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Inference on marginal expected shortfall under multivariate regular variation
The marginal expected shortfall is arguably one of the most popular measures of systemic risk. The study of its extreme behaviour is particularly relevant for protecting against the risk of severe downturns in global financial markets. In this context, statistical inference is typically based on bivariate extreme-value models for a given financial variable of interest and another that incorporates systemic risk information. However, this disregards the more complex extremal dependence structure among a large number of financial institutions, of which the market is composed. To explicitly account for it, we propose an inferential procedure based on the theory of multivariate regular variation. We derive an approximation formula for the extreme marginal expected shortfall and derive an estimator, of which we also propose a bias-corrected version. We prove their asymptotic normality, which in turn allows the derivation of confidence intervals. A simulation study shows that the new estimators significantly improve the performance of the existing ones and the confidence intervals are very accurate. We showcase the usefulness of the proposed inferential procedure by analysing returns on stocks for financial institutions classified as "Global Systemically Important Banks" or "Domestic Systemically Important Banks" from US and Canada. The statistical results are extended to a general beta-mixing context that accommodates popular time series models with heavy-tailed innovations. This is a joint work with Simone Padoan (Bocconi University) and Matteo Schiavone (University of Padova).
Seminar organized by Prof. Hashorva