In the aftermath of the interbank market collapse of 2007-08, the traditional idea that systemic risk is primarily the risk of cascading bank defaults has evolved into the view that it involves both cascading bank defaults as well as funding liquidity shocks, and that both types of shocks impair the functioning of the remaining undefaulted banks . In current models of systemic risk, these two facets , namely funding illiquidity and insolvency, are treated as two  separate phenomena.  Our paper introduces a deliberately simplified model which integrates insolvency and illiquidity in financial networks and that can provide answers to the question of how illiquidity or default of one bank can influence the overall level of liquidity stress and default in the network. First, this paper proposes a stylized model of individual bank balance sheets that builds in regulatory constraints. Secondly, three different possible states of a bank, namely the normal state, the stressed state and the insolvent state, are identified with conditions on the bank's balance sheet. Thirdly, the paper models the behavioural response of a bank when it finds itself in the stressed or insolvent states. Importantly, a stressed bank seeks to protect itself from the default of its counterparties, but creates stress in the network by forcing its debtor banks to raise cash. Versions of these proposed models can be solved by large-network asymptotic cascade formulas. Details of numerical experiments are given that verify that these asymptotic formulas yield the expected quantitative agreement with Monte Carlo results for large finite networks  . These experiments illustrate clearly our main conclusion that in financial networks, the average default probability is inversely related to strength of banks' stress response and therefore to the overall level of stress in the network.
In the aftermath of the interbank market collapse of 2007-08, the scope of systemic risk research has broadened to encompass a wide range of channels, notably asset correlations, default contagion, illiquidity contagion, and asset firesales . In current models of systemic risk, two facets of contagion , namely funding illiquidity and insolvency, are treated as two distinct and separate phenomena. The main goal of the double cascade model we introduce is to integrate these two facets. In a default cascade, insolvency of a given bank will create a shock to the asset side of the balance sheet of each of its creditor banks. Under some circumstances, such "downstream" shocks can cause further insolvencies that may build up to create a global insolvency cascade. On the other hand, in a stress cascade, illiquidity that hits a given bank will create a shock to the liability side of the balance sheet of each of its debtor banks. Such "upstream" shocks can cause further illiquidity stresses that may build up to create a global illiquidity cascade. Our paper introduces a deliberately simplified network model of insolvency and illiquidity that can quantify how illiquidity or default of one bank influences the overall level of liquidity stress and default in the network. Under an assumption we call "locally tree-like independence", we derive large-network asymptotic cascade formulas. Results of numerical experiments then demonstrate that these asymptotic formulas agree qualitatively with Monte Carlo results for large finite networks , and quantitatively except when the system is placed in an exceptional "knife-edge" configuration . These experiments illustrate clearly our main conclusion that in financial networks, the average default probability is inversely related to strength of banks' stress response and therefore to the overall level of stress in the network.
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traditional idea that systemic risk is primarily the risk of cascading bank defaults has evolved into the view that it involves both cascading bank defaults as well as funding liquidity shocks, and that both types of shocks impair the functioning of the remaining undefaulted banks
scope of systemic risk research has broadened to encompass a wide range of channels, notably asset correlations, default contagion, illiquidity contagion, and asset firesales
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these two facets
two facets of contagion
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distinct and
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The main goal of the double cascade model we introduce is to integrate these two facets. In a default cascade, insolvency of a given bank will create a shock to the asset side of the balance sheet of each of its creditor banks. Under some circumstances, such "downstream" shocks can cause further insolvencies that may build up to create a global insolvency cascade. On the other hand, in a stress cascade, illiquidity that hits a given bank will create a shock to the liability side of the balance sheet of each of its debtor banks. Such "upstream" shocks can cause further illiquidity stresses that may build up to create a global illiquidity cascade.
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model which integrates
network model of
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in financial networks and that can provide answers to the question of
that can quantify
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can influence
influences
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First, this paper proposes a stylized model of individual bank balance sheets that builds in regulatory constraints. Secondly, three different possible states of a bank, namely the normal state, the stressed state and the insolvent state, are identified with conditions on the bank's balance sheet. Thirdly, the paper models the behavioural response of a bank when it finds itself in the stressed or insolvent states. Importantly, a stressed bank seeks to protect itself from the default of its counterparties, but creates stress in the network by forcing its debtor banks to raise cash. Versions of these proposed models can be solved by
Under an assumption we call "locally tree-like independence", we derive
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Details
Results
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are given that verify that
then demonstrate that
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yield the expected quantitative agreement
agree qualitatively
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, and quantitatively except when the system is placed in an exceptional "knife-edge" configuration