# How big is too big? Critical Shocks for Systemic Failure Cascades

## Author Info

• Claudio J. Tessone

()

• Antonios Garas
• Beniamino Guerra
• Frank Schweitzer

## Abstract

External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighoring agents. Several critical constellations determine whether this cascade remains finite or reaches the size of the system, i.e. leads to systemic risk. We investigate the critical parameters for such cascades in a simple model, where agents are characterized by an individual threshold $\theta_{i}$ determining their capacity to handle a load $\alpha\theta_{i}$ with $1-\alpha$ being their safety margin. If agents fail, they redistribute their load equally to $K$ neiboring agents in a regular network. For three different threshold distributions $P(\theta)$, we derive analytical results for the size of the cascade, $X(t)$, which is regarded as a measure of systemic risk, and the time when it stops. We focus on two different regimes, (i) \emph{EEE}, an external extreme event where the size of the shock is of the order of the total capacity of the network, and (ii) \emph{RIE}, a random internal event where the size of the shock is of the order of the capacity of an agent. We find that even for large extreme events that exceed the capacity of the network finite cascades are still possible, if a power-law threshold distribution is assumed. On the other hand, even small random fluctuations may lead to full cascades if critical conditions are met. Most importantly, we demonstrate that the size of the big'' shock is not the problem, as the systemic risk only varies slightly for changes of 10 to 50 percent of the external shock. Systemic risk depends much more on ingredients such as the network topology, the safety margin and the threshold distribution, which gives hints on how to reduce systemic risk.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: ftp://web.sg.ethz.ch/RePEc/stz/wpaper/pdf/ETH-RC-12-015.pdf
Our checks indicate that this address may not be valid because: 500 Failed to connect to FTP server web.sg.ethz.ch: Net::FTP: connect: 10060. If this is indeed the case, please notify (Claudio J. Tessone)

## Bibliographic Info

Paper provided by ETH Zurich, Chair of Systems Design in its series Working Papers with number ETH-RC-12-015.

as
in new window

 Length: Date of creation: Date of revision: Handle: RePEc:stz:wpaper:eth-rc-12-015 Contact details of provider: Postal: ETH Zentrum KPL F 38.1, Kreuzplatz 5, 8032 ZürichPhone: +41 1 632 57 18Fax: +41 1 632 10 47Web page: http://web.sg.ethz.ch/wpsMore information through EDIRC

## References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
1. J. Lorenz & S. Battiston & F. Schweitzer, 2009. "Systemic risk in a unifying framework for cascading processes on networks," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 71(4), pages 441-460, October.
2. Stefano Battiston & Domenico Delli Gatti & Mauro Gallegati & Bruce C. Greenwald & Joseph E. Stiglitz, 2009. "Liaisons Dangereuses: Increasing Connectivity, Risk Sharing, and Systemic Risk," NBER Working Papers 15611, National Bureau of Economic Research, Inc.
3. Claudio J. Tessone & Markus M. Geipel & F. Schweitzer, . "Sustainable growth in complex networks," Working Papers CCSS-10-008, ETH Zurich, Chair of Systems Design.
Full references (including those not matched with items on IDEAS)

## Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

## Corrections

When requesting a correction, please mention this item's handle: RePEc:stz:wpaper:eth-rc-12-015. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Claudio J. Tessone)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.