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.
The scope of financial systemic risk research encompasses a wide range of channels and effects, including asset correlation shocks , default contagion, illiquidity contagion, and asset firesales. For example, insolvency of a given bank will create a shock to the asset side of the balance sheet of each of its creditor banks and under some circumstances, such "downstream" shocks can cause further insolvencies that may build up to create what is called an insolvency or default cascade. On the other hand, funding illiquidity that hits a given bank will create a shock to the liability side of the balance sheet of each of its debtor banks. Under some circumstances, such "upstream" shocks can cause illiquidity in further banks that may build up to create an illiquidity cascade. This paper introduces a deliberately simplified financial network model that combines the default and liquidity stress mechanisms into a "double cascade mapping". The progress and eventual result of the crisis is obtained by iterating this mapping to its fixed point. Unlike simpler models, this model can therefore quantify how illiquidity or default of one bank influences the eventual overall level of liquidity stress and default in the system. Large-network asymptotic cascade mapping formulas are derived that can be used for efficient network computations of the double cascade. Numerical experiments then demonstrate that these asymptotic formulas agree qualitatively with Monte Carlo results for large finite networks, and quantitatively except when the initial system is placed in an exceptional "knife-edge" configuration. The experiments clearly support the main conclusion that in the absence of fire sales , the average eventual level of defaults in a financial network is negatively related to the strength of banks' liquidity stress response and the eventual level of stress in the network.
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