"Approximating the #tail #risk #measure by its sample average approximation, while appealing due to its simplicity and universality in use, requires a large number of samples to be able to arrive at risk-minimizing decisions with high confidence. This is primarily due to the rarity with which the relevant tail events get observed in the samples. In simulation, Importance Sampling is among the most prominent methods for substantially reducing the sample requirement while estimating #probabilities of #rareevents."
"We discuss different properties and representations of default #riskmeasures via monetary risk measures, families of related #tailrisk measures, and Choquet capacities. In a second step, we turn our focus on #defaultrisk measures, which are given as worst-case [#probability of #default] PDs and distorted PDs. The latter are frequently used in order to take into account model risk for the computation of #capitalrequirements through risk-weighted assets (#rwas), as demanded by the Capital Requirement #regulation (#crr). In this context, we discuss the impact of different default risk measures and margins of conservatism on the amount of risk-weighted assets."
"We respond to Tetlock et al. (2022) showing 1) how expert judgment fails to reflect tail risk, 2) the lack of compatibility between forecasting tournaments and tail risk assessment methods (such as extreme value theory). More importantly, we communicate a new result showing a greater gap between the properties of tail expectation and those of the corresponding probability."
"...we argue that... the median shortfall—that is, the median of the tail loss distribution—is a better option than the expected shortfall for setting the Basel Accords capital requirements due to statistical and economic considerations such as capturing tail risk, robustness, elicitability, backtesting, and surplus invariance."