Estimating the probability of Loss of Credit Portfolio using the sharp asymptotic method and Latent variable model

Subject Areas : Financial engineering

Mohammad reza  Haddadi ¹ (Assistant Professor, Department of mathematics, Faculty of Basic Sciences, Univercity of Ayatollah Boroujerdi, Lorestan, Boroujerd, Iran)
Reza  Maaboudi ² (Assistant Professor, Department of Economics, Faculty of Humanities, Univercity of Ayatollah Boroujerdi, Lorestan, Boroujerd, Iran)
Saeedeh  Fallahyan ³ (Master of Financial Mathematics, Department of mathematics, Faculty of Basic Sciences, Univercity of Ayatollah Boroujerdi, Boroujerd, Iran)

Received: 2018-12-18 Accepted : 2019-04-16 Published : 2019-06-22

Keywords: Monte Carlo Simulation, Credit Risk, Copula Function, Probability of Default, Hidden Variables,

Abstract :

The purpose of the study is to obtain a probability of a very high loss for a credit portfolio in a fixed time horizon and to calculate the loss of this portfolio in the worst possible case (the defaults of all customers). For this purpose, the Copula function approach is used. A Copula function is a new tool that increases the accuracy of the calculation of this probability. Gaussian Copulas cannot simulate the dependence between the members of the portfolio. For this reason, the T- Copula method has been used as an alternative model in this paper. The T-Copula pattern, in contrast to the normal Copula method, supports the extreme dependence between variables. The structure of a multivariate distribution t is the ratio of a multivariate normal distribution on the second root of a Chi-square random variable. If the denominator of the distribution chooses values ​​close to zero, then the corresponding vector coordinates of the random variables are distributed t , Can record large joint movements. The Chi-square random variable plays "common shock" roles. The present study, using the hidden variables method, has calculated the probable unpredictability of loss for a heterogeneous portfolio of given facilities consisting of 250 borrowers. For this purpose, based on the type of borrowed loans, borrowers are divided into three groups. Using the Monte Carlo simulation method, the probability of a loss in this portfolio is estimated, then the residue levels in each group of agents and the total amount of exposure are calculated. The findings showed that, considering the degree of freedom 2 for the distribution of the student's t-test related to the vector of hidden variables, the maximum probability of loss of credit portfolio Has been 11.01.