Closed Form Solutions of Measures of Systemic Risk

Abstract

This paper derives -- considering a Gaussian setting -- closed form solutions of the statistics that Adrian and Brunnermeier (2010) and Acharya et al. (2009) 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. It may be relatively easy to convince the regulators to use a closed form solution, especially so if the statistics involved are well known and can easily be communicated to the financial community. Also, the statistics may be analyzed using dynamic econometric models of volatility and correlation (Engle (2009), McNeil et al. (2005, chapter 4.6)).

Keywords: Systemic Risk, Value at Risk, Expected Shortfall, Conditional Value at Risk, Conditional Expected Shortfall, M-Garch, Capital requirements, Regulation, Basel III

JEL Classification: G10, G18, G20, C32, C58