Parameter Estimation And Bias Analysis Of Some Interest Rate Models

As one of the common economic variables in the economic society,interest rate has always been focus of study in field of finance.It goes without saying that parameter estimation of the stochastic interest rate models has great significance on the modeling and application of the interest rate models.This paper considers parameter estimation of continuous-time diffusion processes which are commonly used to model dynamics of interest rate in the financial market.First of all,the author obtains the likelihood function of Vasicek model, and gets the maximum likelihood estimator (MLE) when some of the parameters are known. Then the author considers another widely-used interest rate model——CIR model. Since the explicit expression of the MLEs is not attainable, the author gets the corre-sponding pseudo-MLE by maximizing the approximate likelihood function discretized by Euler method and Nowman's method. The paper points out that when the volatility parameter is known, the author cannot get the pseudo-MLE of the draft parameter if the author use Nowman's method,while a explicit solution of the draft parameter is attainable if Euler discretization is used.Secondly, the author develops expansions for bias and variance of parameter esti-mators of Vasicek and CIR model using the properties of the processes. The asymptotic properties and the convergence orders can be derived from these expansions.This paper then considers parameter estimation for three nonlinear model:Gom-pertz model, Rayleigh model and Ahn-Gao (AG) model. By Ito formula, the three models can be transformated into Vasicek or CIR model. Therefore, the parameter es-timation problem of the 3 models can be solved by the study of parameter estimation and bias analysis for Vasicek and CIR models. In addition,simulation studies are carried out to(ⅰ) confirm the theoretical findings of bias and variance analysis; (ⅱ) simulate parameter estimator, the distribution and the confidence interval. CAO Jingjing (Applied mathematics) Supervised by HU Liangjian...