The Research For Default Amount Following The Non-central Gamma Distribution In Credit Risk

In this paper,we study the aggregate model about the default amount following the non-central gamma distribution in the commercial bank credit risk.Firstly,this paper introduces what the aggregation model of credit risk is,and we give three methods to study the credit aggregation risk model and the two properties of it.Secondly,this paper introduces the total default distribution of the single default amount following the non-central gamma distribution with the same parameters.Then,we give some conclusions of total default S in the commercial bank credit risk under the default following non-center gamma distribution with both the same parameters and different parameters and the methods to determine credit portfolio default distribution.Finally we give confidence interval estimation of the total default amount in the credit portfolio.Theorem 3.2.1 In a certain period of time occurring N default,and random variable N following distribution:P(N = k)= Pk,k = 0,1,2,…,then assume individual default loss Xi(i=1,2,…,N)following non-central Gamma distribution with parameters?,? and ?,so the density function,expectation and variance of the total loss of the credit portfolio respectively are:Theorem 3.6.1 In a certain period of time occur n default,individual default loss Xi(i=1,2,…,N)follows non-central Gamma distribution with parameters?,? and ?,and the total loss of the credit portfolio is.So with confidence 1-?',the average total default E[S]'s one-sided upper confidence limit is,its one-sided lower confidence limit is and it two-sided confidence interval is X is sample average,namely.