Code for: Foundations of System-Wide Stress Testing

Note: This is a simplified version that only retains a fire sale contagion model, but retains much of the generality of the comprehensive system-wide stress test model.

By: J. Doyne Farmer, Alissa M. Kleinnijenhuis, Paul Nahai-Williamson, and Thom Wetzer.

For questions, contact alissa.kleinnijenhuis [at] maths.ox.ac.uk.

The model.py file is a hybrid source code - Jupyter notebook. There are 3 illustrative experiments:

1. Effect of price impact on systemic risk
2. Effect of initial shock on systemic risk
3. Difference between leverage targeting and threshold model (Cont-Schaanning 2017)

Data taken from 2018 EU-wide stress test results, https://eba.europa.eu/risk-analysis-and-data/eu-wide-stress-testing/2018/results.

Usage

Requires Python 3.

1. pip install -r requirements.txt
2. Comment out the line plt.ion() in simulation.py
3. Add plt.show() at the end of simulation.py
4. python3 simulation.py

To run the model in a Jupyter notebook:

1. pip install -r requirements.txt
2. Edit ~/.jupyter/jupyter_notebook_config.py and add this line c.NotebookApp.contents_manager_class = 'jupytext.TextFileContentsManager' # noqa. This is to make sure that model.py can be read as a jupyter notebook
3. jupyter notebook
4. Execute all the cells in simulation.py

If you want to display model.py in the form of a slideshow, you must do pip install RISE && jupyter-nbextension install rise --py --sys-prefix && jupyter-nbextension enable rise --py --sys-prefix.

Overview

The framework consist of 5 building blocks: institutions, contracts, constraints, markets, and behaviours. The simple asset-sale model fills in the 5 building blocks as follows:

1. Institutions

1. Banks
   Each bank has a balance sheet consisting of the following components:
   • asset: cash, tradable asset, other asset
   • liability: loan, other liability

2. Contracts

Tradable assets T interconnect the banks. The cash C, other assets O and the generic liability L do not.

• Tradable
  • action: sell asset
• Loan
  • action: pay loan
• Other assets and liabilities

3. Constraints

Each bank faces a leverage constraint.

• Leverage constraint
  • λ := E / A
  • Delever if λ < λ^buffer = 4%
  • Delever to λ^target = 5%
  • Default if λ < λ^min = 3%
    When this happens, all tradable assets of a defaulted bank are liquidated.

4. Markets

The price of each tradable asset p_m is determined using a price impact function. The price is a function of the net cumulative number of asset sales. Each asset has its own price impact parameter, which determines the market liquidity of the asset.

Asset market:

• Contains an orderbook
• Price impact (Cifuentes 2005)
  • Price impact formula: new_price = price * exp(-beta * sold / market_cap)
  • By default, β is chosen such that when 5% of the market cap is sold, the price drops by 5%.

5. Behaviours

Bank only acts to avoid default, by de-levering to a leverage target if its buffer has been breached. It does this by selling tradable asset proportionally and paying bank liabilities proportionally.

References

1. Cont, Rama, and Eric Schaanning. "Fire sales, indirect contagion and systemic stress testing." (2017). https://dx.doi.org/10.2139/ssrn.2541114
2. Cifuentes, R., Ferrucci, G. and Shin, H. S. "Liquidity risk and contagion." Journal of the European Economic Association 3(2-3), 556–566. (2005). https://dx.doi.org/10.2139/ssrn.824166
3. Greenwood, Robin, Augustin Landier, and David Thesmar. "Vulnerable banks." Journal of Financial Economics 115, no. 3: 471-485. (2015). https://doi.org/10.3386/w18537
4. Gai, Prasanna, and Sujit Kapadia. "Contagion in financial networks." In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, p. rspa20090410. The Royal Society. (2010). https://doi.org/10.1098/rspa.2009.0410