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.     

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.     

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.     

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。     

Tax Clientele Effects in the Term Structure of UK Interest Rates

This paper tests for tax clientele effects in the term structure of UK interest rates. Five empirical models of the term structure of interest rates, incorporating tax effects, are estimated with daily data covering the period 31 March, 1995 to 3 August, 1995. In May 1995, the British government announced its intention to eliminate the tax exemption on capital gains from government bonds, but subsequently in July 1995 backtracked on some of its initial proposals. This period therefore forms the basis of a crude natural experiment in the sense that it provides an opportunity to examine tax clientele effects 'before' and 'after' an event which should have levelled greatly the taxing of government bonds. The empirical analysis suggests large tax clientele effects. However, there is little evidence of tax-specific term structures of interest rates.     

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.     

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.     

Selecting a Bond-Pricing Model for Trading: Benchmarking, Pooling, and Other Issues

Abstract:  Does one make money trading on the deviations between observed bond prices and values proposed by bond-pricing models? We extend Sercu and Wu's (1997) work to more models and more data, but we especially refine the methodology. In particular, we provide a normal-return benchmark that markedly improves upon the Sercu-Wu ones in terms of noisiness and bias, and we demonstrate that model errors contribute more to the variance of residuals—actual minus fitted prices—than pricing errors made by the market. Trading on the basis of deemed mispricing is profitable indeed no matter what model one uses. But there is remarkably little difference across models, at least when one re-estimates and trades daily; and with pooling and/or longer holding periods the results seem to be all over the place, without any relation to various measures of fit in the estimation stage. We also derive and implement an estimator of how much of the typical deviation consists of mispricing and how much is model mis-estimation or mis-specification. Lastly, we find that pooled time-series and cross-sectional estimation, as applied by e.g., De Munnik and Schotman (1994) , does help in stabilizing the parameter, but; hardly improves the trader's profits.     

The Term Structure of Interest Rates: Bounded or Falling?

This short paper resolves an apparent contradiction between Feldman's (1989) and Riedel's (2000) equilibrium models of the term structure of interest rates under incomplete information. Feldman (1989) showed that in an incomplete information version of Cox, Ingersoll, and Ross (1985), where the stochastic productivity factors are unobservable, equilibrium term structures are ``interior' and bounded. Interestingly, Riedel (2000) showed that an incomplete information version of Lucas (1978), with an unobservable constant growth rate, induces a ``corner' unbounded equilibrium term structure: it decreases to negative infinity. This paper defines constant and stochastic asymptotic moments, clarifies the apparent conflict between Feldman's and Riedel's equilibria, and discusses implications. Because productivity and growth rates are not directly observable in the real world, the question we answer is of particular relevance.     

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。     

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。     

Decreasing Yield Curves in a Model with an Unknown Constant Growth Rate

The effect of incomplete information on the term structure ofinterest rates is examined in the framework of a pure exchangeeconomy under uncertainty where aggregate output grows at aconstant rate. If the growth rate is known, the term structure isflat. In contrast, the term structure is a decreasing curve whenagents do not know the growth rate. Long term yields are less thanthe short rate and the yield of long term bonds is determined bythe worst possible realizations of future short rates.     

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.     

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.     

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.     

Learning about the Term Structure and Optimal Rules for Inflation Targeting

In this paper, we incorporate the term structure of interest rates in the New Keynesian model and analyze optimal policy under uncertainty about private sector expectations and the degree of inflation persistence. The novel result of our paper is that for large deviations of inflation from its target, the active learning policy is less activist—in the sense of responding less aggressively to the state of the economy—than a myopic policy, which ignores the learning channel. Moreover, for most initial beliefs, the incentive for active learning increases as monetary policy’s leverage over the long‐term interest rate increases.     

Cross‐sectional Restrictions on the Spot and Forward Term Structures of Interest Rates and Panel Unit Root Tests

In this paper we examine the stationarity of all the rates comprising the USD, GBP, DM and JPY spot and forward term structures. Instead of focussing on short maturity interest rates, as most other papers do, we perform a detailed analysis of the whole range of spot and forward interest rates of the 4 main currencies. We investigate the issue of stationarity within the framework of an equilibrium interest rate model such as Vasicek (1977), that defines the cross-sectional and time series properties that interest rates of various maturities must satisfy. We show that within a one-factor interest rate model, such as Vasicek, all interest rates are restricted to exhibit the same mean reverting behaviour. This restriction allows us to apply more powerful panel unit root tests. This methodology increases considerably the number of observations available and as a result the power of the unit root tests. The higher power of these tests allows us to demonstrate that there does exist mean reversion on the spot and forward US interest rates and the forward DM and GBP interest rates.     

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.     

Term structure modelling of defaultable bonds

In this paper we present a model of the development of the term structure of defaultable interest rates that is based on a multiple-defaults model. Instead of modelling a cash payoff in default we assume that defaulted debt is restructured and continues to be traded.The term structure of defaultable bond prices is represented in terms of defaultable forward rates similar to the Heath-Jarrow-Morton (HJM) (Heath et al., 1992) approach, and conditions are given under which the dynamics of these rates are arbitrage-free. These conditions are a drift restriction that is closely related to the HJM drift restriction for risk-free bonds, and the restriction that the defaultable short rate must always be not below the risk-free short rate. In its most general version the model is set in a marked point process framework, to allow for jumps in the defaultable rates at times of default.Financial Assistance by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 303, at the University of Bonn and the DAAD is gratefully acknowledged.I thank Pierre Mella-Barral, David Lando and David Webb for helpful conversations, and the participants of the FMG Conference on Defaultable Bonds (March 1997) in London and the QMF 97 conference in Cairns for helpful comments. All errors are of course my own.