Stability in Financial Networks

In the modern financial system banks are linked by the complex web of financial claims into a network structure. As shown by the financial crisis, especially after the failure of Lehman Brothers, these interdependencies have created the possibility to amplified responses to shocks to the financial system. This complex system of financial links has also made it hard to assess the potential for contagion arising from the insolvency of several banks. The main purpose of this paper is to investigate the effect of the network topology properties on the default contagion process. More precisely, in this paper following Gai and Kapadia (2010), we derived the condition under which the default contagion spreads across a significant part of the network. Theoretical and simulation comparisons of the contagion conditions for the Poisson and Scale Free networks were made. Secondly, theoretically and by simulations it was shown that the empirical phenomena of positive correlation between the number of banks-borrowers and banks-lenders of a bank in the Financial Network ("in/out" degree correlation) reduces the likelihood of contagion. Thirdly, the expressions for the probability of default contagion conditional on the default of a random bank and the extent of default contagion were derived and verified by comparison with simulations results. The "robust-yet-fragile" property of the financial network was verified. Fourthly, the model was adjusted allowing the exogenous probability of "cure" of a defaulted bank at any period of time, and interpreted as a SIS model. The solution for the final fraction of insolvent banks and contagion condition were derived via Mean Field analysis. In the adjusted set up the effect of "in/out" degree correlation on the default contagion condition was investigated. In the adjusted setup the nonmonotonic effect of the variance of the degree distribution on the likelihood of contagion was deduced.