Attributing Systemic Risk to Individual Institutions
Bank for International Settlements, 2010 - Banks and banking - 29 pages
An operational macroprudential approach to financial stability requires tools that attribute system-wide risk to individual institutions. Making use of constructs from game theory, we propose an attribution methodology that has a number of appealing features: it can be used in conjunction with popular risk measures, it provides measures of institutions' systemic importance that add up exactly to the measure of system-wide risk and it easily accommodates uncertainty about the validity of the risk model. We apply this methodology to a number of constructed examples and illustrate the interactions between drivers of systemic importance: size, the institution's risk profile and strength of exposures to common risk factors. We also demonstrate how the methodology can be used for the calibration of macroprudential capital rules.
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aggregate capital analysis applied assets attribution procedures bank in group bank’s banks differ banks in G big banks capital charges characteristic function common factor common risk factor common-factor exposure conﬁdence level context contribution to system-wide contributions to systemic CoVaR default correlation deﬁned distribution of losses dollar exposure drivers of systemic efﬁcient equal equalises example expected shortfall exposure to common ﬁnancial system ﬁrst function 9 given group of banks impact implies individual institutions institution’s joint failures level of systemic ln addition ln turn lumpiness macroprudential approach marginal contribution measures of systemic number of banks probability distribution probability of default Procedure 2 Procedure quantile reﬂects result risk is measured risk to individual set of tail Shapley value methodology small banks speciﬁc stylised sub-additivity subgroup G subgroup of banks subsystem system comprises system-wide risk systemic events systemic importance systemic risk systemic tail risk tail events Theorem value of bank