BeschreibungEstimating different risk measures, such as Value at Risk or Expected Shortfall, for reporting as well as testing purposes is a common task in various financial institutions. The question of evaluating and comparing these estimates is closely related to two concepts already well known in the literature: elicitability and identifiability.
A statistical functional, e.g. a risk measure, is called elicitable if there is a strictly consistent scoring function for it, i.e. a function of two arguments, forecast and realization of a random variable, such that its expectation with respect to the second argument is minimized only by the correct forecast. It is called identifiable, if there is a strict identification function, i.e. again a function of two arguments such that the its expectation with respect to the second argument is equal to zero exactly at the correct forecast.
We introduce these concepts for systemic risk measures defined by Feinstein, Rudloff and Weber (2016). A banking system with n participants is represented by a random vector Y and the quantity of interest is its aggregated outcome, using some nondecreasing aggregation function. The measure of systemic risk is defined as the set of n-dimensional capital allocation vectors k such that the aggregated outcome of Y+k is acceptable under a given scalar risk measure.
We establish the link between the elicitability and/or identifiability of the systemic risk measure and the underlying scalar risk measure, taking two perspectives on the measures of systemic risk that stem from their set-valued nature. Moreover, we study secondary quality criteria of the scoring and identification functions of these measures.
|Zeitraum||9 Sept. 2019 → 11 Sept. 2019|
|Ereignistitel||Vienna Congress on Mathematical Finance|