Bayesian Estimation Of Short-rate Models

In financial market,interest rate is the core variable of asset pricing.Therefore,it is very important to study the short-rate models and its parameter estimation.Many literatures have given the classical estimating methods of short-rate model parameters,such as ordinary least squares estimation and maximum likelihood estimation.However,empirical analysis shows that these methods are not very ideal,especially not much historical data.We note that models of setting parameters are often only suitable for a period of time market data.In this case,only the near-term data can be used to estimate the model parameters.This also means that we need a parameter estimation method based on small samples.Unlike the classical parameter estimation methods such as maximum likelihood estimation,the Bayesian method is used to estimate the parameters of the short-rate models based on the data of a certain sample size.Based on the discussion of classical parameter estimation methods of short-rate models,this paper discusses the Bayesian estimation of model parameters based on MCMC method in the known case of likelihood function.However,estimating continuous-time short-rate models are challenging since the likelihood function for most popular models is difficult to handle.Therefore,this paper approximates the likelihood function by using Euler approximation.Although this produces some discretization bias,data augmentation is utilized to mitigate discretization bias.In this case,the Bayesian estimation of the model parameters for the unknown case of the likelihood function is further discussed based on the MCMC method.The simulation results show that the Bayesian estimation method based on MCMC method has a good effect,and a certain degree of data expansion is helpful to improve the accuracy of parameter estimation and reduce the error of bond price.Moreover,Bayesian method based on MCMC method is very effective for certain sample size estimates are more accurate.