Closed form solutions of measures of systemic risk

TL;DR

This paper provides explicit closed form solutions for systemic risk measures in a Gaussian framework, linking them to established financial concepts and facilitating communication with regulators.

Contribution

It derives explicit formulas for systemic risk measures based on Beta-coefficients and Value at Risk, clarifying their relationships and aiding regulatory communication.

Findings

Closed form solutions for systemic risk measures derived.

Connections established between risk measures and financial economics concepts.

Facilitates regulatory understanding and communication of systemic risk.

Abstract

This paper derives -- considering a Gaussian setting -- closed form solutions of the statistics that Adrian and Brunnermeier and Acharya et al. have suggested as measures of systemic risk to be attached to individual banks. The statistics equal the product of statistic specific Beta-coefficients with the mean corrected Value at Risk. Hence, the measures of systemic risks are closely related to well known concepts of financial economics. Another benefit of the analysis is that it is revealed how the concepts are related to each other. Also, it may be relatively easy to convince the regulators to consider a closed form solution, especially so if the statistics involved are well known and can easily be communicated to the financial community.