Solution Space Size in Credit Risk Simulation

In a portfolio of securities, lenders may incur substantial losses if the obligors do not return the money borrowed by them. In credit risk evaluation through simulation, the states of the portfolio associated to large losses are sampled rather than identified exhaustively. Enumeration of all such critical states is however relevant for the early warning of heavy losses. We provide a general enumerative algorithm, and evaluate its computational complexity, which results to be equal to the number of critical states, for three cases of the distribution of losses associated to individual obligors: uniform, linear, and exponential. In the presence of a possibly huge number of critical states, the evaluation of the computational complexity allows us to assess beforehand if the enumeration task is feasible.