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Marginal expected shortfall is unquestionably one of the most popularsystemic risk measures. Studying its extreme behaviour is particularly relevantfor risk protection against severe global financial market downturns. In thiscontext, results of statistical inference rely on the bivariate extreme valuesapproach, disregarding the extremal dependence among a large number offinancial institutions that make up the market. In order to take it intoaccount we propose an inferential procedure based on the multivariate regularvariation theory. We derive an approximating formula for the extreme marginalexpected shortfall and obtain from it an estimator and its bias-correctedversion. Then, we show their asymptotic normality, which allows in turn theconfidence intervals derivation. Simulations show that the new estimatorsgreatly improve upon the performance of existing ones and confidence intervalsare very accurate. An application to financial returns shows the utility of theproposed inferential procedure. Statistical results are extended to a general$\beta$-mixing context that allows to work with popular time series models withheavy-tailed innovations.

Marginal expected shortfall inference under multivariate regular variation