Quotation Fissler, Tobias. 2016. Higher Order Elicitability: Expected Shortfall is jointly elicitable with Value at Risk - Implications for Backtesting. Vienna Congress on Mathematical Finance, WU Wien, Österreich, 12.09.-14.09.


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Abstract

A statistical functional, such as the mean or the median, is called elicitable if there is a scoring function or loss function such that the correct forecast of the functional is the unique minimizer of the expected score. Such scoring functions are called strictly consistent for the functional. The elicitability of a functional opens the possibility to compare competing forecasts and to rank them in terms of their realized scores. In the first part of this talk, we explore the notion of higher order elicitability, that is, we investigate the question of elicitability for higher-dimensional functionals. As a result of particular applied interest we show that the pair (Value at Risk, Expected Shortfall) ((VaR, ES)) is elicitable despite the fact that ES itself is not. More generally, we give a characterization of the class of strictly consistent scoring functions for this pair, making use of a higher dimensional version of Osband's principle. In the second part of the talk, we discuss the consequences of this result for backtesting ES-forecasts. We introduce comparative backtests of Diebold-Mariano type using a strictly consistent scoring function for the pair (VaR, ES). Comparative backtests open the possibility to choose a conservative null hypothesis in contrast to the current state of the art. Emphasizing our argument with a brief simulation study, we demonstrate that the change of the null hypothesis in comparative backtests amounts to a reversed onus of proof in backtesting decisions. This appears to be beneficial to all stakeholders, including banks, regulators, and society at large.

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Status of publication Published
Affiliation External
Type of publication Paper presented at an academic conference or symposium
Language English
Title Higher Order Elicitability: Expected Shortfall is jointly elicitable with Value at Risk - Implications for Backtesting
Event Vienna Congress on Mathematical Finance
Year 2016
Date 12.09.-14.09.
Country Austria
Location WU Wien
URL https://fam.tuwien.ac.at/events/vcmf2016/index.php

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Fissler, Tobias (Details)
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