Exact maximum likelihood estimator for the probability of default on estimation provision consumer credit portfolio of the bank

In the context of increasing competition in the banking market, increasing regulatory requirements for transparency and sound risk-creation on this basis of adequate risk provisions in the banking sector is of paramount importance. In this paper, firstly it is proposed to use for estimating credit risks the exact maximum likelihood estimators (MLE) of the structure of stratified population for any sizes of the credit portfolio. These exact MLE could be applied to estimate Basel-II risk parameter PD (Probability of Default), and could be used to optimize provisions for covering expected losses of consumer credit portfolio. In usual banking practice for estimating risk parameter PD the frequencies (rates) of default credits of the whole consumer portfolio or of sub-portfolios of the whole consumer portfolio are usually using. But the statistical characteristics of these estimates, such as unbiased property, consistency, efficiency, exact and asymptotic distributions, usually are unknown. The new statistical estimations have derived for characteristics used in vintage analysis of consumer credit portfolio. These estimations for delinquency rates with different DPD (Days Past Due) are the exact maximum likelihood estimators (MLE) of the structure of stratified population for any sizes of the credit portfolio. These exact MLE could be applied to estimate Basel-II risk parameter PD (Probability of Default), and could be used to optimize provisions for covering expected losses of consumer credit portfolio. Making the adequate provisions to credit risks in the crisis conditions is the problem which needs to estimate risks with satisfactory accuracy.