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

In this paper 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 so doing we are convinced that geography does matter and evaluate the risk propensity of the bank towards the nonperforming 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.