The Construction Of Interest Rate Model Based On Multivariate Closed-form Logarithmic Likelihood Expansions

Since the People’s Bank of China announced the reform of the exchange rate, Short term interest rate in asset pricing, interest rate term structure and macroeconomic model has been widely used, is one of the most important economic variables in the financial. With the rapid development of China’s interest rate market, the urgency and value of short-term interest rate research is increasing. In view of this, this paper takes the continuous time model to study the dynamic change of short-term interest rate.The parameter estimation of the continuous time interest rate model is a difficult point. Generally, the two fork tree method, effective moment estimation, the method of the simulation, MCMC method, etc., but the obtained parameter estimates are often not accurate enough. In this paper, the maximum likelihood estimation is used to estimate the parameters of a continuous time interest rate model.In this paper, we select the single factor short-term interest rate model, select the CKLS model from many short-term interest rate model to describe the short-term interest rate, and then make the fluctuation rate of interest rate random change, so that it can also meet the continuous time diffusion process, and get the short-term interest rate dispersion model. Based on the two dimensional stochastic volatility interest rate model, a two dimensional jump diffusion model is formed.This paper uses the maximum likelihood estimation method based on closed form log likelihood Taylor to approximate the real short-term interest rate, and then selects the 7 day bond repurchase interest rate variety that is R007 to make the model, improve the parameters of CKLS single factor model, improve the parameters of the model and obtain the short-term interest rate.In this paper, three different models are estimated by two methods, the maximum likelihood estimation and the generalized moment estimation, and the maximum likelihood estimation is better than the generalized moment estimation using Monte Carlo simulation. The closed expression of the rate of the transfer density is generally not obtained, which hinders the use of maximum likelihood estimation. This paper uses the following methods, when the interest rate model is a single factor model, the rate of the transfer of the density of the expression can be used to modify the Hermite polynomial expression. When the interest rate model is a multifactor interest rate model can be reduced, the expansion coefficient of the interest rate transfer density can be obtained by using the coefficient in the time variable. When the interest rate model is the non-reducing multi factor interest rate model, the expansion coefficient can be obtained by using the coefficient in the time variable and the state variable of binary Taylor. The expression of the density of interest rate can also be obtained by the likelihood function, and the model parameters can be obtained by using the maximum likelihood estimation.This paper is divided into the following chapters. The first chapter is the introduction part, introduces the research background research significance and the domestic and foreign research present situation, this paper research method and the research innovation. In the second chapter, the paper introduces the theory of short-term interest rate model, introduces the single factor short-term interest rate model and the multifactor short-term interest rate model, introduces how the domestic and foreign scholars on the basis of the multifactor short-term interest rate model, added a jump, so that the interest rate of the mutation is very well described. The third chapter is the estimation method of the parameters of the model. This paper mainly introduces several methods, namely, the maximum likelihood estimation, the generalized moment estimation, and the simulation moment estimation. The fourth chapter is the empirical part of the paper, the selection principle of the model, the selection of the sample data, the three models are estimated and maximum likelihood estimation. Then the simulation results are obtained by using Monte Carlo simulation. The simulation results show that the model is better than the single factor CKLS model. The model is better than the single factor model.