An Optimization View of Financial Systemic Risk Modeling : The Network Effect and the Market Liquidity Effect

Financial institutions are interconnected directly by holding debt claims against each other (the network channel), and they are also bound by the market liquidity in selling assets to meet debt liabilities when facing distress (the liquidity channel). The goal of our study is to investigate how these two channels of risk interact to propagate individual defaults to a system-wide catastrophe. We formulate the model as an optimization problem with equilibrium constraints and derive a partition algorithm to solve for the market-clearing equilibrium. The solutions so obtained enables us to identify two factors, the network multiplier and the liquidity amplifier, to characterize the contributions of these two channels to financial systemic risk, whereby we can acquire better understanding of the effectiveness of several policy interventions. The analysis behind the algorithm yields estimates for the contagion probability on the basis of the market value of the institutions' net worths, underscoring the importance of equity capital as a cushion against systemic shocks in the presence of the liquidity channel. The optimization formulation also provides more structural insights to allow us to extend the study of systemic risk to a system with debts of different seniorities, and meanwhile presents a close connection to the literature of stochastic networks. Finally, we illustrate the impacts of the network and the liquidity channels -- in particular, the significance of the latter -- in the formation of systemic risk with data on the European banking system