TITLE:
An Analytical Portfolio Credit Risk Model Based on the Extended Binomial Distribution
AUTHORS:
Sven Fischer
KEYWORDS:
Credit Risk, Portfolio Management, Credit Portfolio Risk, Bernoulli Mixture Distribution, General Binomial Distribution, Weighted Distribution
JOURNAL NAME:
Journal of Financial Risk Management,
Vol.8 No.3,
September
26,
2019
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.