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Propagation of balance-sheet or cash-flow insolvency across financial institutions may be modeled as a cascade process on a network representing their mutual exposures. We derive rigorous asymptotic results for the magnitude of contagion in a large financial network and give an analytical expression for the asymptotic fraction of defaults, in terms of network characteristics. Our results extend previous studies on contagion in random graphs to inhomogeneous directed graphs with a given degree sequence and arbitrary distribution of weights. We introduce a criterion for the resilience of a large financial network to the insolvency of a small group of financial institutions and quantify how contagion amplifies small shocks to the network. Our results emphasize the role played by contagious links and show that institutions which contribute most to network instability in case of default have both large connectivity and a large fraction of contagious links. The asymptotic results show good agreement with simulations for networks with realistic sizes.
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Using particle system methodologies we study the propagation of financial distress in a network of firms facing credit risk. We investigate the phenomenon of a credit crisis and quantify the losses that a bank may suffer in a large credit portfolio. Applying a large deviation principle we compute the limiting distributions of the system and determine the time evolution of the credit quality indicators of the firms, deriving moreover the dynamics of a global financial health indicator. We finally describe a suitable version of the Central Limit Theorem useful to study large portfolio losses. Simulation results are provided as well as applications to portfolio loss distribution analysis.
Following the financial crisis of 2007-2008, a deep analogy between the origins of instability in financial systems and complex ecosystems has been pointed out: in both cases, topological features of network structures influence how easily distress can spread within the system. However, in financial network models, the details of how financial institutions interact typically play a decisive role, and a general understanding of precisely how network topology creates instability remains lacking. Here we show how processes that are widely believed to stabilise the financial system, i.e. market integration and diversification, can actually drive it towards instability, as they contribute to create cyclical structures which tend to amplify financial distress, thereby undermining systemic stability and making large crises more likely. This result holds irrespective of the details of how institutions interact, showing that policy-relevant analysis of the factors affecting financial stability can be carried out while abstracting away from such details.
We test the hypothesis that interconnections across financial institutions can be explained by a diversification motive. This idea stems from the empirical evidence of the existence of long-term exposures that cannot be explained by a liquidity motive (maturity or currency mismatch). We model endogenous interconnections of heterogenous financial institutions facing regulatory constraints using a maximization of their expected utility. Both theoretical and simulation-based results are compared to a stylized genuine financial network. The diversification motive appears to plausibly explain interconnections among key players. Using our model, the impact of regulation on interconnections between banks -currently discussed at the Basel Committee on Banking Supervision- is analyzed.
The 2008 financial crisis has been attributed to excessive complexity of the financial system due to financial innovation. We employ computational complexity theory to make this notion precise. Specifically, we consider the problem of clearing a financial network after a shock. Prior work has shown that when banks can only enter into simple debt contracts with each other, then this problem can be solved in polynomial time. In contrast, if they can also enter into credit default swaps (CDSs), i.e., financial derivative contracts that depend on the default of another bank, a solution may not even exist. In this work, we show that deciding if a solution exists is NP-complete if CDSs are allowed. This remains true if we relax the problem to $varepsilon$-approximate solutions, for a constant $varepsilon$. We further show that, under sufficient conditions where a solution is guaranteed to exist, the approximate search problem is PPAD-complete for constant $varepsilon$. We then try to isolate the origin of the complexity. It turns out that already determining which banks default is hard. Further, we show that the complexity is not driven by the dependence of counterparties on each other, but rather hinges on the presence of so-called naked CDSs. If naked CDSs are not present, we receive a simple polynomial-time algorithm. Our results are of practical importance for regulators stress tests and regulatory policy.
We propose a novel credit default model that takes into account the impact of macroeconomic information and contagion effect on the defaults of obligors. We use a set-valued Markov chain to model the default process, which is the set of all defaulted obligors in the group. We obtain analytic characterizations for the default process, and use them to derive pricing formulas in explicit forms for synthetic collateralized debt obligations (CDOs). Furthermore, we use market data to calibrate the model and conduct numerical studies on the tranche spreads of CDOs. We find evidence to support that systematic default risk coupled with default contagion could have the leading component of the total default risk.
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