利率期限结构:理论、模型和实证

本文简要阐述了利率期限结构理论,并分析比较了均衡模型与无套利机会模型、单因子模型和多因子模型的主要特征,最后,利用银行间国债市场1周、2周和4周国债回购利率进行回归得到三个瓦西塞克随机利率期限结构模型,指出了完善中国国债市场的思路。     

Characterizing Gaussian Models of the Term Structure of Interest Rates

Models of the term structure of interest rates are considered for which, under the martingale measure, instantaneous forward rates are Gaussian. The possible forms of the covariance structure are characterized under appropriate formulations of the Markov property. It is demonstrated that imposing Markovian assumptions limits severely the covariances that may be obtained and that the strongest such formulation together with stationarity implies that the whole forward rate surface is necessarily a Gaussian random field described by just three parameters.     

The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates

It is possible to specify a model for interest rates in various ways, by giving the dynamics of the spot rate or of the forward rates, for example. A less well–developed approach is to specify the law of the state–price density process directly. In abstract, the state–price density process is a positive supermartingale, and the theory of Markov processes provides a rich framework for the generation of examples of such things. We show how this can be done, and provide simple examples (some familiar, some new) where prices of derivatives can be computed very easily. One benefit of the potential approach is that it becomes very easy to model the yield curve in many countries at once, together with the exchange rates between them.     

货币政策的利率期限结构效应的理论解释及其经验证据

文章首先运用一个利率期限结构的预期理论模型,证明了“在预期假说框架内货币政策只能引起收益率曲线平行移动而不会改变它的坡度”这一论断是错误的;接下来运用一个局部均衡模型在利率期限结构的预期理论框架下,证明了货币政策行动模式（参数）会影响货币政策对市场利率的影响效果、利率期限结构（收益率曲线）的斜率及其动态特征;之后用一个基于中关两国比较的经验证据说明上述理论解释的可靠性。     

三次样条法估计利率期限结构的加权方式比较研究

利率期限结构的静态估计是验证动态模型以及进行动态变化分析的基础。本文介绍了三次样条法的基本模型结构,指出了传统三次样条法使用久期倒数作为估计误差权重的逻辑错误,并据此提出了"准久期"加权以及成交量排名加权的概念;通过对比多个样本时间点的估计结果,发现成交量排名加权方法无论在样本内的模型估计还是样本外模型预测方面均优于久期以及准久期倒数加权方法。     

基于单因子利率期限结构模型的中国银行间短期利率行为的实证研究

文章采用高斯估计方法,使用中国银行间债券市场国债短期利率数据,对单因子连续时间利率期限结构模型进行了参数估计,实证结果显示我国银行间国债市场的短期利率具有均值恢复特性。和其它模型相比,BS模型在数据拟合方面表现较好。     

Multiple Ratings Model of Defaultable Term Structure

A new approach to modeling credit risk, to valuation of defaultable debt and to pricing of credit derivatives is developed. Our approach, based on the Heath, Jarrow, and Morton (1992) methodology, uses the available information about the credit spreads combined with the available information about the recovery rates to model the intensities of credit migrations between various credit ratings classes. This results in a conditionally Markovian model of credit risk. We then combine our model of credit risk with a model of interest rate risk in order to derive an arbitrage‐free model of defaultable bonds. As expected, the market price processes of interest rate risk and credit risk provide a natural connection between the actual and the martingale probabilities.     

连续时间利率期限结构的无套利模型

由于利率期限结构的均衡模型不能与观察到的期限结构想吻合,提出两种无套利利率期限结构模型———校准模型和HJM模型,试图解释利率期限结构的动态过程。无套利模型中假设经济中无套利机会存在,利用金融经济学第一基本定理,推导利率期限结构的动态过程。     

金融危机冲击下的中国国债利率期限结构分析

美国次贷危机不仅影响到整个美国经济,而且波及全球,导致全球金融危机。文章在阐述国债利率期限结构理论和国内外相关研究文献基础上,采用幂函数这一非线性回归模型对次贷危机时期我国国债收益率曲线的形状进行了静态拟合实证分析以及多个时点国债收益率曲线的动态分析。结果表明,我国国债市场已经逐渐走向成熟,能够较好地反映我国实际的经济运行状况以及世界金融市场受到的冲击,基本符合市场预期理论和流动性偏好理论。     

神经网络在国债利率期限结构中的建模与实证

人工神经网络技术是智能信息科学领域一个近年来得到迅速发展的分支。从信息论的观点来看 ,神经网络是一种自由模型估计器 ,基本特性是模式分类和非线性函数的逼近表示。其对信息是并行分布式处理与存储的 ,可以多输入多输出 ,依据样本对网络连接权和阈值不断进行修改训练 ,具有学习和自适应的能力 ,容错性强 ,对大量信息的非线性和模糊信息的金融系统非常适用。     

The Term Structure of Simple Forward Rates with Jump Risk

This paper characterizes the arbitrage-free dynamics of interest rates, in the presence of both jumps and diffusion, when the term structure is modeled through simple forward rates (i.e., through discretely compounded forward rates evolving continuously in time) or forward swap rates. Whereas instantaneous continuously compounded rates form the basis of most traditional interest rate models, simply compounded rates and their parameters are more directly observable in practice and are the basis of recent research on "market models." We consider very general types of jump processes, modeled through marked point processes, allowing randomness in jump sizes and dependence between jump sizes, jump times, and interest rates. We make explicit how jump and diffusion risk premia enter into the dynamics of simple forward rates. We also formulate reasonably tractable subclasses of models and provide pricing formulas for some derivative securities, including interest rate caps and options on swaps. Through these formulas, we illustrate the effect of jumps on implied volatilities in interest rate derivatives.     

货币政策周期与国债利率期限结构

以银行间隔夜拆借平均利率作为货币政策代理变量,利用2003年10月—2011年3月上交所国债数据估计出Nelson-Siegel模型的水平因子和倾斜度时间序列,运用马尔科夫区制转移向量自回归模型研究不同货币政策周期下货币政策变化对国债利率期限结构的影响,实证结果表明:当货币政策从宽松周期转向紧缩周期时,水平因子变大,倾斜度变小。面对货币政策从紧的冲击,在货币政策的宽松期和紧缩期,水平因子的响应分别为正向和负向,而倾斜度的响应均为负向。     

Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates

Black's (1995) model of interest rates as options assumes that there is a shadow instantaneous interest rate that can become negative, while the nominal instantaneous interest rate is a positive part of the shadow rate due to the option to convert to currency. As a result of this currency option, all term rates are strictly positive. A similar model was independently discussed by Rogers (1995) . When the shadow rate is modeled as a diffusion, we interpret the zero-coupon bond as a Laplace transform of the area functional of the underlying shadow rate diffusion (evaluated at the unit value of the transform parameter). Using the method of eigenfunction expansions, we derive analytical solutions for zero-coupon bonds and bond options under the Vasicek and shifted CIR processes for the shadow rate. This class of models can be used to model low interest rate regimes. As an illustration, we calibrate the model with the Vasicek shadow rate to the Japanese Government Bond data and show that the model provides an excellent fit to the Japanese term structure. The current implied value of the instantaneous shadow rate in Japan is negative.     

A Note on the Stability of Lognormal Interest Rate Models and the Pricing of Eurodollar Futures

The lognormal distribution assumption for the term structure of interest is the most natural way to exclude negative spot and forward rates. However, imposing this assumption on the continuously compounded interest rate has a serious drawback: rates explode and expected rollover returns are infinite even if the rollover period is arbitrarily short. As a consequence, such models cannot price one of the most widely used hedging instruments on the Euromoney market, namely the Eurodollar futures contract.
The purpose of this note is to show that the problems with lognormal models result from modeling the wrong rate, namely the continuously compounded rate. If instead one models the effective annual rate these problems disappear.     

The Market Model of Interest Rate Dynamics

A class of term structure models with volatility of lognormal type is analyzed in the general HJM framework. The corresponding market forward rates do not explode, and are positive and mean reverting. Pricing of caps and floors is consistent with the Black formulas used in the market. Swaptions are priced with closed formulas that reduce (with an extra assumption) to exactly the Black swaption formulas when yield and volatility are flat. A two–factor version of the model is calibrated to the U.K. market price of caps and swaptions and to the historically estimated correlation between the forward rates.     

我国银行间同业拆借利率期限结构的影响因素分析

本文利用Nelson-Siegel模型,通过实证分析发现:存贷差、狭义货币供应量和保费收入对利率水平有负效应,而工业增加值、企业商品价格指数和上证指数对利率水平有正效应;工业增加值与企业商品价格指数的增加会使利率曲线斜率下降,而狭义货币供应量与保费收入的增加则会使斜率上升。这对预测利率曲线的变化,从而规避由于利率曲线的非平行移动所产生的利率风险有重要的参考意义。     

Term Structure Models Driven by General Lévy Processes

As a generalization of the Gaussian Heath–Jarrow–Morton term structure model, we present a new class of bond price models that can be driven by a wide range of Lévy processes. We deduce the forward and short rate processes implied by this model and prove that, under certain assumptions, the short rate is Markovian if and only if the volatility structure has either the Vasicek or the Ho–Lee form. Finally, we compare numerically forward rates and European call option prices in a model driven by a hyperbolic Lévy motion with those in the Gaussian model.     

连续时间利率期限结构的均衡模型

利率期限结构有两种基本模型———无套利模型与均衡模型,其中均衡模型中根据假设短期利率的特定形式,推导利率的动态过程以及给未定权益进行定价。分析均衡模型的基本理论框架,并举例说明分析方法的运用,包括单因子与多因子模型。     

家族企业内部传承进程对贷款期限结构的影响研究

从家族接班人的职位视角,按照家族内部传承的进程,可以把家族内部传承区分为三个阶段：传承前期,传承中期和传承后期。文章基于我国2007-2011年上市家族企业的数据,分析了家族内部传承进程对贷款期限结构的影响。研究结果表明：（1）家族内部传承进程与长期借款比率呈倒“U”型关系。（2）在传承前期,家族内部传承可以促进企业获得长期借款,此结论支持了家族声誉理论。相对于家族间接控制来说,家族直接控制会强化家族内部传承的促进作用。（3）在传承中期,家族内部传承与长期借款比率的关系不显著。（4）在传承后期,家族内部传承会阻碍企业获得长期借款,此结论支持了资产专有理论。与第一代家族成员同时担任董事长和总经理相比,第二代家族成员同时担任董事长和总经理对长期借款比率的负面效应更大。