Shock on Variable or Shock on Distribution with Application to Stress-Tests

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 institutions by means of shocks on systematic factors, for which we distinguish the cases of crystallized and optimally updated portfolios. The approach is illustrated by an analysis of the risk of sovereign bonds of the Eurozone.