Backtesting CoVaR using Multi-Objective Elicitability

Activity: Talk or presentationScience to science


Backtesting risk measure forecasts requires identifiability (for model calibration and validation) and elicitability (for model comparison). We show that the widely-used systemic risk measure conditional value-at-risk (CoVaR), which measures the risk of a position Y given that a reference position X is in distress, fails to be identifiable and elicitable on its own. As a remedy, we establish the joint identifiability of CoVaR 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 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 which is joint work with Yannick Hoga.
Period27 Sep 20211 Oct 2021
Event title15th German Probability and Statistics Days
Event typeUnkonwn
Degree of RecognitionInternational