In our contribution, we model bank profitability 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 investment. As regards the ROE, banks hold capital in order to prevent bank failure and meet bank capital requirements set by the regulatory 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 Levy processes that contain information about the value processes of net profit after tax, equity capital and total assets. In particular, we are able to compare Merton and Black-Scholes type models and provide simulations for the aforementioned profitability indicators.
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