Static Cascade Models

Abstract

Network effects such as default contagion and liquidity hoarding are transmitted between banks by direct contact through their interbank exposures. During asset fire sales, shocks are transmitted indirectly from a bank selling assets to other banks via the impact on the price of their common assets. Banks maintain safety buffers in normal times, but these may be weakened or fail during a crisis. Asset prices that are relatively stable in normal times may collapse during a crisis. Banks react to such stresses by making large adjustments to their balance sheets. Such adjustments send further shocks to their counterparties both directly through their exposures and indirectly via asset price impact, creating a cascade. All these cascade mechanisms can be modelled mathematically starting from a common framework. In such models, the eventual extent of a crisis is a fixed point or equilibrium of a cascade mapping. Towards the end of the chapter, a proposal is made that the properties of cascade mappings can be most clearly understood when implemented on very large random financial networks.