Systemic shock propagation in a complex system

Abstract

We study the effects of delivering a shock to a complex system comprising components (‘agents’) that interact in a pairwise fashion, independent of other parts of the system and with no central control. There are three aspects to the contribution of this paper. First, shock propagation in a network is developed purely from fundamental principles of complex systems. Second, systemic risk is shown to arise naturally in such a complex system. If a shock is delivered either to one agent or to many agents simultaneously, that shock may be transmitted further, thereby resulting in systemic risk. Third, the monetary loss to the entire system as a result of systemic shock is quantified. Simulations are used to study two particular characteristics of the interactions. The first is the resistance or susceptibility of individual agents to a shock. The second is the time it takes for the shock to affect the entire system. The results show that if a shock is applied to all agents in a network, the systemic effect of that shock is transmitted very quickly. Applying a shock to very few agents results only in an idiosyncratic effect. If an agent can transmit the shock further, a systemic effect will result. The recovery period for agents affected by a systemic shock can be orders of magnitude greater than the time taken for the shock to take effect. The overall effect of the shock on the system is quantified by formulating a ‘contagion index’, which measures the ratio of the total capital lost due to the systemic effect to the total capital before the shock was delivered. The result (approximately 7%) is consistent with other studies, but is more widely applicable because it is not based on one empirical data set.