久期

久期（Duration）和凸度（Convexity）是度量普通债券利率风险的常用指标。

Duration and convexity are the most common indicators used to measure bond 's interest rate risks .

接着对利率风险衡量模型进行了分析，比较敏感性缺口、久期、VaR、模拟分析的优缺点。

Then , analyzing evaluation model of interest rate risk , comparing advantage and disadvantage of sensitivity gap 、 duration 、 VaR 、 simulation analysis .

三螺旋DNA分子久期方程的约化

Reduction of the secular equation for triple & helical DNA

导出了任意能级下氢原子一级Stark效应中的久期方程简化后的计算公式。

A simplification formula of any state , s energy level for hydrogen atom in Stark effect is derived .

利用久期模型进行利率风险管理存在的利率期限结构非平行移动问题一直是国际上研究的焦点，M2模型即为解决方法之一。

Study about the assumption of non parallel shift of interest rate term structure has been essentially the subject of many researchers .

又从正规解出发得到了没有久期项的初始层解并讨论了具有小knudsen数的边界层解。

We get its initial layer solutions and boundary layer solution for small knudsen number .

说明在讨论非久期项效应时，一级平均Hamiltonian比只用二阶微扰论的结果更精确。

It is shown that the first-order averaging Hamiltonian is generally more precise than the second-order perturbation when the effects of non-secular terms are considered .

首先，文章介绍了几种利率风险测量的方法，包括基本点价格值、久期以及凸性。接下来文章讨论了两种典型的ALM的技术和策略，即现金流匹配技术和缺口分析技术。

First , the thesis introduces several methods of interest risk measurement including price value of basic point , duration and convexity .

使用3d~3电子久期方程计算3Cr~（3+）在立方场下库仑相互作用参数B、C和内晶格场参数Dq。

The parameters of Coulomb interaction B and C and the parameter of the internal crystal field , D_q , for Or ~ ( 3 + ) under cubic field are calculated using the secular equation of 3d ~ 3 electrons .

使用到期收益率（YTM）来衡量长期投资资产的收益能力，同时通过久期（duration）考察其潜在利率风险。

Using Yield to Maturity ( YTM ) to measure return of long-term investments and using duration to measure the potential interest rate risk .

根据Markowitz（1959）等理论可推导出：资产价格的总风险包括收益的方差和全久期向量两部分；

Following Markowitz ( 1959 ), it can be deduced that the total risks of asset price consist of the variance of return and the total duration vector ;

第三部分在对传统三种利率风险度量工具敏感性缺口、久期缺口、VaR进行解释分析的基础上，阐述了三种主要的利率风险管理方法，进攻型管理、缺口管理以及套期保值管理。

In the third part , based on the traditional interpretation of the three interest rate risk measure sensitivity gap , duration gap , VaR , on three main interest rate risk management methods , aggressive management , gap management and hedging management .

本文首先简要阐述了传统的Macaulay久期模型，Macaulay久期模型是度量利率风险的重要工具，但由于其假设条件与现实不符而严重制约了其有用性和精确性。

Macaulay Duration is an important tool of measuring interest rate risk , but its assumptions with reality has seriously hampered its usefulness and accuracy .

因此，Macaulay久期模型尽管重要，但是其局限也很多，许多研究人员在Macaulay久期模型的基础上，提出了很多改进的久期模型和理论。

Therefore , Macaulay duration model , while important , also has a lot of limitations . Many researchers made a lot of improvement on the basis of the Macaulay model .

包括各种传统的久期模型和随机久期模型，其中传统的久期模型本文分析了Macaulay久期、修正久期和Fisher-Weil久期，随机久期模型本文分析了两种单因子随机久期和一种双因子久期。

The traditional duration models contain Macaulay duration , Modified duration and Fisher-Weil duration . And the stochastic duration models contain two kinds of single-factor stochastic duration and a kind of two-factor stochastic duration .

本文研究了对称分子LCAO-MO的久期矩阵的结构特征，指出凡具有一定对称性的分子，即可利用对称性对其LCAO-MO久期行列式进行因子分解，使其本征值谱的计算简化。

The characteristics of LCAO-MO 's secular matrices of symmetric molecules have been investigated . The symmetry properties of the molecule can be utilized to factorize the secular determinant and simplify the calculation of the eigenvalue spectra .

本文先用Hull-White模型来计算债券中嵌入期权的价值和隐含有期权的债券的价值，然后计算隐含有期权债券的久期和凸度。

The paper at first uses the Hull-White option model to compute the value of option embedded in bond and the value of bond with embedded option , and then computes duration and convexity of bonds with embedded option .

本文用奇异扰动方法讨论了具有小Knudsen数的Boltzmann方程的正规解，证明把Hil-bert展开和Enskog展开加以改进可以消除久期项。

In this paper , we use a kind of singular perturbation method to find the normal solution of the Boltzmann equation with small Knudsen number . It is proved that the secular terms may be removed by improving the Hilbert expansion and Enskog expansion .

最后在结合国债市场数据的基础上，估计出随机久期模型的参数，并就各种久期模型对债券利率风险的免疫效果进行了对比，结果表明Moreno双因子久期模型能更好地度量利率风险。

Finally in conjunction with government bonds market data to estimate the parameters of the stochastic duration model , and compare the immunization effect of the various duration models . This paper finds that two-factor Moreno duration model is the best measurement of interest rate risk .

本文首先使用Nelson-Siegel模型拟合出2002年沪深交易所国债的利率期限结构，然后运用2因子、3因子主成分法及久期、凸度法对交易所上市的债券进行模拟套期保值。

By using Nelson - Siegel model , the paper derives the term structures for bonds in Shanghai & Shenzhen Security Exchange in 2002 , and use two - and three - principal components as well as traditional duration and convexity to simulate a hedging of portfolios .

氢原子斯塔克效应中久期方程的简化公式

Simplified Formula of Secular Equation for Hydrogen Atom in Stark Effect

国债价格行为的布朗桥运动模型与久期方法比较

Brown Motion and Duration Method in Government Bonds ' Price Behavior

一个债券的利率风险的最好评价是它的久期。

A bond 's interest-rate risk is best measured by its duration .

于是产生了有效久期的衡量指标。

So we select effective duration as the measuring index .

对于风险回避型的投资者而言，幂久期方法更具吸引力。

For risk-averse investors , exponential duration is more attractive .

用久期&凸度方法预测企业可转换债券的利率风险

Duration and Convexity Method in Forecasting the Interest Rate Risk of Convertible Bond

浮动利率债券久期和凸性的研究

A Study on Duration and Convexity of Floating-Rate Notes

运用久期模型进行利率风险管理的若干问题分析

An Analysis of Some Problems in Managing Interest Rate Risk with Duration Model

投资者可购买久期长的成长型股票。

Investors pay up for long duration Growth stocks .

久期在债券利率风险度量中的应用及修正

Application and Modification of Duration in Measurement of Interest Rate Risk of Bonds