# Hedge the Stress: Using Stress Tests to Design Hedges for Foreign Currency Loans

## Thomas Breuer, Martin Jandačka, and Klaus Rheinberger and Martin Summer

Stress testing has become an important method of risk analysis for lending acitivities. Worst-case analysis is a special technique of stress testing. It consists of searching for the worst among the macroeconomic scenarios satisfying some plausibility constraint. In this way we can be sure not to miss out any harmful but plausible scenarios, which is a serious danger when considering only predefined stressed scenarios. This chapter uses worst-case analysis to design hedges for market and credit risk in foreign currency (FX) loans.

Systematic worst-case analysis with plausibility constraints was developed for market risk stress testing, see Breuer and Krenn (1999) and Čihák (2004, 2007). Breuer et al (2008b) extended this technique to macro stress testing for loan portfolios. The loss in the worstcase scenario can also be regarded as a risk measure. As such, it was originally introduced under the name maximum loss by Studer (1999, 1997). Maximum loss is a coherent risk measure in the sense of Artzner et al (1999).11 Actually, it is the prototype of a coherent risk measure because by a duality argument every coherent risk measure can be represented as maximum loss over some set of