Fire Sales, Default Cascades and Complex Financial Networks

We present a general tractable framework for understanding the joint impact of fire sales and default cascades on systemic risk in complex financial networks. Our limit theorems quantify how price mediated contagion across institutions with common asset holding could worsen cascades of insolvencies in a heterogeneous financial network, during a financial crisis. For given prices of illiquid assets, we show that, under some regularity assumptions, the default cascade model could be transferred to a death process problem represented by balls-and-bins model. We model the price impact by a given inverse demand function. We state various limit theorems regarding the total sold shares and the equilibrium price of illiquid assets in a stylized fire sales model. In particular, we show that the equilibrium prices of illiquid assets has asymptotically Gaussian fluctuations. Our numerical studies investigate the effect of heterogeneity in network structure and price impact function on the final size of default cascade and fire sales loss.