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.     

Beyond Single-Factor Affine Term Structure Models

This article proposes a new approach to testing for the hypothesisof a single priced risk factor driving the term structure ofinterest rates. The method does not rely on any parametric specificationof the state variable dynamics or the market price of risk.It simply exploits the constraint imposed by the no-arbitragecondition on instantaneous expected bond returns. In order toachieve our goal, we develop a Kolmogorov-Smirnov test and applyit to data on Treasury bills and bonds for both the United Statesand Spain. We find that the single risk factor hypothesis cannotbe rejected for either dataset.     

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.     

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。     

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.     

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.     

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 General Affine Earnings Valuation Model

We introduce a methodology, with two applications, that incorporates stochastic interest rates, heteroskedasticity and risk aversion into the residual income model. In the first application, goodwill is an affine (constant plus linear term) function where the constant and linear coefficients are time-varying. Homoskedastic risk gives rise to a constant risk premium, while heteroskedastic risk gives rise to linear state-dependent risk premiums. In the second application, we present a class of models where a non-linear function for the price-to-book ratio can be derived. We show how interest rates, risk, profitability and growth affect the price-to-book ratio.     

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.     

利率期限结构理论研究综述

本文主要对利率期限结构的理论研究做综述,以20世纪70年代初和90年代末为分界线,70年代以前称为传统的利率期限结构,主要以描述性研究为主;70年代以后称为现代利率期限结构,主要以随机模型研究为主;从20世纪90年代末,开始了两极分化发展。本文分为三个部分：第一部分对20世纪70年代之前传统利率期限结构的描述性理论作了概括;第二部分是现代利率期限结构的定量模型,包括均衡模型和无套利模型;第三部分则主要介绍20世纪90年代末以来的一些最新研究进展,包括市场模型和宏观金融模型等。     

A Simple Multi-Factor,Time-Dependent-Parameter Model for the Term Structure of Interest Rates

In this paper, we present a simple version of the Duffie and Kan model (1996). Our model can perfectly fit the yield curve and the volatility curve and further provide true closed form solutions to the pure discount bond price and its European contingent claims. Due to the specific factor structure in our model, the calibration exercise is easy to implement. This advantage will improve the computational efficiency in pricing American style claims.     

Pricing and Hedging of Contingent Claims in Term Structure Models with Exogenous Issuing of New Bonds

If calibrated to an observed term structure of interest rates that only covers a finite range of times-to-maturity an HJM-model of the term structure of interest rates will eventually die out in finite time as bonds reach maturity. This poses problems for the pricing and hedging of certain contingent claims. Therefore, we extend the HJM-model in such a way that it lives on an arbitrary time horizon and possesses term structures that cover a constant finite interval of times-to-maturity. We consider the pricing and hedging of contingent claims in this framework.     

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.     

A Binomial Basis for the Cox, Ingersoll and Ross Model of the Term Structure of Interest Rates

The technical demands of the Cox, Ingersoll and Ross (1985a and 1985b) papers are such that they can only be mastered by those who have a good understanding of some deep mathematics and statistical concepts, including the techniques of continuous time stochastic calculus and the measure theory upon which it is based, the Kuhn-Tucker theory surrounding non-linear optimisation techniques as well as variational methods founded on solutions of non-linear differential equations. Hence, our purpose here is to formalise both investor preferences and the supply side which underscores the Cox, Ingersoll and Ross (1985b) 'square root' model of the term structure of interest rates in terms of some simple binomial filtration processes, thereby avoiding most of the intricate technical detail contained in the original papers. These procedures not only allow for a more focused evaluation of the model's underlying strengths and weaknesses but also provide a framework for assessing some of the strategies which the model makes available for hedging exposure against adverse interest rate movements.     

基于Nelson—Siegel模型的我国利率期限结构的构建

利率问题一直都是经济金融研究中最基础、最核心的问题。利率可以反映出资金的供求状况,并受到物价水平、经济周期和预期等的影响。本文基于中国银行间债券市场的交易数据,利用基于贝叶斯推断的马尔科夫链蒙特卡罗模拟（MCMC）方法估计Hautsch＆Ou（2008）提出的动态的Nelson—Siegel模型,以构建我国的利率期限结构模型。     

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.     

The Term Structure of Implicit Discount Rates in Security Valuation

Abstract:   A reformulation of the residual income model is used to generate estimates of discount rates implicit in UK security prices. The terminal value of the infinite valuation model is incorporated into the coefficient on current earnings. By varying the length of the forecast horizon, different combinations of implicit discount rates are revealed that allow the estimation of time‐variant costs of equity. Results indicate no specific pattern of discount rates, thus revealing neither myopia on short‐term earnings nor excessive optimism on long(er)‐term earnings. Surprisingly, there is weak evidence that if any myopia exists, it is concentrated in larger and lower price‐earnings firms.     

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.