We consider the problem of measuring risk of a portfolio com- prising loans, bonds, and financial instruments, which is caused by possible default of its obligors. Specifically, we are interested in esti- mating probability that a portfolio incurs large loss over a fixed time horizon. One crucial concern of such problem is how to measure de- pendency among all obligors. Our idea is based on so-called threshold model and normal copula model, which represent dependency by mul- tiple risk factors and their corresponding loading coefficients. In this paper, we develop several novel regression models to determine the risk loading coefficients instead of exploring other copula models to measure dependency among all obligors. Several efficient algorithms are also reviewed or developed aiming to solve the proposed regres- sion models. Using these generated optimal risk loading coefficients, we derive a more robust large loss probability distribution. Numerical experiments show that we can efficiently estimate the large loss prob- abilities while make use of dependency knowledge among all obligors as much as possible.
Siemens Corporation, 07/2015