Solvency II, or how to sweep the downside risk under the carpet

Abstract

Under Solvency II the computation of capital requirements is based on value at risk (V@R). V@R is a quantile-based risk measure and neglects extreme risks in the tail. V@R belongs to the family of distortion risk measures. A serious deficiency of V@R is that firms can hide their total downside risk in corporate networks, unless a consolidated solvency balance sheet is required for each economic scenario. In this case, they can largely reduce their total capital requirements via appropriate transfer agreements within a network structure consisting of sufficiently many entities and thereby circumvent capital regulation. We prove several versions of such a result for general distortion risk measures of V@R-type, explicitly construct suitable allocations of the network portfolio, and finally demonstrate how these findings can be extended beyond distortion risk measures. We also discuss why consolidation requirements cannot completely eliminate this problem. Capital regulation should thus be based on coherent or convex risk measures like average value at risk or expectiles.

Systemic optimal risk transfer equilibrium

“…Existence of optimal risk sharing for lawdetermined monetary utility functions is obtained in Jouini et al [30] and then generalized to the case of non-monotone risk measures by Acciaio [1] and Filipović and Svindland [25], to multivariate risks by Carlier and Dana [15] and Carlier et al [16], to cash-subadditive and quasi-convex measures by Mastrogiacomo and Rosazza Gianin [35]. Further works on risk sharing are also Dana and Le Van [19], Heath and Ku [28], Tsanakas [39], Weber [40]. Risk sharing problems with quantile-based risk measures are studied in Embrechts et al [22] by explicit construction, and in [21] for heterogeneous beliefs.…”

Risk Measures Based on Benchmark Loss Distributions

“…This "blindness" of VaR to the tail of the loss distribution arguably constitutes the most fundamental deficiency of VaR and its undesirable financial implications have been analyzed by a vast literature, see e.g. Artzner et al (1999), Daníelsson et al (2001), Acerbi and Tasche (2002), Albanese and Lawi (2004), Galichon (2010), Jarrow (2013), Embrechts et al (2018), Wang (2016), Weber (2018).…”

Risk Measures Based on Benchmark Loss Distributions

“…As, by definition, VaR depends only on the frequency of losses but not on their severity, one could in principle accumulate arbitrary loss peaks beyond the chosen quantile without being detected by VaR. This “blindness” of VaR to the tail of the loss distribution arguably constitutes the most fundamental deficiency of VaR and its undesirable financial implications have been analyzed by a vast literature, see, for example, Artzner et al., (), Daní elsson et al., (), Acerbi and Tasche, (), Albanese and Lawi, (), Galichon, (), Jarrow, (), Wang, (), Embrechts, Liu, and Wang (), Weber, ().…”