2012/10/17 by Brice Hakwa, Hakwa, Brice, Manfred Jäger-Ambrożewicz +3
Economics, Econometrics and Finance · #62H20 #62H99 #62P05 #90A09 #91B30 #91B82 #91G10 #91G40 #FOS: Economics and business #Risk Management (q-fin.RM) #msc:62H20 #msc:62H99 #msc:62P05 #msc:90A09 #msc:91B30 #msc:91B82 #msc:91G10 #msc:91G40 #q-fin.RM
paper · pdf · doi:10.48550/arxiv.1210.4713
26 pages, 5 figures
arxiv created 2012/11/24 · arxiv updated 2012/11/27
This paper is devoted to the quantification and analysis of marginal risk contribution of a given single financial institution i to the risk of a financial system s. Our work expands on the CoVaR concept proposed by Adrian and Brunnermeier as a tool for the measurement of marginal systemic risk contribution. We first give a mathematical definition of CoVaRαs|Li=l. Our definition improves the CoVaR concept by expressing CoVaRαs|Li=l as a function of a state l and of a given probability level αrelative to i and s respectively. Based on Copula theory we connect CoVaRαs|Li=l to the partial derivatives of Copula through their probabilistic interpretation and definitions (Conditional Probability). Using this we provide a closed formula for the calculation of CoVaRαs|Li=l for a large class of (marginal) distributions and dependence structures (linear and non-linear). Our formula allows a better analysis of systemic risk using CoVaR in the sense that it allows to define CoVaRαs|Li=l depending on the marginal distributions of the losses of i and s respectively and the copula between Li and Ls. We discuss the implications of this in the context of the quantification and analysis of systemic risk contributions. %some mathematical This makes possible the For example we will analyse the marginal effects of Li, Ls and C of the risk contribution of i.