An Analytical Portfolio Credit Risk Model Based on the Extended Binomial Distribution
- 1 Department of Credit Management, Sparkasse Chemnitz, Chemnitz, Germany
Abstract
The binomial distribution describes the probability of the number of successes for a fixed number of identical independent experiments, each with binary out-put. In real life, practical applications like portfolio credit risk management trials are not identical and have different realization probabilities. In addition to the number, the quantitative impacts of the respective outputs are also important. There exist no complete model-side implementations for the expansion of the binomial distribution, especially not in the case of specific quantitative parameters up to now. Here, a solution of this issue is described by the extended binomial distribution. The key for solving the problem lies in the use of bijection between the elementary events of the binomial distribution and the digit sequences of binary numbers. Based on the extended binomial distribution, an analytical portfolio credit risk model is described. The binomial distribution approach minimizes the approximation error in modeling. In particular, the edges of the loss distribution can be determined in a realistic manner. This analytical portfolio credit risk model is especially predestined for management of risk concentrations and tail risks.
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