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

TL;DR

This paper links queueing theory to financial market models, showing how threshold-based agent behaviors can produce fat-tailed price returns and stylized facts, useful for stress-testing and understanding market panics.

Contribution

It introduces a novel queueing theory framework for modeling fat-tailed returns in imperfect markets, bridging agent thresholds with queue busy periods.

Findings

Large price changes correspond to queue busy periods.

Model replicates stylized facts of financial returns.

Excess kurtosis observed in busy period distributions.

Abstract

In a financial market, for agents with long investment horizons or at times of severe market stress, it is often changes in the asset price that act as the trigger for transactions or shifts in investment position. This suggests the use of price thresholds to simulate agent behavior over much longer timescales than are currently used in models of order-books. We show that many phenomena, routinely ignored in efficient market theory, can be systematically introduced into an otherwise efficient market, resulting in models that robustly replicate the most important stylized facts. We then demonstrate a close link between such threshold models and queueing theory, with large price changes corresponding to the busy periods of a single-server queue. The distribution of the busy periods is known to have excess kurtosis and non-exponential decay under various assumptions on the queue parameters. Such an approach may prove useful in the development of mathematical models for rapid deleveraging and panics in financial markets, and the stress-testing of financial institutions.