest rates, and that the values of mortgage-backed securities and discount bond options derived from such a term structure model are correct. Differences in the prices of interest rate derivative securities based on single-factor term structure models are therefore due to pricing bias resulting from the term structure model. The price biases that result from the use of single-factor models are compared and attributed to differences in the underlying models and implications for the selection of alternative term structure models are considered.     

A Semiparametric Two-Factor Term Structure Model

This article proposes a semiparametric two-factor term structuremodel based on a consol rate and the spread between a shortrate and the consol rate. The diffusion functions in both theconsol rate and spread processes are nonparametrically specifiedso that the model allows for maximal flexibility of diffusionfunctions in fitting into data. The drift function of the spreadprocess is specified as a mean-reverting function, while thedrift function of the consol rate process is left unrestricted.A nonparametric procedure is developed for estimating the diffusionfunctions. The asymptotic biases of the nonparametric estimatorsare quantified when the step of discretization is fixed, whilethe asymptotic distributions of the nonparametric estimatorsare derived when the step of discretization tends to zero. Thepricing and hedging performances of the model are evaluatedin a simulated economic environment. Results show that the modelperforms quite well in the simulated economy.     

Switching VARMA Term Structure Models

The purpose of this article is to propose a global discrete-timemodeling of the term structure of interest rates which is ableto capture simultaneously the following important features:(i) a historical dynamics of the factor driving term structureshapes involving several lagged values, and switching regimes;(ii) a specification of the stochastic discount factor (SDF)with time-varying and regime-dependent risk-premia; (iii) explicitor quasi explicit formulas for zero-coupon bond (ZCB) and interestrate derivative prices. We develop the switching autoregressivenormal (SARN) and the switching vector autoregressive normal(SVARN) Factor-Based Term Structure Models of order p. The factoris considered as a latent variable or an observable variable:in the second case the factor is a vector of several yields.Regime shifts are described by a Markov chain with (historical)nonhomogeneous transition probabilities. An empirical analysisof bivariate VAR(p) and SVARN(p) Factor-Based Term StructureModels, using monthly observations of the U.S. term structureof interest rates, and a goodness-of-fit and expectation hypothesispuzzle comparison with competing models in the literature, showsthe determinant role played by the observable nature of thefactor, lags, and switching regimes in the term structure modeling.     

Gaussian Estimation and Forecasting of Multi-Factor Term Structure Models with an Application to Japan and the United Kingdom

In this paper we extend the exact discrete model of Bergstrom (1966) first used in empirical finance by Brennan and Schwartz (1979) to estimate their two-factor term structure model to estimate other two-factor term structure models using the recent assumption in Nowman (1997) for single factor models. Following Nowman (1997) we use the exact Gaussian estimation methods of Bergstrom (1983–1986, 1990) to estimate two-factor CKLS, Vasicek and CIR models. We estimate the models using monthly UK and Japanese interest rate data and our results indicate that the estimation method works well in practice.     

基于预测利率期限结构变动的债券投资策略实证研究

利用交易所国债的交易数据,对基于利率期限结构预测的积极债券投资策略进行实证研究。结果表明,将该策略应用于中国的债券市场能够获得较好的投资绩效。     

Design and Estimation of Quadratic Term Structure Models

We consider the design and estimation of quadratic term structuremodels. We start with a list of stylized facts on interest ratesand interest rate derivatives, classified into three layers: (1)general statistical properties, (2) forecasting relations, and (3)conditional dynamics. We then investigate the implications of eachlayer of property on model design and strive to establish amapping between evidence and model structures. We calibrate atwo-factor model that approximates these three layers ofproperties well, and show that a flexible specification for themarket price of risk is important in capturing the stylizedevidence in forecasting relations while factor interactions areindispensable in generating the hump-shaped dynamics of bondyields.     

Estimating and Testing Exponential-Affine Term Structure Models by Kalman Filter

This paper proposes a unified state-space formulation for parameter estimation of exponential-affine term structure models. The proposed method uses an approximate linear Kalman filter which only requires specifying the conditional mean and variance of the system in an approximate sense. The method allows for measurement errors in the observed yields to maturity, and can simultaneously deal with many yields on bonds with different maturities. An empirical analysis of two special cases of this general class of model is carried out: the Gaussian case (Vasicek 1977) and the non-Gaussian case (Cox Ingersoll and Ross 1985 and Chen and Scott 1992). Our test results indicate a strong rejection of these two cases. A Monte Carlo study indicates that the procedure is reliable for moderate sample sizes.     

Affine Models for Credit Risk Analysis

Continuous-time affine models have been recently introducedin the theoretical financial literature on credit risk. Theyprovide a coherent modeling, rather easy to implement, but havenot yet encountered the expected success among practitionersand regulators. This is likely due to a lack of flexibilityof these models, which often implied poor fit, especially comparedto more ad hoc approaches proposed by the industry. The aimof this article is to explain that this lack of flexibilityis mainly due to the continuous-time assumption. We developa discrete-time affine analysis of credit risk, explain howdifferent types of factors can be introduced to capture separatelythe term structure of default correlation, default heterogeneity,correlation between default, and loss-given-default; we alsoexplain why the factor dynamics are less constrained in discretetime and are able to reproduce complicated cycle effects. Thesemodels are finally used to derive a credit-VaR and various decompositionsof the spreads for corporate bonds or first-to-default basket.     

A New Stochastic Duration Based on the Vasicek and CIR Term Structure Theories

The stochastic duration based on the Vasicek and CIR models is theoretically superior to Macaulay's duration. However, empirical tests on bond immunization performance have so far failed to show its superiority. Within the one-factor framework, this paper proposes to use a longer zero-curve yield instead of the original instantaneous interest rate as a proxy for the relevant risk source(s). We prove that the new duration becomes larger, increasing with bond maturity, than the original duration. Bond immunization using Belgian data shows that the new duration definitely beats the original duration and can in some cases outperform Macaulay's duration.     

Are Indexed Bonds Really Inflation Proof? A Model of Real and Nominal Term Structures when Money has Real Effects

This paper studies the general behavior of the nominal and real term structures of interest rates in a general equilibrium framework. A central bank is introduced in the model as an agent facing a tradeoff between inflation and output and choosing a monetary policy variable. Prices and output are jointly determined in our model endogenously. Two multi-factor nominal and real term structure models are given as examples to illustrate the general model. In our economies, inflation indexed bonds are not completely inflation proof, but are still subject to the influence of inflation uncertainties. The models offer us an empirical framework that can be studied with indexed bond data and nominal bond data together in a single estimation.     

Forecasting the Term Structure of South African Government Bond Yields

This article uses the parsimonious dynamic Nelson–Siegel model to fit the yields of South African government bonds. We find that the dynamic Nelson–Siegel model has good fitting abilities for all maturities. We further forecast the term structure by seven different dynamic Nelson–Siegel models with time series models. We find that the DNS–VAR–GARCH model is useful for forecasting the short-term rates, the DNS–VAR best predicts the medium-term rates, and the DNS–RW best predicts the long-term rates. In addition, the dynamic Nelson–Siegel models provide better forecasts of yield data than a random walk model, especially for the 12-month forecasting horizons.     

交易所国债期限风险溢价的实证研究

本文考察了上海证券交易所国债期限风险溢价的时间变化特征及决定因素。实证结果显示，债券剩余期限越长，平均风险溢价越高；通过对不同期限债券组合的风险溢价序列建立回归模型，发现长短期利差及风险溢价的前期值对中长期债券期限风险溢价的时变性具有明显的解释能力。     

On the Information in the Interest Rate Term Structure and Option Prices

We examine whether the information in cap and swaption prices is consistent with realized movements of the interest rate term structure. To extract an option-implied interest rate covariance matrix from cap and swaption prices, we use Libor market models as a modelling framework. We propose a flexible parameterization of the interest rate covariance matrix, which cannot be generated by standard low-factor term structure models. The empirical analysis, based on US data from 1995 to 1999, shows that option prices imply an interest rate covariance matrix that is significantly different from the covariance matrix estimated from interest rate data. If one uses the latter covariance matrix to price caps and swaptions, one significantly underprices these options. We discuss and analyze several explanations for our findings.     

Multi-Factor Cox-Ingersoll-Ross Models of the Term Structure: Estimates and Tests from a Kalman Filter Model

This paper presents a method for estimating multi-factor versions of the Cox-Ingersoll-Ross (1985b) model of the term structure of interest rates. The fixed parameters in one, two, and three factor models are estimated by applying an approximate maximum likelihood estimator in a state-space model using data for the U.S. treasury market. A nonlinear Kalman filter is used to estimate the unobservable factors. Multi-factor models are necessary to characterize the changing shape of the yield curve over time, and the statistical tests support the case for two and three factor models. A three factor model would be able to incorporate random variation in short term interest rates, long term rates, and interest rate volatility.     

中国国债利率期限结构模型研究与实证分析

本文在概述国债利率期限结构模型的基础上,针对当前被发达国家广泛采用的NS和SV模型所存在的不足,通过扩展指数多项式的方法,构建出NSM模型。为了更好地估算利率期限结构模型中的参数,本研究针对目标函数优化求解,经分析比较多种优化算法后,确定选用GRG2非线性最优化算法。通过使用上海证券交易所2005.1.4～2007.11.30的国债每日交易数据对NS、SV、NSM三个模型的实证分析比较,表明NSM模型不仅保留了NS模型的经济含义,克服了SV模型参数估计依赖初值的缺点,能够反映出利率曲线多峰的情况;而且其在拟合精度、价格误差等多项指标上均优于NS模型和SV模型,并具有良好的适应性和稳健性,能够满足我国当前的国债市场需要。     

Implicit Inflation and Risk Premiums in the Brazilian Fixed Income Market

The breakeven inflation, the differential between nominal and real yields of bonds, is often used as a predictor of future inflation. The model presented here decomposes this interest rate differential into a risk premium and implicit inflation using a parametric formulation based on no-arbitrage conditions using nominal and indexed yield curves in Brazil, via an affine model of the Nelson–Siegel family. The measures of implicit inflation obtained from the model are shown to be unbiased estimators of future inflation for short horizons and carry some information for long horizons, and the model forecasts are superior to market surveys.     

Heterogeneous Beliefs, the Term Structure and Time-varying Risk Premia

This paper demonstrates theoretically and empirically that one possible economic explanation of the dynamics of the term structure of interest rates is the time-varying heterogeneous beliefs about future economic conditions. Assuming that each agent forms heterogeneous expectations about both his income shock and others’ beliefs about their income shocks each period, the paper illustrates that heterogeneous beliefs generate time-varying risk premia of the term structure in a closed-form solution. Motivated by this theory, several empirical tests are conducted using the cross-sectional mean and dispersion of belief indices that are extracted as the differences between non-judgemental econometric forecasts based on diffusion indices in Stock and Watson (J Bus Econ Stat, 2002) and professional survey forecasts. It is shown that (a) an increase in the mean belief about inflation steepens the yield curve, (b) the mean and dispersion of interest rate beliefs help explain the mean and the stochastic volatility of the term structure, suggesting that time-varying risk premia may be explained by endogenous uncertainty caused by heterogeneous beliefs in the economy.I am indebted to Mordecai Kurz, Timothy Cogley and Narayana Kocherlakota for constant support and extensive discussions that inspired this work. I would like to thank Randall Moore for providing the Blue Chip financial forecast data. The financial support from the Smith Richardson Foundation to the Stanford Institute for Economic Policy Research is gratefully acknowledged.     

Risk structure of interest rates: an empirical analysis for Deutschemark‐denominated bonds

This paper empirically studies the risk structure of interest rates for Deutschemark‐denominated bonds. For this purpose, we estimate term structures of interest rates using the parsimonious fitting function of Nelson and Siegel (1987) for virtually risk free Government bonds and five different rating categories classified by Moody's ratings (Aaa, Aa, A, Baa, Ba). The sample period covers the time interval from July 1990 to December 1996. We investigate the pricing errors resulting from our estimation procedure and analyse credit spreads over the term structure of Government bonds.