Algorithm for solving the reverse stress testing problem of the bank's loan portfolio on basis of system dynamic models of borrowers

Abstract

The key mechanisms to determine the effectiveness of bank's activities is the credit risk management. One of the main procedures recommended to banks for risk assessment is reverse stress testing. Reverse stress testing is the construction of realistic scenarios that lead to a given level of financial loss, or the formation of realistic scenarios that maximize bank losses. Knowledge of such scenarios allows banks to mitigate the consequences of their implementation.

The current credit risk assessment models are not suitable for solving the problems of reverse stress testing. Widely known models do not take into account the structure of specific companies, do not allow investigating the development of crisis scenarios in time and assuming a large sample of data on similar enterprises. To avoid of the noted disadvantages of the traditional approaches allows the use system-dynamic models of borrowers. System dynamics provides the possibility of reproducing the enterprise’s structure under study in the form of continuously interacting elements and external factors. The links between the elements are described by functional dependencies and differential equations that determine the dynamics of the company and the degree of its stability in relation to various macroeconomic scenarios. The article is devoted to approximate dynamic programming algorithm, which solves the reverse stress testing problem for the bank's loan portfolio on the basis of system-dynamic models of borrowers. The algorithm uses classical quasi-Newton optimization methods. The results of the method work are compared with the results of genetic algorithms. The statements proved in the article justify correctness of the algorithm and give an idea of its applicability to nonsmooth optimization problems arising in the context of reverse stress testing and system dynamics. The main tool for implementing the described algorithm is Matlab.