Modelling non-performing loans probability in the commercial banking system: efficiency and effectiveness related to credit risk in Italy

In this article, we model the effect of the non-performing loans on the cost structure of the commercial banking system. With this aim, we comment on an increase in the non-performing loans by studying the consequences of such a change on the cost function and compute the probability of failure of maintaining a performing loan as such. In doing so, we are convinced that geography does matter and evaluate the risk propensity of the bank towards the non-performing loans accordingly. We finally stress that traditional efficiency indicators of cost elasticity do not fit properly with such a problem and propose a measure based on the costs for managing and monitoring the loans which, according to the related density function, will reveal effectively as non performing.