Contagion risk in the interbank market: a probabilistic approach to cope with incomplete structural information

One lesson of the financial crisis erupting in 2008 has been that domino effects constitute a serious threat to the stability of the financial sector, i.e. the failure of one node in the interbank network might entail the danger of contagion to large parts of the entire system. How important this effect is, depends on the exact topology of the network on which the supervisory authorities have typically very incomplete knowledge. In order to explore the extent of contagion effects and to analyse the effectiveness of macroprudential measures to contain such effects, a reconstruction of the quantitative features of the empirical network would be needed. We propose a probabilistic approach to such a reconstruction: we propose to combine some important known quantities (like the size of the banks) with a realistic stochastic representation of the remaining structural elements. Our approach allows us to evaluate relevant measures for the contagion risk after default of one unit (i.e. the number of expected subsequent defaults, or their probabilities). For some quantities we are able to derive closed form solutions, others can be obtained via computational mean-field approximations.