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Parametric measures of variability induced by risk measures

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 (Unpublished)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: 06 Jan 2022 14:32
URI: http://repository.essex.ac.uk/id/eprint/31406

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