Exploring Risk Contagion Using Graph Theory and Markov Chains

Recent financial crises and periods of market volatility have heightened awareness of risk contagion and systemic risk among financial analysts. As a result, financial professionals are often tasked with constructing and analyzing models that will yield insight into the potential impact of risk on investments, portfolios, and business operations.

Several authors have described the use of advanced mathematical and statistical techniques for quantifying the dependent relationships between investments, foreign exchange rates, industrial sectors, or geographical regions. Bridging the gap between formal methods and a working code implementation is a key challenge for analysts.

This code, along with the corresponding technical article shows how MATLAB® can be used to analyze aspects of risk contagion using various mathematical tools. Topics covered include:

• Data aggregation, preprocessing, and risk benchmarking
• Quantifying dependent relationships between financial variables
• Visualizing the resulting network of dependencies together with proximity information
• Analyzing periods of risk contagion using hidden Markov models

Installation and Getting Started

The examples are provided in a MATLAB project.

1. Double-click on the project archive (Contagion.mlproj) to extract it using MATLAB.
2. With MATLAB open, navigate to the newly-created project folder and double-click on the project file (Contagion.prj) to open the project.
3. The example file is the live script RiskContagion.mlx within the project.

MathWorks® Product Requirements

This example was updated using MATLAB release R2022b.

• MATLAB®
• Statistics and Machine Learning Toolbox™
• Parallel Computing Toolbox™ (Optional)

License

The license for this entry is available in the license.txt file in this GitHub repository.

Copyright 2016-2023 The MathWorks, Inc.

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