[Paper Review] Market Dynamics of Information Avalanches

Bernhard K. Meister|arXiv (Cornell University)|Feb 27, 2026

Complex Systems and Time Series Analysis0 citations

TL;DR

The paper models information flow in financial markets as a sandpile with self-organized criticality, analyzes geodesic (no-arbitrage) paths on an information-manifold, and derives a dynamic arbitrage strategy exploiting deviations from geodesic flow.

ABSTRACT

Financial markets convert the incremental arrival of information into asset price changes. In a sandpile model grains of sand represent bits of data, and the size of an avalanche, governed by a scaling law, is linked to price volatility. While this model of self-organized criticality reproduces stylized facts, it also identifies a structural tension between the non-arbitrage condition and price adjustments consistent with a constant Sharpe ratio.

Motivation & Objective

• Motivate how incremental information arrivals trigger price volatility through a sandpile mechanism and SOC.
• Connect information processing to a two-dimensional Gaussian market representation (drift and volatility) on a hyperbolic geometry.
• Show that geodesic paths on the Fisher information metric represent zero-dissipation transitions and no-arbitrage constraints.
• Quantify arbitrage opportunities arising from deviations from geodesic flow and outline a dynamic trading strategy.

Proposed method

• Model information as a sandpile with slow loading and fast avalanches.
• Use the Fisher information metric on the upper half-plane to describe the Gaussian market manifold with coordinates (μ, σ).
• Derive geodesic paths as semicircles and compute their hyperbolic length between states.
• Establish a no-arbitrage geodesic relation and express excess action as a difference between Euclidean and geodesic path lengths.
• Propose a dynamic hedge-rebalancing strategy that exploits the arbitrage between geodesic and Euclidean paths.

Experimental results

Research questions

• RQ1 What is the geometric structure of market states (μ, σ) under information-driven dynamics in this model?
• RQ2 How do avalanches map to volatility changes, and what is the resulting geodesic no-arbitrage condition?
• RQ3 What is the quantitative arbitrage potential when markets follow non-geodesic (Euclidean) paths?
• RQ4 How can one dynamically exploit deviations from geodesic flow to form an optimal trading strategy?

Key findings

• Avalanches in the sandpile model drive instantaneous volatility jumps, while between avalanches volatility mean-reverts.
• Geodesics on the Fisher information metric in the μ–σ upper half-plane provide the zero-dissipation (no-arbitrage) paths between market states.
• The geodesic length between states is given by hyperbolic distance L_geo = arcosh(1 + ((μ2−μ1)² + 2(σ2−σ1)²)/(4σ1σ2)).
• The Euclidean (constant Sharpe) path has a calculable excess action ΔL compared to the geodesic, representing a harvestable arbitrage opportunity.
• A local arbitrage strategy involves long the underlying and short volatility in proportions tied to derivatives of the pricing function to exploit the ΔL mispricing.
• The framework distinguishes geodesic flow from Onsager excursions, with the Banker lag arising from slow Sharpe-ratio adjustments rather than market breakdown.