BeschreibungWe establish elicitability and identifiability results for measures of systemic risk introduced in Feinstein, Rudloff and Weber (2017). These risk measures determine the set of all capital allocations that make a financial system acceptable. Hence, they take an ex ante angle, specifying those capital allocations that prevent the system from default. At the same time, they allow to capture the dependence structure of different financial firms.
The elicitability of a risk measure, or more generally, a statistical functional amounts to the existence of a strictly consistent scoring or loss function. That is a function in two arguments, a forecast and an observation, such that the expected score is minimised by the correctly specified functional value, thereby encouraging truthful forecasts. Prominent examples are the squared loss for the mean and the absolute loss for the median. Hence, the elicitability of a functional is crucial for meaningful forecast comparison and forecast ranking, but also opens the way to M-estimation and regression. An identification function is similar to a scoring function, however, the correctly specified forecast is the zero of the expected identification function rather than its minimiser, thus giving rise to Z-estimation and possibilities to assess the calibration of forecasts.
To allow for a rigorous treatment of elicitability of set-valued functionals, we introduce two modes of elicitability: a weak and a strong version. We show that these two modes are mutually exclusive and establish strong elicitability results for the systemic risk measures under consideration. That means we construct strictly consistent scoring functions taking sets as input arguments for forecasts.
The results turn out to be practically relevant since they open the way to comparative backtests of Diebold-Mariano type and regression with set-valued models. On the other hand, they constitute a novelty of theoretical interest on its own.
|Zeitraum||10 Sep. 2018 → 11 Sep. 2018|
|Ereignistitel||Finance, Insurance, Probability and Statistics Workshop|