DescriptionBacktesting 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 https://arxiv.org/abs/2104.10673 which is joint work with Yannick Hoga.
|Period||27 Sep 2021 → 1 Oct 2021|
|Event title||15th German Probability and Statistics Days|
|Degree of Recognition||International|