An Modified Vasicek Model Of The Term Structure Of Interest Rates And Its Empirical Study

Term structure of interest rates,also known as the yield curve,is a curve composed of yields with different terms at a certain time. The study of term structure of interest rates has become an important basic research of the micro-finance and macroeconomics. Foreign scholars have done deeply research in this field, obtaining rich achievements of theory, model and empirical research. However, most domestic scholars have done much less in this field, just focusing on the empirical study, lacking of related theoretical and model innovation, which relates with the imperfections of China’s financial market——especially the bond market. Facing the unbalanced bond market, the restarting of treasury bond future, and other practical problems, we urgently need more precise term structure model to analyze China’s actual situation deeply. It is just under this circumstance that this paper attempts to modify the defect of linearity of Vasicek model, and proposes a nonlinear model.Based on the carding of the static estimation of term structure of interest rates and dynamic models, this paper tests the nonlinearity of drift function of the model of interest rate, and proposes a nonlinear modified Vasicek model, whose drift function contains the squared term of interest rate, and then uses the OLS method to test the validity of the model.The paper uses a generalized NS model to acquire the spot rates,selecting three interest rates with different term(short-term, medium-term and long-term interest rates),then uses MCMC method to estimate the modified Vasicek model,and tests the validity of the model using the method of Monte Carlo Simulation. The paper applies the model to price the treasury bonds after the test, and constructs a modified model of pricing error to overcome the pricing error of the model,and then uses the estimated pricing error model to modify the pricing of treasury bonds.Conclusions of this study are:The drift function of instantaneous rate process presents obvious nonlinear characteristic;The goodness of fit and overall significance of the modified Vasicek model are better than Vasicek model;the Monte Carlo Simulation error of modified Vasicek model estimated by short-term and medium-term interest rates significantly reduces, but the simulation error estimated by long-term interest rate doesn’t reduce significantly. The volatilities of the three models with different terms present negative correlation with the remaining term, which is accorded with the theoretical expectation, and the results of the Granger causality test of the three interest rates also prove this point; The results of bond pricing show that the pricing error presents positive correlation with the remaining term. Assuming the liquidity premium and other factors is a function of remaining term, the paper proposes a modified model of pricing error, showing that the result of error correction is ideal, for example, the modified price of bond with the longest remaining term is very close to the market price.Although the modified Vasicek model can not overcome all flaws of the Vasicek model, the extension on the base model (such as the extension to stochastic volatility model,Regime-Switching model,jump-diffusion model or threshold model), and it will both greatly enrich the term structure model and solve the practical problems such as bonds pricing in a better way.