Bond Immunization for Affine Term Structures

This paper generalizes a number of important immunization theorems. We show that the Fisher and Weil immunization, Bierwag and Khang minimax, Redington multiple liability, and Bierwag, Kaufman, and Toevs coverage theorems can be generalized to the class of affine term structures. This class of term structures contains many models that are commonly used in the finance literature.     

Mortgage Termination: An Empirical Hazard Model with a Stochastic Term Structure

Pricing for mortgage and mortgage-backed securities is complicated due to the stochastic and interdependent nature of prepayment and default risks. This paper presents a unified economic model of the contingent claims and competing risks of mortgage termination by prepayment and default. I adopt a proportional hazard framework to analyze these competing and interdependent risks in a model with time-varying covariates. The paper incorporates a stochastic interest rate model into the hazard function for prepayment. The empirical results reported in the paper provide new evidence about the ruthlessness of default and prepayment behavior and the sensitivity of these decisions to demographic as well as financial phenomena. The results also illustrate that evaluating the interest rate contingent claims with a stochastic term structure has effects on predicting not only the mortgage prepayment behavior but also the mortgage default behavior.     

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。     

The Effective Duration and Convexity of Liabilities for Property-Liability Insurers Under Stochastic Interest Rates

Managing interest rate risk for property-liability insurers requires appropriate measurement of the sensitivity of liabilities to movements in interest rates. Most prior studies have assumed that interest rates shift in a parallel fashion and that the cash flows from liabilities are unaffected by interest rate changes. This article recognizes that unpaid property-liability (P-L) insurance losses are inflation-sensitive, that movements in interest rates will affect future claim payouts due to the correlation between interest rates and inflation and that interest rates are stochastic. The effective duration and convexity of P-L insurance liabilities calculated based on this approach are substantially lower than those measured using traditional approaches, which has important implications for asset-liability management by P-L insurers.     

Stochastic duration and fast coupon bond option pricing in multi-factor models

Generalizing Cox, Ingersoll, and Ross (1979), this paper defines the stochastic duration of a bond in a general multi-factor diffusion model as the time to maturity of the zero-coupon bond with the same relative volatility as the bond. Important general properties of the stochastic duration measure are derived analytically, and the stochastic duration is studied in detail in various well-known models. It is also demonstrated by analytical arguments and numerical examples that the price of a European option on a coupon bond (and, hence, of a European swaption) can be approximated very accurately by a multiple of the price of a European option on a zero-coupon bond with a time to maturity equal to the stochastic duration of the coupon bond. This revised version was published online in June 2006 with corrections to the Cover Date.     

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.     

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.     

Expectations Hypothesis of the Term Structure of Implied Volatility: Evidence from Foreign Currency and Stock Index Options

Using a stochastic volatility option pricing model, we showthat the implied volatilities of at-the-money options are notnecessarily unbiased and that the fixed interval time-seriescan produce misleading results. Our results do not support theexpectations hypothesis: long-term volatilities rise relativeto short-term volatilities, but the increases are not matchedas predicted by the expectations hypothesis. In addition, anincrease in the current long-term volatility relative to thecurrent short-term volatility is followed by a subsequent decline.The results are similar for both foreign currency and the S&P500 stock index options.     

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。     

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。     

An alternative approach to the calibration of the Vasicek and CIR interest rate models via generating functions

We propose a new method to calibrate the Vasicek and Cox--Ingersoll--Ross interest rate models from bond prices. We define an appropriate generating function and derive recursive relations between the derivatives of the generating function and the bond prices. The parameters of the Vasicek and CIR models are then obtained by solving a system of linearly independent equations arising from the recursive relations. We include numerical results that show the method’s accuracy when bond prices generated from the exact formulas are used.     

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.     

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.     

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.     

A Complete Markovian Stochastic Volatility Model in the HJM Framework

This paper considers a stochastic volatility version of the Heath, Jarrow and and Morton (1992) term structure model. Market completeness is obtained by adapting the Hobson and Rogers (1998) complete stochastic volatility stock market model to the interest rate setting. Numerical simulation for a special case is used to compare the stochastic volatility model against the traditional Vasicek (1977) model.     

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.     

中国金融市场通胀预期——基于利率期限结构的量度

通胀预期量度在以通胀预期为导向的货币政策中的意义重大。本文利用卡尔曼滤波法将离散时间两因子无套利广义高斯仿射模型运用于我国银行间债券市场,第一次从中国国债收益率曲线中分解出金融市场的中长期通胀预期L。将L与居民通胀预期和经济学家通胀预期比较,发现从事前看,L优于经济学家通胀预期,稍逊于居民通胀预期;从事后看,L优于居民通胀预期,稍逊于经济学家通胀预期。综合看,L作为金融市场形成的、高频的、反映中长期通胀的预期指数,对货币政策制定具有现实的参考意义。     

二叉树利率期限结构模型应用初探——以寿险公司资产负债管理为例

近年来我国寿险公司经营风险加剧，寿险公司资产负债管理正逐渐成为实务界和学术界关注的焦点。本文在深入研究随机规划、利率期限结构、投资组合等相关理论的基础上，对比分析均衡模型和无套利模型的差异，指出无套利模型更适于构楚随机规划问题中利率情景树的构建。在无套利模型中，二叉树Black-Derman-Toy模型简单易操作，可以避免三叉树模型计算量大，效率不高等缺点。因此本文采用二叉树方法以Black-Derman-Toy模型构造利率情景树，与随机规划模型相结合的资产负偾管理方法，协调、管理寿险公司资产负偾现金流，减少了随机规划模型处理随机利率分布的技术性难度。     

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.