Systemic Shock Propagation in a Complex System

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. Such pairwise interactions ensure that the system develops with time in a self-determining non-linear way. 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. The particular points of interest are, first, the characteristics of the system before and after the shock is delivered. The second point is how long it takes the shock to affect the entire system. The study proceeds by simulating multiple interactions, and is applicable to both social and business contexts. 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 in an idiosyncratic effect only for the agents concerned. However, if an agent is capable of transmitting 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. We also formulate a 'contagion index' to measure the extent of loss by debt default within a group of financial institutions