Stefano Battiston, Guido Caldarelli, Robert M. May, Tarik Roukny, and Joseph E. Stiglitz

ECONOMICS

Significance

Estimating systemic risk in networks of financial institutions represents, today, a major challenge in both science and financial policy making. This work shows how the increasing complexity of the network of contracts among institutions comes with the price of increasing inaccuracy in the estimation of systemic risk. The paper offers a quantitative method to estimate systemic risk and its accuracy.

Abstract

Financial institutions form multilayer networks by engaging in contracts with each other and by holding exposures to common assets. As a result, the default probability of one institution depends on the default probability of all of the other institutions in the network. Here, we show how small errors on the knowledge of the network of contracts can lead to large errors in the probability of systemic defaults. From the point of view of financial regulators, our findings show that the complexity of financial networks may decrease the ability to mitigate systemic risk, and thus it may increase the social cost of financial crises.

See: http://www.pnas.org/content/113/36/10031.abstract.html?etoc

PNAS September 6 2016; vol.113; no. 36: 10031–10036

Fig. 2.

Systemic default probability vs. relative error on the contract’s characteristics. Each pair of curves of a given color represents the minimum and maximum values of the default probability as a function of the relative error on one given parameter (see figure key). (Left) For instance, with an error on R (purple curves) larger than 20%, the default probability can take any value between 0.4 and 1. In fact, the maximum value of default probability is 1 for all of the parameters when the error is large enough. The green dashed curve refers to the case in which all parameters at the same time contain a given relative error. Shocks are uniformly distributed. Parameter values: β=3, ϵ=10, σ=0.005, R=0.5, P0=0.1, and μ=−0.08. (Right) The maximum probability is 1 in this case. For instance, with a 10% error on β, the default probability can take any value between 0 and 1. Shocks are uniformly distributed. Parameter values: β=3, ϵ=10, σ=0.005, R=0.2, P0=0.4, and μ=−0.01.