Quotation Fissler, Tobias. 2021. Backtesting Systemic Risk Forecasts using Multi-Objective Elicitability. ISOR Colloquium University of Vienna, University of Vienna (online), 21.06.21


RIS


BibTeX

Abstract

Backtesting risk measure forecasts requires identifiability (for model calibration and validation) and elicitability (for model comparison). We show that the three widely-used systemic risk measures conditional value-at-risk (CoVaR), conditional expected shortfall (CoES) and marginal expected shortfall (MES), which measure the risk of a position Y given that a reference position X is in distress, fail to be identifiable and elicitable on their own. As a remedy, we establish the joint identifiability of CoVaR, MES and (CoVaR, CoES) together with the value-at-risk (VaR) of the reference position X. While this resembles the situation of the classical risk measures expected shortfall (ES) and VaR concerning identifiability, a joint elicitability result fails. Therefore, we introduce a completely novel notion of multivariate scoring functions equipped with some order, which are therefore called multi-objective scores. We introduce and investigate corresponding notions of multi-objective elicitability, which may prove beneficial in various applications beyond finance. In particular, we prove that conditional elicitability of two functionals implies joint multi-objective elicitability with respect to the lexicographic order on the two-dimensional Euclidean space, which makes it applicable in the context of CoVaR, MES or (CoVaR, CoES), together with VaR. We describe corresponding comparative backtests of Diebold-Mariano type, for two-sided and 'one and a half'-sided hypotheses, which respect the particularities of the lexicographic order and which can be used in a regulatory setting. We demonstrate the viability of these backtesting approaches in simulations and in an empirical application to DAX 30 and S&P 500 returns. The talk is based on the preprint https://arxiv.org/abs/2104.10673 which is joint work with Yannick Hoga.

Tags

Press 'enter' for creating the tag

Publication's profile

Status of publication Published
Affiliation WU
Type of publication Unpublished lecture
Language English
Title Backtesting Systemic Risk Forecasts using Multi-Objective Elicitability
Event ISOR Colloquium University of Vienna
Location University of Vienna (online)
Event country Austria
Date June 21, 2021

Associations

People
Fissler, Tobias (Details)
Organization
Institute for Statistics and Mathematics IN (Details)
Google Scholar: Search