Dr. Arzé Karam - Blog II: Quantum Walk for liquidity crises predictions

During Japan’s August 2024 market collapse, our QW simulations (shown in gray) closely replicated the real price trajectory (in red).

The “scale factor” below captures rising instability as liquidity evaporates.
The Quantum Walk not only reproduced the magnitude of the crash but also detected its pre-collapse phase, when feedback loops intensified just before noon Tokyo time.

In contrast, traditional volatility models failed to detect this buildup, interpreting it as routine noise until the crash was already underway.

The 2014 Treasury flash rally — one of the fastest bond repricings in history — also exhibits the same signature:

QW simulations captured a liquidity-driven regime shift, where buying pressure and algorithmic autocorrelation reinforced each other.
The model revealed how the market moved from equilibrium to explosive upward motion without new information.

This illustrates that market fragility can be endogenous — born from within the market’s structure rather than external shocks.

⚡ Quantum Walks and the Anatomy of Market Collapses / RALLIES

When markets crash, they rarely do so smoothly. Liquidity vanishes, spreads explode, and feedback loops between traders amplify each tick into an avalanche. Traditional financial models — from Geometric Brownian Motion to Markov-switching frameworks — fail to capture these self-reinforcing, nonlinear dynamics.

In our latest study, we take a new path: modeling market collapses through Quantum Walk (QW) simulations, a framework inspired by quantum mechanics and adapted to high-frequency trading environments.

🧠 What Is a Quantum Walk Model?

A Quantum Walk (QW) is the quantum analog of a random walk — but instead of moving randomly with fixed probabilities, the walker’s path evolves under superposition and interference. This structure allows price movements to reflect the entanglement of liquidity, order flow, and trader behavior, rather than assuming independence between ticks.

In finance, that means QW models can simulate multiple overlapping market states — such as panic selling and algorithmic buying — and observe how they interact before one dominates.

🔍 Modeling Flash Crashes with QW: additional results on Covid-19 and War samples in the paper.

We parameterize the Quantum Walk process using liquidity conditions derived from order book data and machine learning measures like Quote Volatility Pressure (QVP).

When depth is high, interference between market states remains stable — prices move smoothly.
As liquidity thins, interference collapses into a dominant downward path — a crash.

This approach allows us to visualize and predict nonlinear transitions where classical models remain blind.

🔮 Why Quantum Walks Matter

The strength of Quantum Walk models lies in their discrete-time precision and adaptive structure.
They enable:

Early warning signals linking thinning liquidity to rising crash probabilities.
Realistic simulations of feedback loops between order flow, volatility, and trader reactions.
Better alignment with empirical return distributions, capturing fat tails and skewness organically.

Where classical finance smooths over discontinuities, QW models embrace them — turning micro-level chaos into predictive insight.

⚙️ A New Frontier for Market Microstructure?

This framework extends beyond reduced-form or regime-switching models, offering a complexity-based approach to price formation and liquidity risk. By integrating machine learning features like Quote Volatility Pressure into QW dynamics, we create a bridge between quantum-inspired computation and modern market analytics.

In doing so, Quantum Walks redefine how we think about crashes:

Not as unpredictable “black swans,” but as computable outcomes of emergent liquidity feedback.

🧩 Key Takeaways

Quantum Walks provide a new lens to understand how markets move from stability to collapse. They offer traders, researchers, and regulators a model that learns from microstructure, adapts to complexity, and captures the heartbeat of liquidity itself.

As high-frequency trading and algorithmic strategies dominate global markets, tools like QW simulations may become essential — not just to explain the past, but to anticipate the next liquidity shock before it unfolds.

🔗 Read the paper: “A discrete-time quantum walk model of extreme market events: a complexity-based approach”