Market-Implied Systemic Risk and Shadow Capital Adequacy

Abstract

This paper presents a forward-looking approach to measure systemic solvency risk using contingent claims analysis (CCA) as a theoretical foundation for determining an institution’s default risk based on the uncertainty in its asset value relative to promised debt payments over time. Default risk can be quantified as market-implied expected losses calculated from integrating equity market and balance sheet information in a structural default risk model. The expected losses of multiple banks and their non-parametric dependence structure define a multivariate distribution that generates portfolio-based estimates of the joint default risk using the aggregation technique of the Systemic CCA framework (Jobst and Gray, 2013). This market-implied valuation approach (‘shadow capital adequacy’) endogenises bank solvency as a probabilistic concept based on the perceived default risk (in contrast to accounting-based prudential measures of capital adequacy). The presented model adds to the literature of analytical tools estimating market-implied systemic risk by augmenting the CCA approach with a jump diffusion process of asset changes to inform a more comprehensive and flexible assessment of common vulnerabilities to tail risks of the four largest UK commercial banks.

Keywords: systemic risk, contingent claims analysis, jump diffusion, CoVaR, systemic expected shortfall, conditional tail expectation, capital adequacy

JEL Classification: C61, C63, G01, G21, G28