An Empirical Analysis For The Term Structure Of Interest Rates In China Based On Vasicek And CIR Models

An Empirical Analysis for the Term Structure of Interest Rates in China Based on Vasicek and CIR ModelsThe term structure of interest rates has always been the basis topic in the financial research,with the study for term structure of interest rates,it is helpful to do financial interest rates risk management for institutions,and it is also valuable to do economic analysis and policy constitution.This paper first briefly introduced the term structure of interest rates and reviewed the basic theory of the term structure of interest rates at home and abroad. The basis theory consists of three theories:expectations hypothesis,market segmentation theory and liquidity preference hypothesis.These three theories are qualitative analysis to study the shape of yield curve and its causes.These theories are foundation of modeling,comprehensive analysis,as well as contrast,and provide a reference theory of practical application.In the subsequent introduction of the dynamic model,we first introduced equilibrium model,no-arbitrage model and the general expansion model,which are quantitative research combined with the qualitative theories and mathematical models play an important role in these quantitative theories.Then in the dynamic models,we found there was a assumption that the instantaneous interest rate volatility is fixed in the Vasicek mode,and the instantaneous interest rate volatility was only associated with the root-mean-square of current interest rates.However,in the actual economic life,instantaneous interest rate volatility will be affected by some other factors,such as time,external shocks. Therefore,we added GARCH model in Vasicek model and CIR mode to simulate the dynamic changes,which are Vasicek-GACH(1,1) model and the CIR-GACH(1,1) model.In this paper we put up an empirical analysis,using the overnight interest rate of CHIBOR to substitute for short-term interest rate,the sample is from Jul 1996 to Mar 2008.First,we analysis the data statistical character,and qualitatively described the trends of interest rates in line with the state policy.We used ADF test to analysis the data stability,test results showed that the samples was a stable range of timeCseries, in other words,there was mean-reversion process,so the sample can represent the short-term interest rates to empirical analysis.Then,we simulated Vasicek and CIR model,adopt the method of least squares and weighted least squares.Although the degree of simulation is high,statistics also obvious,by observing the residual curve of regression equation,we found the phenomenon of residual fluctuations. Fluctuations over a period of time is big,but the fluctuations in another period of time is small,we found the existence of ARCH effects in residual sequence by ARCH-LM test.Third,From the empirical simulation of the Vasicek-GACH(1,1) model and the CIR-GARCH(1,1),found that compared to the original Vasicek model and CIR model,log-likelihood value of Vasicek-GARCH(1,1) model and the CIR-GARCH (1,1) model have become larger,which significantly improve the fitting accuracy; Finally,respectively gave fitting Figs of Vasicek-GARCH(1,1) model and the CIR-GARCH(1,1) model.In a comparative analysis of empirical models,we also found that although parameters were different,but there were some characteristics in common,which were that the fluctuations of Interbank Offered Rate was small and adjustment was not dramatic(the adjust speed were all less 0.3).The main conclusions of this paper are:(1) CHIBOR has not a unit root,there is obvious correlation between Central Bank interest rates and market rates,to a certain extent,market rates can reflect the central bank monetary policy and fiscal policy information.;(2) In the model of term structure of interest rates,Equilibrium model of the single-factor model is the simplest model,for example Classic Vasicek model and CIR model,but the degree of simulation is high,statistics also obvious,these simple models can describe the dynamic evolution of China's short-term interest rate;(3) Although the CIR model contains a wealth constraints,the time consumption preferences,risk aversion,factors resulting in the risk,investment portfolio including a large number of compensation,and many other advantages,but empirical results showed that the Vasicek model could better estimated simulate the data of China's financial market than CIR model;(4) There was residual heteroscedasticity sequence in the overnight interest rate of CHIBOR,interest rates changes were impacted by historical information,at the same time,the term structure of interest rates with the variance model is incompatible with the inter-bank lending market actual interest rates,the Vasicek-GARCH(1,1) model and the CIR-ARCH(1,1) model can better simulate the behavior of China's short-term interest rates,especially Vasicek-GARCH(1,1);(5) Compared to CIR-GARCH(1,1),Vasicek-GARCH(1,1) better simulate the inter-bank lending market interest rates,explain China's money market interest rates changes very well.China's market interest rates has an obvious mean reversion,market interest rates over a period of time will get out of the long-term average,but over time,mean-reversion in interest rates under the driving factor,the interest rate will return to the vicinity of the long-term average.