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Abstract: Reverse stress testing of a financial portfolio aims to identify scenarios for risk factors that lead to a specified adverse portfolio outcome. The stress scenarios of interest naturally need to be extreme yet plausible. A statistical formulation of these requirements is to define a stress scenario at extreme threshold as the mode of the conditional density of the random vector of risk factors given that the loss on the portfolio exceeds the threshold.
In situations where the interest is in an extreme conditioning event corresponding to a large value of the threshold, traditional multivariate mode estimators would not perform well due to very limited sample of observations in the conditioning event. Under this consideration, we propose an estimator based on techniques from multivariate extreme value theory under the assumption of multivariate regular variation and tail dependence. The method effectively addresses data scarcity in the joint tail regions while allowing for more flexible model assumptions focusing on extremes. We study the asymptotic behaviour of the proposed estimator, investigate its finite-sample performance in simulation studies and apply it to real data in a case study.