# The price of complexity in financial networks

Increasing the complexity of the network of contracts between financial institutions decreases the accuracy of estimating systemic risk.

*Proceedings of the National Academy of Sciences of the USA* 113, 36 (2016)

S. Battiston, G. Caldarelli, R. May, T. Roukny, J. Stiglitz

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 de- pends 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 de- crease the ability to mitigate systemic risk, and thus it may increase the social cost of financial crises.

#### More in Systemic risk

### Modelling financial systemic risk

Complex networks model the links between financial institutions and how these channels can transition from diversifying to propagating risk.

### Default cascades in networks

The optimal architecture of a financial system is only dependent on its topology when the market is illiquid, and no topology is always superior.

### Non-linear distress propagation

Non-linear models of distress propagation in financial networks characterise key regimes where shocks are either amplified or suppressed.

### Cascades in flow networks

Coupled distribution grids are more vulnerable to a cascading systemic failure but they have larger safe regions within their networks.

### Immunisation of systemic risk

Targeted immunisation policies limit distress propagation and prevent system-wide crises in financial networks according to sandpile models.

### The interbank network

The large-scale structure of the interbank network changes drastically in times of crisis due to the effect of measures from central banks.

### Interbank controllability

Complex networks detect the driver institutions of an interbank market and ascertain that intervention policies should be time-scale dependent.

### Fragility of the interbank network

The speed of a financial crisis outbreak sets the maximum delay before intervention by central authorities is no longer effective.

### DebtRank and shock propagation

A dynamical microscopic theory of instability for financial networks reformulates the DebtRank algorithm in terms of basic accounting principles.

### Bootstrapping topology and risk

Information about 10% of the links in a complex network is sufficient to reconstruct its main features and resilience with the fitness model.