A queueing theory description of cascades in financial markets and fat-tailed price returns

In a financial market, it is often changes in the asset price that act as the trigger for transactions or shifts in investment position. For agents with long investment horizons, and under normal market conditions, trades may only occur infrequently, while for other agents, or at times of severe market stress, the timescales involved may be much shorter. We argue that in either case the use of price thresholds to simulate agent behaviour has some important and desirable features. We then demonstrate a very close link between such threshold models and queueing theory, with the largest price changes corresponding to the busy period in a single-server queue. The distribution of this busy period is known to have excess kurtosis and non-exponential decay under various assumptions on the queue parameters. Such an approach may also prove useful in the development of mathematical models for rapid deleveraging in financial markets and the stress-testing of financial institutions. PACS numbers 89.65.Gh 89.75.Da