The Parameter Estimation And Bias Correction Of Short-term Interest Rate Model

Interest rate is the core variable in the financial market. In recent years, as China continues to accelerate the process of interest rates marketability, the theoretical study and practical value of the interest rate has become increasingly prominent. This paper serves the short-term interest rates as a research object and discusses the method of parameter estimation about single factor short-term interest rate model, then proposes a bias correction method based on generalized bootstrapping, finally, this article uses the Shibor of the three-month interbank term as samples to take empirical analysis.As for parameter estimation, the paper takes the comparative analysis between Euler likelihood method and SMLE; both methods are pseudo-likelihood estimation method. Among them, simulated likelihood method is a combination of Euler likelihood method and Monte Carlo method; it has better statistical properties, but has the computational complexity. By contrast, Euler likelihood method is more simple and easy to calculate. When the sample size is not large enough, both estimation methods have a large deviation. Therefore, we propose a new error correction method based on the generalized bootstrap, the basic idea is to give the likelihood function of random weights and construct weighted likelihood function to obtain new parameter estimation, in order to estimate the parameter estimation error and offset correction ultimately. By stochastic simulation experiments, we find that this method can reduce the bias of Euler likelihood estimation in some extent.In addition, this paper uses Shibor rate to take empirical research and estimates the parameter values of the eight common short-term interest rate models, then take the bias correction. Finally, we use the CIR model to price zero-coupon bonds, analyze the interest rate term structure then obtain price change curve and returns ratio change curve.