Modeling of Banking Profit via Return-on-Assets and Return-on-Equity

Abstract

In our contribution, we model bank profitabil- ity via return-on-assets (ROA) and return-on-equity (ROE) in a stochastic setting. We recall that the ROA is an indication of the operational efficiency of the bank while the ROE is a measure of equity holder returns and the potential growth on their invest- ment. As regards the ROE, banks hold capital in order to prevent bank failure and meet bank capital requirements set by the reg- ulatory authorities. However, they do not want to hold too much capital because by doing so they will lower the returns to equity holders. In order to model the dynamics of the ROA and ROE, we derive stochastic differential equations driven by L ´ evy pro- cesses that contain information about the value processes of net profit after tax, equity capital and total assets. In particu lar, we are able to compare Merton and Black-Scholes type models and provide simulations for the aforementioned profitability i ndica- tors.