[Paper Review] Contagion in the world's stock exchanges seen as a set of coupled oscillators

Lucia Bellenzier, Jørgen Vitting Andersen+1 more|arXiv (Cornell University)|Feb 24, 2016

Complex Systems and Time Series Analysis53 references17 citations

TL;DR

This paper models the world's stock exchanges as coupled integrate-and-fire (IAF) oscillators to study financial contagion, leveraging a behavioral trait—'blindness to small changes'—to explain delayed collective responses. The model identifies direct cause-effect relationships in price movements without statistical tests, revealing Germany and France as top contagion sources, while the U.S. and U.K. drive broader positive and negative market spillovers, respectively.

ABSTRACT

We study how the phenomenon of contagion can take place in the network of the world's stock exchanges due to the behavioral trait "blindeness to small changes". On large scale individual, the delay in the collective response may significantly change the dynamics of the overall system. We explicitely insert a term describing the behavioral phenomenon in a system of equations that describe the build and release of stress across the worldwide stock markets. In the mathematical formulation of the model, each stock exchange acts as an integrate-and-fire oscillator. Calibration on market data validate the model. One advantage of the integrate-and-fire dynamics is that it enables for a direct identification of cause and effect of price movements, without the need for statistical tests such as for example Granger causality tests often used in the identification of causes of contagion. Our methodology can thereby identify the most relevant nodes with respect to onset of contagion in the network of stock exchanges, as well as identify potential periods of high vulnerability of the network. The model is characterized by a separation of time scales created by a slow build up of stresses, for example due to (say monthly/yearly) macroeconomic factors, and then a fast (say hourly/daily) release of stresses through "price-quakes" of price movements across the worlds network of stock exchanges.

Motivation & Objective

• To understand how financial contagion spreads across global stock exchanges through non-linear price dynamics.
• To address the limitations of correlation-based methods in identifying cause and effect in contagion by introducing a mechanistic model.
• To identify the most influential markets in initiating contagion avalanches using a behavioral, time-scale-separated framework.
• To validate the model using real market data and provide direct causal inference without relying on Granger causality or similar statistical tests.

Proposed method

• Each stock exchange is modeled as an integrate-and-fire (IAF) oscillator, where stress accumulates slowly and is released suddenly in 'price-quakes'.
• A behavioral term for 'blindness to small changes' is explicitly embedded, delaying response to minor market movements and enabling delayed, synchronized responses.
• The model features a separation of time scales: slow build-up of stress from macroeconomic fundamentals and fast release via inter-market price propagation.
• Contagion is modeled as 'avalanches'—synchronized bursts of price movements—triggered when a market reaches a critical threshold.
• Network-level contagion is analyzed by tracking the origin and spread of these avalanches across exchanges, identifying source and impact nodes.
• Calibration on historical market data validates the model’s ability to reproduce observed non-linear dynamics and avalanche behavior.

Experimental results

Research questions

• RQ1 Which stock exchanges are the primary sources of contagion in the global market network?
• RQ2 How does the delay in response to small price changes influence the synchronization and propagation of market stress?
• RQ3 What is the average number of markets affected by a contagion avalanche originating from a given exchange?
• RQ4 How do positive and negative price movements differ in their propagation patterns across the network?
• RQ5 Can direct cause-effect relationships in price movements be identified without relying on statistical causality tests like Granger causality?

Key findings

• Germany and France are the top sources of contagion, each initiating 15.8% and 14.4% of all systemic price-quakes (SIPQs), respectively.
• The U.S. market is responsible for 9.7% of SIPQ onsets but drives the largest average number of impacted markets (14.0) in positive avalanches.
• The U.K. is a dominant source of positive contagion, affecting 15.2 markets on average per avalanche, while Switzerland is a major source of negative contagion, affecting 12.0 markets on average.
• The Netherlands appears to have a spurious influence due to its early market open, creating a false impression of causality in price transmission.
• Markets like Egypt show no role in initiating avalanches, with 0% of SIPQs originating there, highlighting their low systemic influence.
• The model successfully identifies cause-effect relationships in price dynamics without statistical tests, enabling direct inference of contagion origins and propagation paths.