Set-valued intrinsic measures of systemic risk

Abstract: In recent years, it has become apparent that an isolated microprudential approach to capital adequacy requirements of individual institutions is insufficient. It can increase the homogeneity of the financial system and ultimately the cost to society. For this reason, the focus of the financial and mathematical literature has shifted towards the macroprudential regulation of the financial network as a whole. In particular, systemic risk measures have been discussed as a risk measurement and mitigation tool. In this spirit, we adopt a general approach of multivariate, set-valued risk measures and combine it with the notion of intrinsic risk measures. In order to define the risk of a financial position, intrinsic risk measures utilise only internal capital, which is received when part of the currently held assets are sold, instead of relying on external capital. We translate this methodology into the systemic framework and show that systemic intrinsic risk measures have desirable properties such as the set-valued equivalents of monotonicity and quasi-convexity. Furthermore, for convex acceptance sets we derive a dual representation of the systemic intrinsic risk measure. We apply our methodology to a modified Eisenberg-Noe network of banks and discuss the appeal of this approach from a regulatory perspective, as it does not elevate the financial system with external capital. We show evidence that this approach allows to mitigate systemic risk by moving the network towards more stable assets.