On the Computational Complexity of Measuring Global Stability of Banking Networks

Threats on the stability of a financial system may severely affect the functioning of the entire economy, and thus considerable emphasis is placed on the analyzing the cause and effect of such threats. The financial crisis in the current and past decade has shown that one important cause of instability in global markets is the so-called financial contagion, namely the spreading of instabilities or failures of individual components of the network to other, perhaps healthier, components. This leads to a natural question of whether the regulatory authorities could have predicted and perhaps mitigated the current economic crisis by effective computations of some stability measure of the banking networks. Motivated by such observations, we consider the problem of defining and evaluating stabilities of both homogeneous and heterogeneous banking networks against propagation of synchronous idiosyncratic shocks given to a subset of banks. We formalize the homogeneous banking network model of Nier et al. and its corresponding heterogeneous version, formalize the synchronous shock propagation procedures, define two appropriate stability measures and investigate the computational complexities of evaluating these measures for various network topologies and parameters of interest. Our results and proofs also shed some light on the properties of topologies and parameters of the network that may lead to higher or lower stabilities.Comment: to appear in Algorithmic

Global Stability of Financial Networks : Measures, Evaluations and Policy Implications

Threats on the stability of a financial system can severely affect the functioning of the entire economy. Thus considerable emphasis was placed on analyzing the cause and effects of such threats. Recent crisis in the global financial world has generated renewed interests in fragilities of global financial networks among economists and regulatory authorities. The financial crisis in the current and the past decade has shown that one important cause of instability in global markets was the so-called financial contagion, namely the instabilities or failures of individual components in the network spreads to otherwise healthier components, affecting the entire system. In the first part of the thesis we formalized the homogeneous banking network model of Nier et al. (78), its corresponding heterogeneous version, formalize the synchronous shock propagation procedure outlined in (78; 40). We defined appropriate stability measures and investigate the computational complexity of evaluating these measures for various network topologies and parameters of interest. We performed a comprehensive empirical evaluation over more than 700,000 combinations of network types and parameter combinations. Our results and proofs also shed some light on the properties of topologies and parameters of network that may lead to higher or lower stabilities. In the second part of the thesis we consider a banking network model introduced by (91) A. Zawadoski. In his model the asset risks and counter party risks are treated separately and each bank has only two counter party neighbors, a bank fails due to the counter party risk only if at least one of its two neighbors default. We consider the above model for more general network topologies, namely when each node has exactly 2r counter party neighbors for some integer r > 0 and show that as the number of counter party neighbors increase the probability of counter party risk also increases, hence banks not only hedge their asset risk but also hedge its counter party risk

On the Computational Complexity of Measuring Global Stability of Banking Networks

Threats on the stability of a financial system may severely affect the functioning of the entire economy, and thus considerable emphasis is placed on the analyzing the cause and effect of such threats. The financial crisis in the current and past decade has shown that one important cause of instability in global markets is the so-called financial contagion, namely the spreading of instabilities or failures of individual components of the network to other, perhaps healthier, components. This leads to a natural question of whether the regulatory authorities could have predicted and perhaps mitigated the current economic crisis by effective computations of some stability measure of the banking networks. Motivated by such observations, we consider the problem of defining and evaluating stabilities of both homogeneous and heterogeneous banking networks against propagation of synchronous idiosyncratic shocks given to a subset of banks. We formalize the homogeneous banking network model of Nier et al. and its corresponding heterogeneous version, formalize the synchronous shock propagation procedures, define two appropriate stability measures and investigate the computational complexities of evaluating these measures for various network topologies and parameters of interest. Our results and proofs also shed some light on the properties of topologies and parameters of the network that may lead to higher or lower stabilities.