Affine Term Structure Of Interest Rate:Theory And Applications

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.