[Paper Review] A queueing theory description of cascades in financial markets and fat-tailed price returns

Harbir Lamba|arXiv (Cornell University)|Aug 6, 2009

Complex Systems and Time Series Analysis2 citations

TL;DR

The paper proposes a threshold-based agent model in financial markets where price changes trigger trading decisions, linking these to queueing theory: large price movements correspond to busy periods in a single-server queue. This framework naturally generates fat-tailed return distributions and excess kurtosis, offering a systematic way to model market panics and deleveraging without abandoning market efficiency.

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.

Motivation & Objective

• To explain stylized facts of financial markets—like fat-tailed returns and volatility clustering—within a framework that preserves market efficiency.
• To model long-horizon agent behavior using price thresholds, extending beyond typical order-book time scales.
• To establish a formal connection between market dynamics and queueing theory, particularly busy periods in single-server queues.
• To provide a mechanism for generating excess kurtosis and non-exponential decay in price changes without introducing inefficiencies.

Proposed method

• Agents make trades when asset prices cross predefined thresholds, simulating long-horizon or stress-driven behavior.
• The model maps price movements to the busy periods of a single-server queue, where arrivals represent price changes and service represents market clearing.
• The system assumes a queue with general inter-arrival and service time distributions, allowing for analytical tractability under known queueing theory results.
• The distribution of busy periods is derived using renewal theory and embedded Markov chains, capturing the statistical properties of large price moves.
• The model incorporates parameters such as arrival rate and service time distribution to control the tail behavior of return distributions.
• The framework is validated by showing that the resulting return distribution exhibits excess kurtosis and power-law decay, matching empirical stylized facts.

Experimental results

Research questions

• RQ1 How can price-triggered agent behavior be modeled to replicate fat-tailed price returns without violating market efficiency?
• RQ2 What is the mathematical relationship between price threshold triggers and queueing system busy periods?
• RQ3 Can queueing theory explain the emergence of excess kurtosis and non-exponential decay in financial return distributions?
• RQ4 How do the parameters of a queueing system map to observable market phenomena like volatility clustering and panic-driven deleveraging?
• RQ5 To what extent can this model serve as a foundation for stress-testing financial institutions under extreme market conditions?

Key findings

• The distribution of busy periods in a single-server queue exhibits excess kurtosis, matching the leptokurtic nature of empirical financial return distributions.
• Non-exponential decay in the tail of the busy period distribution emerges under general assumptions on queue parameters, replicating the heavy-tailed behavior seen in real market returns.
• The model generates fat-tailed returns and volatility clustering through a mechanism rooted in queueing dynamics, without requiring market inefficiencies or complex agent interactions.
• Price threshold-based trading leads to systemic behavior that mirrors real market panics, particularly during periods of rapid deleveraging.
• The framework provides a mathematically sound and analytically tractable method to model extreme market events, enabling stress-testing of financial institutions.