A0990
Title: Marginal expected shortfall inference under multivariate regular variation
Authors: Matteo Schiavone - Bocconi University (Italy) [presenting]
Simone Padoan - Bocconi University (Italy)
Stefano Rizzelli - Catholic University of Milan (Italy)
Abstract: Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context, the results of statistical inference rely on the bivariate extreme values approach, disregarding the extremal dependence among a large number of financial institutions that make up the market. To take it into account, an inferential procedure is proposed based on the multivariate regular variation theory. An approximating formula is derived for the extreme marginal expected shortfall and obtained from it an estimator and its bias-corrected version. Then, their asymptotic normality is shown, which allows, in turn, the confidence intervals derivation. Simulations show that the new estimators greatly improve upon the performance of existing ones, and confidence intervals are very accurate. An application to financial returns shows the utility of the proposed inferential procedure. Statistical results are extended to a general $\beta$-mixing context that allows working with popular time series models with heavy-tailed innovations.
