仿射利率期限结构：理论和应用
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摘要
利率期限结构是利率衍生品定价和风险管理的基础,也是研究微观和宏观变量之间关系的桥梁,同时还是货币政策制定和实施效果检验的依据,因此长期以来一直是金融理论与宏观经济理论研究的中心话题。
仿射期限结构模型本质上假设期限结构的动态性依赖于可观测或不可观测的因子,因子的动态性由随机过程决定,而债券价格是因子的指数仿射形式,而到期收益是因子的仿射函数。这一仿射架构使一些衍生品定价和信用风险问题有闭式解,而且模型本身能灵活刻画利率的动态行为特征,能便宜考察不同驱动因素对期限结构的影响机制并给出恰当解释,还能方便的用来分解利率中隐含的经济信息。
就我国来说,宏观经济政策调控的主方向就是要逐步推进利率市场化、货币政策逐步转向以利率为主的价格调控。而当前,无论是基准利率的选择还是货币政策的制定及其传导机制,我国与其他国家都有不同的特征,这样深刻分析我国利率的性态特征,掌握利率的行为演化规则,发掘宏观政策变化对利率变动的影响,成为利率市场化和深化金融市场的基础。
2011年我国长短期收益利差进一步扩大,长期利率对短期利率的敏感度进一步降低,在短期利率升高时长期利率出现了减小的现象。这种现象与美国在1990到1996年、从2002到2006年两个时间段时,以期通过加息政策提高远期利率而结果却出现了短期利率上升,但长期利率反而下降的所谓“格林斯潘之谜”现象极为一致。风险溢价是区分纯预期理论和理性预期理论的关键,也是预期假设成立与否的决定因素。如果预期理论成立,当短期利率上升时,长期利率也应该相应提高,可见在我国这种理论作用的发挥受到了限制,长短期利率变化的关系与理论并不一致,其适用性值得进一步深思探讨。
我国当前经济发展面临着诸多不确定性,特别是在改革开放不断开创新局面的情形下,融入世界经济活动的程度日益加深,这样不仅是国内的,国外的经济波动对我国经济状况也产生了越来越大的影响。2008年开始的经济危机犹在,各国货币量化宽松政策层出不穷,物价高企,我国2009年国务院明确提出“管理好通胀预期,保持价格基本稳定”且已被列为“十二五”规划中经济社会发展的主要目标之一。由于经济周期波动使利率期限结构发生变化、宏观因子变量(如经济政策、供给与需求)的变化对利率期限结构产生重要影响。将金融市场理论和宏观经济理论结合,将可观测的宏观因子和不可观测的潜在因子结合起来解析供给冲击、货币政策及经济不确定性对预期通胀、溢价及期限结构的影响,分析利率期限结构、预期通胀、期限溢价的典型特征,这对于完善我国利率期限结构理论与货币政策理论将有重要意义。
从上述角度出发,本文对仿射期限结构模型的相关理论进行了梳理,结合我国实际利率数据针对不同的仿射模型进行了应用研究。具体说主要做了以下五方面的工作：
第一：在国内外学者的研究基础上,详细论述了利率期限结构的研究历程、方法及仿射期限结构模型的研究现状。然后,主要从风险中性定价开始,介绍了仿射模型的定义、债券定价的微分方程表示、仿射一般均衡、仿射模型下风险价格的设定及仿射模型的参数求解方法。而且在考察了基本仿射模型之外,又引入了仿射跳扩散模型、简约式和结构式宏观金融模型,一类特殊的仿射模型既NS类模型及其动态NS和无套利NS模型。
第二：进行了短期利率的行为特征研究,主要借助含有泊松跳和异方差的单因子CKLS模型建模,结合差分方程的滞后算子表示,借助似然函数法进行参数估计。研究认为单因子模型中,加入跳和异方差的CKLS模型更适合刻画我国短期利率行为,它能够同时捕获利率的连续和间断性变化,恰当反应短期利率的均值回复性,且具有较好的样本外预测能力。
第三：基于我国利率数据考察了远期利率预期和风险溢价的相关问题,主要是详细的阐述了远期利率仿射模型、风险溢价的模型、因子构建和选择的过程,并对利率预期和溢价进行了探讨。研究认为,回报因子有助于预测远期风险溢价；我国风险溢价具有时变性,整体平均为正,但在2005年到2007年一度为负；我国利率中存在的格林斯潘现象主要由短期利率预期变大、风险溢价下降引起。
第四：应用宏观金融模型和潜在因子模型对利率建模,借助极大似然函数法对参数进行求解,随后应用方差分解、脉冲响应和因子回归等技术,考察了两类模型对利率数据的拟合、预测能力；并且以宏观金融模型为基础,分析了因子对我国收益的影响机制。研究认为,宏观金融模型比潜在因子模型更适合刻画我国债券收益结构,在利率拟合,预测能力上占优,同时宏观因子也能部分解释潜在因子；宏观因子和潜在因子对真实收益和名义收益作用方式及影响程度都不尽相同,宏观因子对收益的影响显著高于潜在因子,是引起预测误差的主要变量。
第五：在第七章基础上考察了以宏观金融模型为基础结合仿射一般均衡方法而分解出的不同期限的通胀预期的性态,具体的分析了通胀预期与通胀率的关系、通胀预期的影响因素、通胀预期的理性与适应性等问题。研究认为,文中分解出的短期和中期通胀预期与通胀率的动态关联性较强；分解出通胀预期都不是理性预期,但中期和长期预期是适应性预期；发现CPI是影响通胀预期的最重要因素,其影响效果随着期限增加而增大；文中短期预期事前和事后预测能力都优于央行调查预期和朗润预期,而中期预期的预测能力与朗润预期预测能力相当但优于调查预期。
本文的创新之处在于：
1.在CKLS模型中引入跳和异方差项并结合似然函数进行了参数估计,从而深入分析了短期利率的动态行为；
2.根据我国远期利率数据特征,引入回报预测因子且给出简易可行的风险价格形式,进行建模和参数估计后,进而考察了远期风险溢价、利率预期的性质；
3.结合了宏观金融模型、潜在因子模型和仿射一般均衡框架,且通过构建恰当的宏观因子和收益方程的似然函数进行参数求解,对比的考察了模型对收益数据的刻画能力和因子对收益曲线的影响机制,同时分解出了不同期限的通胀预期并对其性态特征进行了研究。
通过研究以期为国家有针对性的制定和实施宏观调控政策提供理论参考,不过,尽管笔者在研究过程中,力求全文尽善尽美,但是必定会有值得推敲之处,仍需在将来的工作和学习中进一步完善。
The term structure of interest rate is a hot research for macro and micro-economics always, and how to accurately depict its behavior change is the key part of the research. The term structure of interest rates is the basis of the interest rate derivatives pricing and risk management, and is the medium of studying the relationship between micro and macro variables.In the same time it is the key factor of macro policy formulation, implementation and inspection of implementation effect.
The affine term structure model assumes that the dynamics of the term structure relies on observable or unobservable factors, while the dynamics of the factors are determined by a random process. Thus under these conditions bond price is exponential affine formation and the yield to maturity is affine process of these factors. Within this framework, we can get closed-form solution of some derivatives products pricing issues and estimate easily the parameters. The affine models have the flexibility to characterize the dynamic behavior of the interest rate and reflect the mechanism for the evolution of interest rates. Of course it will help to investigate the effect of different driving factors on the term structure and provide us the proper interpretation.
For China, the general direction of macro-policy regulation will be that improving market-base of interest rates and converting monetary policy to policy control which based on interest rate price. However as so far, our country has the different characteristics, for example the choice of the benchmark market interest rate or monetary policy formulation and conduction mechanism, with others. So, here analyzing the characteristics of interest rate deeply, mastering the behavior of the interest rate rule of evolution, and exploring the influence of macroeconomic policy changes on changes of interest rate, which would be the basis of interest rate marketing and deepen the reform of the financial markets.
In2011, the difference between short and long term bond yields further expanded and the dependent-sensitivity of long-term interest rates to short-term interest rate going further weakened. This phenomenon is very consistent with US Greenspan mystery phenomenon, which took place in the US between1990and1996, and2002to2006. In that time monetary authorities hope improving long-term interest rates by raising interest rates policy, but the surprising result was that though there was a rise in short-term interest rates but long-term interest rate declined. The risk premium is the key distinction between the pure expectations assumption and rational expectations assumption, at the same time it is the determinants which indicates whether expectations assumption been formed or not. Expectations theory shows that long-term interest rates should also reach a corresponding increase when short-term interest rates to rise. However obviously its applicability is worth pondering further because the effect of this theory is considerable restricted and the changing relationship between long-term and short-term interest rates is not consistent in China.
Our county economic development faces many uncertainties always, especially the more deepening extent of China's integration into the world economy in recent years, the more growing affected by worldwide economic crisis and economic volatility. The lingering impact of the financial crisis starting in2008, and the emergence in endless of quantitative easing monetary policy, and the common occurrence of high commodity prices, which all augur instability. In2009, managing inflation expectations and maintain the general stability of prices has been listed as one of the main objectives of economic and social development in the "12th Five-Year Plan" by the State Council clearly.
The fluctuations and change in the economic will alter the term structure of interest rates. The volatility of macroeconomic factor variables, such as economic policy, supply and demand, has an important impact on the term structure. Therefore combining the theory of financial markets to macroeconomic theory, and combining the observable macro factors and the unobservable potential factors will help to analytic the impact of the supply shocks, monetary polices, uncertainty on the expected inflation and the term structure. Also analyzing the typical characteristics of the term structure, inflation expectations and term premium, will have important theoretical significance for perfecting the term structure theory and monetary policy theory.
Base on above, we outline the theory of affine term structure model, and use the different affine model combined with our country interest rate data to research essential attributes of interest rate.In all, we discussed mainly the following five aspects.
First, on the basis of research of scholars both at home and abroad, we study on the research status of term structure and affine term structure model, the methods of interest rate model be shown. In the part of affine model theory, we analyze the definition of affine model, the differential equations under the affine model pricing, the affine general equilibrium model, the forms of the marker price of risk and estimations of parameters under affine model. Then, we analyze the extent contents of affine term structure model. The affine jump-diffusion model, the simple and structural Macro-financial model will be discussed, so as to the special NS model with its dynamic and no-arbitrage forms.
Second, we study the character of short term rate based on the single-factor CKLS model with jump and heteroscedasticity terms. We found that the CKLS model which contained the jump and heteroscedasticity terms can characterize the dynamic behavior of interest rates proper, and it have the more ability to capture its continuous and discontinuous change, and to portray interest rates mean reversion appropriately.
Third, we empirically research the forward rate expectations and risk-premium base on our country forward rate data. We specified the process of constructing model and selecting factors, and the characteristics of the decomposed forward interest rate expectations and risk premium. The results showed that the return factor help to predict forward-term risk premium. Risk premium always varied with time and gone into negative in2005to2007at one time. The same time, we found that Greenspan phenomenon of our interest rates mainly caused by the lager short-term interest rates expectations and by the far decreasing risk premium.
Fourth, based on the variance decomposition, impulse response and factor regression, we test the different ability of fitting and predicting for the rate of macro-financial model and latent factor model. By employing the macro-financial model we analyzed the mechanism on factors effect yield. The empirical results showed that the macro-financial model has the more ability to depict the bonds term structure than latent-factor model. The macro factors and latent factors have different role on the nominal rate and rear rate. The impact of macro factors which was the main variables of causing the prediction error was significantly higher than the potential factors.
Finally, on the basis of macro-finance model combined with the affine general equilibrium model we decomposed the inflation expectations. Here we investigates the decomposed different term inflation expectations, a detailed analysis of the relationship between inflation expectations and the inflation rate, the inflation expectations impact factors, and problems about rationality and adaptability will be given. The results show that the short and medium expectations and the real inflation have strong influence each other, however the long term expectations and the real inflation have influence relatively weak each other. All term expectations are not the rational expectations, but the medium and long expectations are adaptive expectations. Here to expectations, the CPI is the most important influencing factor and its effect will increase with time. The short expectations have the better predictive power of ex ante and ex post than the investigation expectations and Lang Run expectations, and the ability of medium expectations no less than Lang Run's but better than the expectations of the depositor-survey.
Above all, we discuss the theory of affine term structure model, and give some commentary on its development and application. The innovation point of this paper as follows.
First, we in-depth analyze the dynamic behavior of the short-term interest rates by mean of CKLS model in which the jump item and heteroscedasticity item was added, and its parameters were estimated by the likelihood function.
Second, this paper models the forward rate and forward premium through introducing the return forecast factor and the simple feasible price process, after estimating the parameters we examine the nature characteristics of term premium and interest rate expectations.
Third, with the help of building the appropriate macroeconomic factors and the likelihood function of yield equations based on macro-finance model combined with latent-factor model and affine general equilibrium framework, the model's ability of data depict are investigated and the character of decomposed different term inflation expectations are analyzed.
Through my research, this paper hopes to provide a theoretical reference to targeted the formulation and implementation of macroeconomic regulation. In the course of the study, despite the author strive to be more complete, perfect, however the matters is still inadequate and still need to be improved further in the future.
仿射期限结构模型本质上假设期限结构的动态性依赖于可观测或不可观测的因子,因子的动态性由随机过程决定,而债券价格是因子的指数仿射形式,而到期收益是因子的仿射函数。这一仿射架构使一些衍生品定价和信用风险问题有闭式解,而且模型本身能灵活刻画利率的动态行为特征,能便宜考察不同驱动因素对期限结构的影响机制并给出恰当解释,还能方便的用来分解利率中隐含的经济信息。
就我国来说,宏观经济政策调控的主方向就是要逐步推进利率市场化、货币政策逐步转向以利率为主的价格调控。而当前,无论是基准利率的选择还是货币政策的制定及其传导机制,我国与其他国家都有不同的特征,这样深刻分析我国利率的性态特征,掌握利率的行为演化规则,发掘宏观政策变化对利率变动的影响,成为利率市场化和深化金融市场的基础。
2011年我国长短期收益利差进一步扩大,长期利率对短期利率的敏感度进一步降低,在短期利率升高时长期利率出现了减小的现象。这种现象与美国在1990到1996年、从2002到2006年两个时间段时,以期通过加息政策提高远期利率而结果却出现了短期利率上升,但长期利率反而下降的所谓“格林斯潘之谜”现象极为一致。风险溢价是区分纯预期理论和理性预期理论的关键,也是预期假设成立与否的决定因素。如果预期理论成立,当短期利率上升时,长期利率也应该相应提高,可见在我国这种理论作用的发挥受到了限制,长短期利率变化的关系与理论并不一致,其适用性值得进一步深思探讨。
我国当前经济发展面临着诸多不确定性,特别是在改革开放不断开创新局面的情形下,融入世界经济活动的程度日益加深,这样不仅是国内的,国外的经济波动对我国经济状况也产生了越来越大的影响。2008年开始的经济危机犹在,各国货币量化宽松政策层出不穷,物价高企,我国2009年国务院明确提出“管理好通胀预期,保持价格基本稳定”且已被列为“十二五”规划中经济社会发展的主要目标之一。由于经济周期波动使利率期限结构发生变化、宏观因子变量(如经济政策、供给与需求)的变化对利率期限结构产生重要影响。将金融市场理论和宏观经济理论结合,将可观测的宏观因子和不可观测的潜在因子结合起来解析供给冲击、货币政策及经济不确定性对预期通胀、溢价及期限结构的影响,分析利率期限结构、预期通胀、期限溢价的典型特征,这对于完善我国利率期限结构理论与货币政策理论将有重要意义。
从上述角度出发,本文对仿射期限结构模型的相关理论进行了梳理,结合我国实际利率数据针对不同的仿射模型进行了应用研究。具体说主要做了以下五方面的工作：
第一：在国内外学者的研究基础上,详细论述了利率期限结构的研究历程、方法及仿射期限结构模型的研究现状。然后,主要从风险中性定价开始,介绍了仿射模型的定义、债券定价的微分方程表示、仿射一般均衡、仿射模型下风险价格的设定及仿射模型的参数求解方法。而且在考察了基本仿射模型之外,又引入了仿射跳扩散模型、简约式和结构式宏观金融模型,一类特殊的仿射模型既NS类模型及其动态NS和无套利NS模型。
第二：进行了短期利率的行为特征研究,主要借助含有泊松跳和异方差的单因子CKLS模型建模,结合差分方程的滞后算子表示,借助似然函数法进行参数估计。研究认为单因子模型中,加入跳和异方差的CKLS模型更适合刻画我国短期利率行为,它能够同时捕获利率的连续和间断性变化,恰当反应短期利率的均值回复性,且具有较好的样本外预测能力。
第三：基于我国利率数据考察了远期利率预期和风险溢价的相关问题,主要是详细的阐述了远期利率仿射模型、风险溢价的模型、因子构建和选择的过程,并对利率预期和溢价进行了探讨。研究认为,回报因子有助于预测远期风险溢价；我国风险溢价具有时变性,整体平均为正,但在2005年到2007年一度为负；我国利率中存在的格林斯潘现象主要由短期利率预期变大、风险溢价下降引起。
第四：应用宏观金融模型和潜在因子模型对利率建模,借助极大似然函数法对参数进行求解,随后应用方差分解、脉冲响应和因子回归等技术,考察了两类模型对利率数据的拟合、预测能力；并且以宏观金融模型为基础,分析了因子对我国收益的影响机制。研究认为,宏观金融模型比潜在因子模型更适合刻画我国债券收益结构,在利率拟合,预测能力上占优,同时宏观因子也能部分解释潜在因子；宏观因子和潜在因子对真实收益和名义收益作用方式及影响程度都不尽相同,宏观因子对收益的影响显著高于潜在因子,是引起预测误差的主要变量。
第五：在第七章基础上考察了以宏观金融模型为基础结合仿射一般均衡方法而分解出的不同期限的通胀预期的性态,具体的分析了通胀预期与通胀率的关系、通胀预期的影响因素、通胀预期的理性与适应性等问题。研究认为,文中分解出的短期和中期通胀预期与通胀率的动态关联性较强；分解出通胀预期都不是理性预期,但中期和长期预期是适应性预期；发现CPI是影响通胀预期的最重要因素,其影响效果随着期限增加而增大；文中短期预期事前和事后预测能力都优于央行调查预期和朗润预期,而中期预期的预测能力与朗润预期预测能力相当但优于调查预期。
本文的创新之处在于：
1.在CKLS模型中引入跳和异方差项并结合似然函数进行了参数估计,从而深入分析了短期利率的动态行为；
2.根据我国远期利率数据特征,引入回报预测因子且给出简易可行的风险价格形式,进行建模和参数估计后,进而考察了远期风险溢价、利率预期的性质；
3.结合了宏观金融模型、潜在因子模型和仿射一般均衡框架,且通过构建恰当的宏观因子和收益方程的似然函数进行参数求解,对比的考察了模型对收益数据的刻画能力和因子对收益曲线的影响机制,同时分解出了不同期限的通胀预期并对其性态特征进行了研究。
通过研究以期为国家有针对性的制定和实施宏观调控政策提供理论参考,不过,尽管笔者在研究过程中,力求全文尽善尽美,但是必定会有值得推敲之处,仍需在将来的工作和学习中进一步完善。
The term structure of interest rate is a hot research for macro and micro-economics always, and how to accurately depict its behavior change is the key part of the research. The term structure of interest rates is the basis of the interest rate derivatives pricing and risk management, and is the medium of studying the relationship between micro and macro variables.In the same time it is the key factor of macro policy formulation, implementation and inspection of implementation effect.
The affine term structure model assumes that the dynamics of the term structure relies on observable or unobservable factors, while the dynamics of the factors are determined by a random process. Thus under these conditions bond price is exponential affine formation and the yield to maturity is affine process of these factors. Within this framework, we can get closed-form solution of some derivatives products pricing issues and estimate easily the parameters. The affine models have the flexibility to characterize the dynamic behavior of the interest rate and reflect the mechanism for the evolution of interest rates. Of course it will help to investigate the effect of different driving factors on the term structure and provide us the proper interpretation.
For China, the general direction of macro-policy regulation will be that improving market-base of interest rates and converting monetary policy to policy control which based on interest rate price. However as so far, our country has the different characteristics, for example the choice of the benchmark market interest rate or monetary policy formulation and conduction mechanism, with others. So, here analyzing the characteristics of interest rate deeply, mastering the behavior of the interest rate rule of evolution, and exploring the influence of macroeconomic policy changes on changes of interest rate, which would be the basis of interest rate marketing and deepen the reform of the financial markets.
In2011, the difference between short and long term bond yields further expanded and the dependent-sensitivity of long-term interest rates to short-term interest rate going further weakened. This phenomenon is very consistent with US Greenspan mystery phenomenon, which took place in the US between1990and1996, and2002to2006. In that time monetary authorities hope improving long-term interest rates by raising interest rates policy, but the surprising result was that though there was a rise in short-term interest rates but long-term interest rate declined. The risk premium is the key distinction between the pure expectations assumption and rational expectations assumption, at the same time it is the determinants which indicates whether expectations assumption been formed or not. Expectations theory shows that long-term interest rates should also reach a corresponding increase when short-term interest rates to rise. However obviously its applicability is worth pondering further because the effect of this theory is considerable restricted and the changing relationship between long-term and short-term interest rates is not consistent in China.
Our county economic development faces many uncertainties always, especially the more deepening extent of China's integration into the world economy in recent years, the more growing affected by worldwide economic crisis and economic volatility. The lingering impact of the financial crisis starting in2008, and the emergence in endless of quantitative easing monetary policy, and the common occurrence of high commodity prices, which all augur instability. In2009, managing inflation expectations and maintain the general stability of prices has been listed as one of the main objectives of economic and social development in the "12th Five-Year Plan" by the State Council clearly.
The fluctuations and change in the economic will alter the term structure of interest rates. The volatility of macroeconomic factor variables, such as economic policy, supply and demand, has an important impact on the term structure. Therefore combining the theory of financial markets to macroeconomic theory, and combining the observable macro factors and the unobservable potential factors will help to analytic the impact of the supply shocks, monetary polices, uncertainty on the expected inflation and the term structure. Also analyzing the typical characteristics of the term structure, inflation expectations and term premium, will have important theoretical significance for perfecting the term structure theory and monetary policy theory.
Base on above, we outline the theory of affine term structure model, and use the different affine model combined with our country interest rate data to research essential attributes of interest rate.In all, we discussed mainly the following five aspects.
First, on the basis of research of scholars both at home and abroad, we study on the research status of term structure and affine term structure model, the methods of interest rate model be shown. In the part of affine model theory, we analyze the definition of affine model, the differential equations under the affine model pricing, the affine general equilibrium model, the forms of the marker price of risk and estimations of parameters under affine model. Then, we analyze the extent contents of affine term structure model. The affine jump-diffusion model, the simple and structural Macro-financial model will be discussed, so as to the special NS model with its dynamic and no-arbitrage forms.
Second, we study the character of short term rate based on the single-factor CKLS model with jump and heteroscedasticity terms. We found that the CKLS model which contained the jump and heteroscedasticity terms can characterize the dynamic behavior of interest rates proper, and it have the more ability to capture its continuous and discontinuous change, and to portray interest rates mean reversion appropriately.
Third, we empirically research the forward rate expectations and risk-premium base on our country forward rate data. We specified the process of constructing model and selecting factors, and the characteristics of the decomposed forward interest rate expectations and risk premium. The results showed that the return factor help to predict forward-term risk premium. Risk premium always varied with time and gone into negative in2005to2007at one time. The same time, we found that Greenspan phenomenon of our interest rates mainly caused by the lager short-term interest rates expectations and by the far decreasing risk premium.
Fourth, based on the variance decomposition, impulse response and factor regression, we test the different ability of fitting and predicting for the rate of macro-financial model and latent factor model. By employing the macro-financial model we analyzed the mechanism on factors effect yield. The empirical results showed that the macro-financial model has the more ability to depict the bonds term structure than latent-factor model. The macro factors and latent factors have different role on the nominal rate and rear rate. The impact of macro factors which was the main variables of causing the prediction error was significantly higher than the potential factors.
Finally, on the basis of macro-finance model combined with the affine general equilibrium model we decomposed the inflation expectations. Here we investigates the decomposed different term inflation expectations, a detailed analysis of the relationship between inflation expectations and the inflation rate, the inflation expectations impact factors, and problems about rationality and adaptability will be given. The results show that the short and medium expectations and the real inflation have strong influence each other, however the long term expectations and the real inflation have influence relatively weak each other. All term expectations are not the rational expectations, but the medium and long expectations are adaptive expectations. Here to expectations, the CPI is the most important influencing factor and its effect will increase with time. The short expectations have the better predictive power of ex ante and ex post than the investigation expectations and Lang Run expectations, and the ability of medium expectations no less than Lang Run's but better than the expectations of the depositor-survey.
Above all, we discuss the theory of affine term structure model, and give some commentary on its development and application. The innovation point of this paper as follows.
First, we in-depth analyze the dynamic behavior of the short-term interest rates by mean of CKLS model in which the jump item and heteroscedasticity item was added, and its parameters were estimated by the likelihood function.
Second, this paper models the forward rate and forward premium through introducing the return forecast factor and the simple feasible price process, after estimating the parameters we examine the nature characteristics of term premium and interest rate expectations.
Third, with the help of building the appropriate macroeconomic factors and the likelihood function of yield equations based on macro-finance model combined with latent-factor model and affine general equilibrium framework, the model's ability of data depict are investigated and the character of decomposed different term inflation expectations are analyzed.
Through my research, this paper hopes to provide a theoretical reference to targeted the formulation and implementation of macroeconomic regulation. In the course of the study, despite the author strive to be more complete, perfect, however the matters is still inadequate and still need to be improved further in the future.
引文
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