Studia Mathematica XIV (2015)

Generalized CreditRisk+ model and applications Abstract. In the paper we give a mathematical overview of the CreditRisk+ model as a tool used for calculating credit risk in a portfolio of debts and suggest some other applications of the same method of analysis. In this paper we will give a condensed mathematical overview of the Credit-Risk+ model and attempt to generalize it to be applicable in more situations that it was originally created for. CreditRisk+ model was formed in 1997 by Credit Suisse First Boston bank. It is a tool used to calculate the level of credit risk for a portfolio of debts. The main purpose of the model is to determine the probability distribution for the amount of debt that will not be repaid in a given set of debts in a unit of time, usually one year. Once the probability distribution is estimated it becomes possible to calculate the expected loss, the level of value at risk, the amount of capital necessary to cover an unexpected loss. This information later allows a credit institution to compute the proper interest rate of a granted loan ensuring the maximum profit for the company. The reasoning presented in this paper that concerns the mathematical struc-ture of the model is based on [3]. The input data necessary to apply the Credit-Risk+ model is the following: i. The number of debts in the portfolio. ii. The value of each debt (this is the amount that a debtor fails to repay in the event of default). iii. The probability of default for each debtor. The model is used as an approximation tool, so it will make sense to employ it in case of a large number of debts in the portfolio and relatively small probabilities of default