A8: How Financial Crises Spread Through Networks

Introduction

When one bank fails, its losses can spread to connected banks, triggering a cascade (a chain reaction where failures cause more failures). This model simulates financial contagion (the spread of financial distress from one institution to others through direct connections) on a random network of 20 financial institutions.

Each institution has a capital buffer $B_i$ (money set aside to absorb losses -- like a safety cushion). When institution $i$ fails, it spreads losses to its neighbors. If a neighbor's accumulated losses exceed its buffer, it also fails -- creating a cascade.

The formula for losses received by institution $i$ is:

$$\text{Loss}_i = \sum_{j \in \text{failed neighbors}} \frac{\text{Loss}_j}{\text{degree}_j}$$

where $\text{degree}_j$ is the number of connections that institution $j$ has.

Your Task

Run the baseline simulation, then implement three variations to explore how different factors affect systemic risk. Create a 7-slide presentation (using Marp or PowerPoint) summarizing your findings.

Variations to Implement

Variation 1: Double All Buffers

Change: On line 42, modify the capital buffer range from [0.05, 0.20] to [0.10, 0.40]:

buffers = np.random.uniform(0.10, 0.40, N)

Question: How many nodes fail now compared to baseline? What does this tell you about capital requirements as a policy tool?

Variation 2: Increase Network Density

Change: On line 36, make the network more connected by changing < 0.3 to < 0.7:

adj = np.random.rand(N, N) < 0.7

Question: Does more connectivity help or hurt financial stability? Why might dense networks be "robust-yet-fragile"?

Variation 3: Multiple Initial Failures

Change: After line 53, add two more initial failures:

failed[shock_node] = True
failed[1] = True
failed[2] = True

Also update line 56 to reflect 3 initial failures:

round_failures = [3]  # Initial shocks

Question: How does the cascade differ when 3 banks fail simultaneously versus a single shock?

Open Extension (Optional)

Add a circuit breaker mechanism: any node that has lost 50% of its buffer freezes all outgoing connections (stops spreading losses to neighbors). This simulates emergency liquidity injections or regulatory interventions.

Implementation hint: Track a new boolean array frozen and modify the loss propagation loop to skip frozen nodes.

How to Run

1. Upload the provided chart.py file to Google Colab
2. Run the baseline version first to understand the output
3. Make each variation change one at a time
4. Save the network visualizations and failure counts for each variation
5. Create your presentation comparing all four scenarios

Deliverables

Submit a 7-slide presentation (PDF or PPTX):

1. Title slide with your name and the reference: Acemoglu et al. (2015) - Systemic Risk and Network Topology
2. The Model -- explain the mechanics (20 nodes, random connections, capital buffers, loss propagation formula)
3. Baseline Results -- network visualization + total failures
4. Variation 1 -- doubled buffers analysis
5. Variation 2 -- dense network analysis
6. Variation 3 -- multiple shocks analysis
7. Key Insights -- what did you learn about systemic risk and network structure?

Time Allocation

• 45 minutes: Run simulations and analyze results
• 10 minutes: Create presentation slides

Assessment Criteria

• Correctness: All three variations implemented correctly (30%)
• Analysis: Clear explanations of how each change affects contagion (40%)
• Insight: Understanding of the "robust-yet-fragile" paradox and policy implications (20%)
• Presentation: Clear visuals and concise explanations (10%)

Learning Objectives

By completing this assignment, you will:

• Understand how financial contagion spreads through networks
• Recognize the counterintuitive effects of network density on systemic risk
• Evaluate the effectiveness of capital buffers as a policy tool
• Appreciate why regulators monitor interconnectedness in financial systems