Maximum Likelihood Estimation Of Poisson Mixed Model

In the context of economic globalization,the degree of banking indstry's opening is also gradually increasing. When our Banking participates in the international finance activities, how to guard against the financial risk already has been the important issue it facing. In all of the risks the commercial bank facing , the credit risks throughout the entire operating process , which highlights the importance of credit risk management. In this article,we introduced the two traditional methods of credit risk measurement briefly as well as four modern risks management models—CreditMetrics, KMV, CPV and the CreditRisk+ model. Then we have compared their advantages and disadvantages.The determination of probability of default is the core content of "New Basel Capital Accord ".In the article ,we introduced three commonly used methods of calculation of default probability.And then ,we focus on Logistic Model which is the most commonly used in practice. The following is Poisson mixed model modeling of the default intensity directly,which is the innovation of the article.In this paper,we have showed the reasonableness of the proposal of the Poisson mixed model ,then estimate the parameters using the maximum likelihood estimation methods.In the process ,we have used the recursion formula of normal distribution's k-moment. As a result of the complexity of the likelihood function,with the analysis method estimate parameter is not feasible, therefore,for estimating the parameters, we propose to use numerical methods to solve the maximum likelihood function.The numerical method used in the article is the steepest descent method.Suppose there is only one macro-economic indicator affect the default intensity,then modeling based on the suppose and take it as an example. To estimate parameters of the Poisson mixed model using the numerical methods.The estimation of the parameters and the normal distribution have a good fitness,which show that our model is reasonable.And it is easy to make a statistical inference of the parameter estimation.