A unified approach to systemic risk measures via acceptance sets

Abstract

We specify a general methodological framework for systemic risk measures via multidimensional acceptance sets and aggregation functions. Existing systemic risk measures can usually be interpreted as the minimal amount of cash needed to secure the system after aggregating individual risks. In contrast, our approach also includes systemic risk measures that can be interpreted as the minimal amount of cash that secures the aggregated system by allocating capital to the single institutions before aggregating the individual risks. An important feature of our approach is the possibility of allocating cash according to the future state of the system (scenario-dependent allocation). We also provide conditions that ensure monotonicity, convexity, or quasiconvexity of our systemic risk measures. K E Y W O R D Sacceptance set, aggregation, systemic risk, risk measures INTRODUCTIONThe financial crisis has dramatically demonstrated that traditional risk management strategies of financial systems, which predominantly focus on the solvency of individual institutions as if they were in isolation, insufficiently capture the perilous systemic risk that is generated by the interconnectedness of the system entities and the corresponding contagion effects. This has brought awareness of the urgent need for novel approaches that capture systemic riskiness. A large part of the current literature on systemic financial risk is concerned with the modeling structure of financial networks, the analysis of the contagion, and the spread of a potential exogenous (or even endogenous) shock into the system. For a given financial (possibly random) network and a given random shock, one then Mathematical Finance. 2019;29:329-367.wileyonlinelibrary.com/journal/mafi

On fairness of systemic risk measures

“…It might be more relevant to measure systemic risk as the minimal cash that secures Here, the amount m i is added to the financial position X i of institution i ∈ {1, · · · , N } before the corresponding total loss Λ(X + m) is computed (we refer to [3], [7] and [27]).…”

What is the Minimal Systemic Risk in Financial Exposure Networks?

“…This approach can be extended to determine the capital requirements for financial institutions to bring systemic risk to levels, which are acceptable to the regulator, see e.g. Feinstein et al (2017) or Biagini et al (2018).…”

Financial Asset Bubbles in Banking Networks

“…One stream of research aims at extending the traditional regulatory framework of monetary risk measures, that quantify the risk of financial institutions based on a stand alone basis, to multivariate systemic risk measures that take as a primitive the whole financial system. For an overview about this topic, see Biagini et al [6,7], Bisias et al [10], Chen et al [16], Drapeau et al [21], Feinstein et al [24], Hoffmann et al [30,31], Kromer et al [35] and references therein. Another popular ansatz to analyse systemic risk is based on explicit network models for the financial system and the study of potential default cascades due to various contagion affects.…”