Sensitivity and Computational Complexity in Financial Networks

35 Pages Posted: 24 Aug 2020

See all articles by Sanjeev Khanna

Sanjeev Khanna

University of Pennsylvania

Brett Hemenway Falk

University of Pennsylvania - Department of Computer and Information Science

Date Written: August 24, 2020

Abstract

Determining the causes of instability and contagion in financial networks is necessary to inform policy and avoid future financial collapse. In the American Economic Review, Elliott, Golub and Jackson proposed a simple model for capturing the dynamics of complex financial networks. In Elliott, Golub and Jackson’s model, the institutions in the network are connected by linear dependencies (cross-holdings) and if any institution’s value drops below a critical threshold, its value suffers an additional failure cost. This work shows that even in this simple model there are fundamental barriers to understanding the risks that are inherent in a network. First, if institutions are not required to maintain a minimum amount of self-holdings, any change in investments by a single institution can have an arbitrarily magnified influence on the net worth of the institutions in the system. This implies that if institutions have small selfholdings, then estimating the market value of an institution requires almost perfect information about every cross-holding in the system. Second, even if a regulator has complete information about all cross-holdings in the system, it may be computationally intractable to estimate the number of failures that could be caused by a small shock to the system.

Keywords: Financial Contagion; Computational Complexity; Network Analysis; Network Stability; Sensitivity

Suggested Citation

Khanna, Sanjeev and Hemenway Falk, Brett, Sensitivity and Computational Complexity in Financial Networks (August 24, 2020). Jacobs Levy Equity Management Center for Quantitative Financial Research Paper, Available at SSRN: https://ssrn.com/abstract=3680255 or http://dx.doi.org/10.2139/ssrn.3680255

Sanjeev Khanna

University of Pennsylvania ( email )

3330 Walnut Street
Philadelphia, PA 19104
United States

Brett Hemenway Falk (Contact Author)

University of Pennsylvania - Department of Computer and Information Science ( email )

3330 Walnut Street
Philadelphia, PA 19104
United States

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