Study On Term Structure Of Interest Rates And Stochasic Rate Based On Vasicek And CIR Models

Interest rate is an important economic indicator and becom-ing prominent role increasingly in the financial markets, therefore, changes of interest rates has a real demand for research, analysis and estimates of interest rates has become a fundamental problem in the field of financial engineering.Term structure of interest rates which is an interest rate curve composed of different interest rate period with the same risk and liquidity at some time-point. We introduces the theory of term structure of interest rates in the second chapter of the thesis. The theory term structure of interest rates has developed through two stages:before 70 years of the 20th century, it was mainly stage of qualitative description:late 70s,the modern theory of term structure of interest rates was developing, it was mainly the stage of quantitative building models.1. Vasicek model, dynamic changes of the instantaneous in- terest rates which are assumed follow the stochastic differential equation:Which (?)>0,μandσare constants.(?)is the average response coefficient,μis the average response level of the instantaneous interest rates,σis the stochastic volatility of the interest rates, W is the Brownian motion.2.CIR,model was a single factor model of equilibrium inter-est rate which was made by Cox,Ingersoll and Ross in 1985:3.Ho-Lee model,was proposed through the use of bond graph form of a binary tree.Short-term interest rates meet the following stochastic equation:θ(t) was determined byθ(t)=(?)+σ2t,f(0,t)was the forward interest rate.4.HJM model,was proposed by Heath,Jarrow and Mor-ton in 1992.The main object of the model is the instantaneous forward rate,It assumed that dynamic changes in the instanta-neous forward rate f(t,T)at time T followed the under stochastic differential equation: f(t,T) was the instantaneous forward rate at t which wsa over at T.With the complexity of financial markets, monetary policy and interest rate markets, the constant interest rate model can not reflect the image of changes in interest rates, the appearance of the stochastic interest rate model solves this problem. In the third chapter focuses on the stochastic differential equation in the article of the effects of the monetary policy regime shift to inflation targeting on the real interest rate in the United Kingdom which was written by Andreas Reschreiter.It is taken the case of the United Kingdom in 1992 as an example in this thesis, and it built a stochastic interest rate model of continuous change over time based on Vasicek and CIR models. This is a simple stochastic process of continuous time, describe the changes of the real interest rates, and the change in each variable is a random process.This model mainly researched the random effects of mone-tary policy on real interest rates. As can be seen from the chart, the results suggest that the central bank can affect the stochastic properties of the real interest rate through the choice of mone-tary policy regime over a long period of time. The mean-reverting level of the real interest rate has decreased from 5.1 monetary pol-icy to inflation targeting. In addition, the shift in monetary policy regime to inflation targeting has reduced the volatility of the real interest rate and increased the persistence of real interest rate deviations from the mean. In addition, the implementation of monetary policy, a certain delay.The fourth chapter of the thesis introduces the term struc-ture of interest rates and the application. It has great significance on the implementation of monetary policy and the development of interest rate marketed that focus on the term structure of in-terest rates in China. However, China has lagged behind the development of bond market, the reseach of the term structure of interest rates in the Chinese market is still in a primary level, and we shuold establish the formation of a consistent point of view and conclusions.