# Illiquidity and Insolvency: A Double Cascade Model of Financial Crises

28 Pages Posted: 19 Apr 2014 Last revised: 12 Nov 2014

See all articles by Thomas R. Hurd

## Thomas R. Hurd

McMaster University - Department of Mathematics and Statistics

## Davide Cellai

University of Limerick - Department of Mathematics and Statistics

## Sergey Melnik

University of Limerick

## Quentin Shao

McMaster University - Department of Mathematics and Statistics

Date Written: April 14, 2014

### Abstract

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.

Keywords: systemic risk, banking network, contagion, random graph, default, funding liquidity, credit risk, financial mathematics

Suggested Citation

Hurd, Thomas R. and Cellai, Davide and Melnik, Sergey and Shao, Quentin, Illiquidity and Insolvency: A Double Cascade Model of Financial Crises (April 14, 2014). Available at SSRN: https://ssrn.com/abstract=2424877 or http://dx.doi.org/10.2139/ssrn.2424877