Sensitivities and worst-case correlations for hitting probabilities of portfolio tranches

Stefan Huschens, Christoph Lehmann and Daniel Tillich

Abstract

ABSTRACT

We analyze the hitting probability of a portfolio tranche under the assumption of a Vasicek-distributed portfolio loss. The sensitivities of the hitting probability with respect to the default probability and the asset correlation of the portfolio are derived. We show that the hitting probability as a function of the correlation is non-monotonic for certain parameter constellations; this leads to worst-case hitting probabilities and worstcase correlations for each tranche. Thus, stress-testing procedures require different worst-case scenarios for different tranches depending on the parameters. All the findings on hitting probabilities carry over to wipe-out probabilities.