Modeling Systemic Risk with Correlated Stochastic Processes

In this work we propose a novel systemic risk model, based on stochastic processes and correlation networks. For each country we consider three different spread measures, one for each sector of the economy (sovereign, corporates, banks), and we model each of them as a linear combination of two stochastic processes: a country-specific idiosyncratic component and a common systematic factor. We provide an estimation model for the parameters of the processes and, for each country, we derive the aggregate default probabilities of each sector. Systemic risk is then estimated by means of a network model based on the partial correlations between the estimated processes of all sectors and countries. Our model is applied to understand the time evolution of systemic risk in the economies of the European monetary union, in the recent period. The results show that systemic risk has increased during the crisis years and that, after the crisis, a clear separation between core and peripheral economies has emerged, for all sectors of the economy.