A bank merger predictive model using the Smoluchowski stochastic coagulation equation and reverse engineering

PURPOSE: The purpose of this paper is to provide a theoretical framework for predicting the next period financial behavior of bank mergers within a statistical-oriented setting. DESIGN/METHODOLOGY/APPROACH: Bank mergers are modeled combining a discrete variant of the Smoluchowski coagulation equation with a reverse engineering method. This new approach allows to compute the correct merging probability values via the construction and solution of a multi-variable matrix equation. The model is tested on real financial data relative to US banks collected from the National Information Centre. FINDINGS: Bank size distributions predicted by the proposed method are much more adherent to real data than those derived from the estimation method. The proposed method provides a valid alternative to estimation approaches while overcoming some of their typical drawbacks. RESEARCH LIMITATIONS/IMPLICATIONS: Bank mergers are interpreted as stochastic processes focusing on two main parameters, that is, number of banks and asset size. Future research could expand the model analyzing the micro-dynamic taking place behind bank mergers. Furthermore, bank demerging and partial bank merging could be considered in order to complete and strengthen the proposed approach. PRACTICAL IMPLICATIONS: The implementation of the proposed method assists managers in making informed decisions regarding future merging actions and marketing strategies so as to maximize the benefits of merging actions while reducing the associated potential risks from both a financial and marketing viewpoint. ORIGINALITY/VALUE: To the best of the authors’ knowledge, this is the first study where bank merging is analyzed using a dynamic stochastic model and the merging probabilities are determined by a multi-variable matrix equation in place of an estimation procedure.