The shocks on a stochastic system can be defined by means of either distribution, or variable. We relate these approaches and provide the link between the global and local effects of both types of shocks. These methodologies are used to perform stress-tests on the portfolio of financial...

We provide a rigorous proof of granularity adjustment (GA) formulas to evaluate loss distributions and risk measures (value-at-risk) in the case of heterogenous portfolios, multiple systematic factors and random recoveries. As a significant improvement with respect to the literature, we detail...