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

Claudio J. Tessone, Antonios Garas, Beniamino Guerra and Frank Schweitzer

Working Papers from ETH Zurich, Chair of Systems Design

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.

Keywords: systemic risk; cascading processes; robustness (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
ftp://web.sg.ethz.ch/RePEc/stz/wpaper/pdf/ETH-RC-12-015.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 500 Failed to connect to FTP server web.sg.ethz.ch: A connection attempt failed because the connected party did not properly respond after a period of time, or established connection failed because connected host has failed to respond.

Related works:
Working Paper: How big is too big? Critical Shocks for Systemic Failure Cascades (2013)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:stz:wpaper:eth-rc-12-015

Access Statistics for this paper

More papers in Working Papers from ETH Zurich, Chair of Systems Design Contact information at EDIRC.
Bibliographic data for series maintained by Claudio J. Tessone ( this e-mail address is bad, please contact ).