### Discussion Paper

## Abstract

The ability to accurately estimate the extent to which the failure of a bank disrupts the financial system is very valuable for regulators of the financial system. One important part of the financial system is the interbank payment system. This paper develops a robust measure, SinkRank, that accurately predicts the magnitude of disruption caused by the failure of a bank in a payment system and identifies banks most affected by the failure. SinkRank is based on absorbing Markov chains, which are well-suited to model liquidity dynamics in payment systems. Because actual bank failures are rare and the data is not generally publicly available, the authors test the metric by simulating payment networks and inducing failures in them. The authors use two metrics to evaluate the magnitude of the disruption: the duration of delays in the system (Congestion) aggregated over all banks and the average reduction in available funds of the other banks due to the failing bank (Liquidity dislocation). The authors test SinkRank on Barabasi–Albert types of scale-free networks modeled on the Fedwire system and find that the failing bank’s SinkRank is highly correlated with the resulting disruption in the system overall; moreover, the SinkRank technology can identify which individual banks would be most disrupted by a given failure.

Paper submitted to the special issue Coping with Systemic Risk

## Comments and Questions

The paper presents a novel algorithm for identifying systemically important banks which is based on the application of the theory of absorbing state markov chains. The proposed measure has the advantage of being simple and intuitive, and it displays a very high correlation with the disruption caused by the default ...[more]

... of the same bank.

The paper is indeed original and relevant for the special issue. Because of its merits, I believe it deserves an additional effort from authors to improve its clarity and completeness.

Main points

1. It is unclear whether sinkrank is computed on each strongly connected component (the formulation of sec. 2 seems to suggest that this is the case).

2. The authors should clarify the following conceptual point: on the one hand they suppose that there is a fixed number k of transactions between two nodes i and j. Then a walk visits the link i → j at most k times. But this is at odds with the claim, made at p. 5, that the number of payments is unconstrained.

3. The supposition that failing banks continue to receive payments (p. 9) should find a sound justification in real markets. Otherwise, it should be clearly stated how this supposition affects the simulation results. In principle, this supposition doesn't look to be necessary to produce liquidity dislocations, since for this effect to take place it suffices that the failing nodes misses its payments. The extra-liquidity of debtors of failing banks doesn't necessarily compensate the shortfall of liquidity of creditors.

4. The results of fig. 5 show that the proposed measure is no more efficient predictor than other centrality measures for the more realistic BA network. So why should we prefer it? This point should be elaborated by the authors, possibly in the final section. An answer could come also from comparison with other recently proposed measures, like DebtRank (http://www.nature.com/srep/2012/120802/srep00541/full/srep00541.html).

Minor points:

p. 4, first paragraph. It is unclear why multiple individuals cannot be infected at the same time by the same person.

p.7, beginning of sec. 3. The abbreviation BA should be explained. The description of the algorithm can be improved (e.g. it is not clear at the first reading whether the FNA payment simulator is the one described in annex I). Possibly a short description of its basic assumptions could be added to the main text.

Fig. 2 it is unclear whether we are talking about weak or strong components.

p. 12, fig. 4. It is not explained which disruption measure is employed.

p. 13 authors should explain the 'linear scaling of payment', at list in the annex.

p.13 “failure distance” should be explicitly defined making reference to the fundamental matrix Q.

p. 14, fig. 6. which topology does the graph refers to? (results for all topologies should be at least mentioned if not displayed).