Asymptotics for credit portfolio losses due to defaults in a multi-sector model

Consider a credit portfolio with the investments in various sectors and exposed to an external stochastic environment. The portfolio loss due to defaults is of critical importance for social and economic security particularly in times of financial distress. We argue that the dependences among obligors within sectors (intradependence) and across sectors (interdependence) may coexist and influence the portfolio loss. To quantify the portfolio loss, we develop a multi-sector structural model in which a multivariate regular variation structure is employed to model the intradependence within sectors, and the interdependence across sectors is implied in the arbitrarily dependent macroeconomic factors, although, given them, obligors in different sectors are conditionally independent. We establish some sharp asymptotic formulas for the tail probability and the (tail) distortion risk measures of the portfolio loss. Our results show that the portfolio loss is mainly driven by the latent variables and the recovery rate function, and is also potentially affected by the macroeconomic factors and the intradependence within sectors. Moreover, we implement intensive numerical studies to examine the accuracy of the obtained approximations and conduct some sensitivity analysis.