# Evolution of controllability in interbank networks

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

*Scientific Reports* 3, 1626 (2013)

D. Delpini, S. Battiston, M. Riccaboni, G. Gabbi, F. Pammolli, G. Caldarelli

The Statistical Physics of Complex Networks has recently provided new theoretical tools for policy makers. Here we extend the notion of network controllability to detect the financial institutions, i.e. the drivers, that are most crucial to the functioning of an interbank market. The system we investigate is a paradigmatic case study for complex networks since it undergoes dramatic structural changes over time and links among nodes can be observed at several time scales. We find a scale-free decay of the fraction of drivers with increasing time resolution, implying that policies have to be adjusted to the time scales in order to be effective. Moreover, drivers are often not the most highly connected ‘‘hub’’ institutions, nor the largest lenders, contrary to the results of other studies. Our findings contribute quantitative indicators which can support regulators in developing more effective supervision and intervention policies.

## 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.

### 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.

### The price of complexity

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

### 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.