Under the new capital accord stress tests are to be included in market risk regulatory capital calculations. This development necessitates a coherent and objective framework for stress testing portfolios exposed to market risk. Following recent criticism of stress testing methods our tests are conducted in the context of risk models, building on the VaR literature. First, to identify the most suitable risk models for stress testing, we apply an extensive back testing procedure that focuses on extreme market movements. We consider eight possible risk models including both conditional and unconditional models and four possible return distributions (normal, Student’s t, empirical and normal mixture) applied to three heavily traded currency pairs using a sample of daily data spanning more than 20 years. Finding that risk models accommodating both volatility clustering and heavy tails are the most accurate predictors of extreme returns, we develop a corresponding model-based stress testing methodology. Our results are compared with traditional stress tests and we assess the implications for capital adequacy. On the basis of our results we conclude that the new recommendations for market risk regulatory capital calculation will have little impact on current levels of foreign exchange regulatory capital.