Parameter Estimation Of CKLS Model Based On Skew Distribution

For the important indicator interest rate in the financial market,it has always been a problem that theoretical and applied economists continue to study.Since Merton(1973)first proposed the short-term interest rate model,many scholars have continuously improved it in order to use more suitable financial instruments.Among the data,the CKLS model proposed by Chan et al(1992)later unifies the various classic interest rate models in the early stage,so that the short-term interest rate model has been perfected and has become an important financial model.The short-term interest rate model is based on the interest rate model under Brownian motion,that is to say,they are all based on the assumption of normal distribution.However,in actual financial markets,a large number of financial interest rate data do not follow a normal distribution,and usually have the characteristics of sharp peaks,thick tails,and skew.Especially skewness,it is difficult not to consider its impact.Therefore,this article attempts to introduce the nature of the partial distribution into the interest rate model,assuming that its distribution obeys the partial normal distribution and the partial t distribution.Based on the CKLS model,the distribution of interest rate changes under the partial distribution of the interest rate model is derived.,And its corresponding maximum likelihood function,deduced the parameter estimation process of CKLS model using maximum likelihood and generalized moment estimation under partial normal distribution,and applied it in empirical analysis and numerical simulation.As an application,the daily data of bank lending rates in the past seven days in my country are selected,and two maximum likelihood estimation methods are used to estimate the parameter estimation results under the assumption of a partial normal distribution and a partial distribution,and compare them.At the same time,it is estimated that the model still assumes the parameter estimation result under the standard normal state and compares the parameter estimation result with the skew distribution state.In addition,the confidence interval of the parameter estimation of the partial normal distribution of the model under the maximum likelihood estimation is given.It can be seen from the empirical analysis results of the model that after introducing the skew distribution,we can fit the model well and have a good estimation effect on the introduced skewness parameters.However,after the skewness is introduced,the mean value of the model The regression speed effect is weakened,and the model parameter estimation under the maximum likelihood estimation cannot detect the mean regression speed well.Finally,we refer to the empirical estimation parameter estimation results,perform simulation training on the model to generate interest rate data,and give the parameter estimation mean and error under different sample lengths,and analyze this.The results show that the parameter estimation and model fitting of the interest rate model are feasible after the introduction of the partial distribution,and for the CKLS model after the introduction of the skewness coefficient ?,whether it is for the assumed partial normal distribution or the partial distribution,the original Both the parameters and the newly introduced parameters can be better estimated.This also provides some reference for us to continue to study the interest rate model under the partial distribution in the future.