Fadina, Tolulope and Bellini, Fabio and Wang, Ruodu and Wei, Yunran (2021) Parametric measures of variability induced by risk measures. Working Paper. arXiv. (Unpublished)

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Abstract

We present a general framework for a comparative theory of variability measures, with a particular focus on the recently introduced one-parameter families of inter-Expected Shortfall differences and inter-expectile differences, that are explored in detail and compared with the widely known and applied inter-quantile differences. From the mathematical point of view, our main result is a characterization of symmetric and comonotonic variability measures as mixtures of inter-Expected Shortfall differences, under a few additional technical conditions. Further, we study the stochastic orders induced by the pointwise comparison of inter-Expected Shortfall and inter-expectile differences, and discuss their relationship with the dilation order. From the statistical point of view, we establish asymptotic consistency and normality of the natural estimators and provide a rule of the thumb for cross-comparisons. Finally, we study the empirical behaviour of the considered classes of variability measures on the S&P 500 Index under various economic regimes, and explore the comparability of different time series according to the introduced stochastic orders.

Item Type:	Monograph (Working Paper)
Uncontrolled Keywords:	Variability measures, quantiles, Value-at-Risk, Expected Shortfall, expectiles, stochastic orders.
Divisions:	Faculty of Science and Health Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor:	Elements
Depositing User:	Elements
Date Deposited:	02 Nov 2021 11:18
Last Modified:	18 Jul 2022 16:12
URI:	http://repository.essex.ac.uk/id/eprint/31406

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