A credit contagion model for the dynamics of the rating transitions in a SME bank loan portfolio

In this work we analyze the effects of credit contagion on the credit quality of a portfolio of bank loans issued to SMEs. To this aim we start from the discrete time model proposed in Barro and Basso (2005), that considers the counterparty risk generated by the business relations in a network of firms, and we modify it by introducing different rating classes in order to manage the case of firms with different credit qualities. The transitions from a rating class to another occurs when a proxy for the asset value of the firm crosses some rating specific thresholds. We assume that the initial rating transition matrix of the system is known, and compute the thresholds using the probability distribution of the steady state of the model. A wide Monte Carlo simulation analysis is carried out in order to study the dynamic behaviour of the model, and in particular to analyze how the default contagion present in the model affects the output rating transition matrix of the portfolio.