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DebtRank-transparency: Controlling systemic risk in financial networks

Stefan Thurner, Sebastian Poledna

arXiv:1301.6115v1q-fin.RMphysics.soc-ph

TL;DR

The paper addresses systemic risk created when banks cannot correctly estimate counterparties' risk. It uses an agent-based model with transparent centrality information and an incentive to favor safer lenders. The authors report more even risk distribution and practically eliminated cascading failures, with the regulation dynamics still requiring further investigation.

  • Problem

    The paper addresses systemic risk arising when banks cannot correctly estimate their counterparties’ risk.

    Source: DISCUSSION · p. 7

  • Method

    An agent-based model makes a centrality measure such as DebtRank available to banks and incentivizes borrowers to favor systemically safer lenders.

    Source: THE MODEL · p. 3, DISCUSSION · p. 7

  • Results

    Risk is spread more evenly and practically eliminates cascading failures; maximum cascade size is 40 banks in transparent mode and about 30 in fast mode.

    Source: RESULTS · p. 4, DISCUSSION · p. 7

  • Takeaways & Limitations

    The proposed regulation does not affect financial-network efficiency in the model, with E ∼1 in all modes.

    Source: DISCUSSION · p. 7

    The same self-organized-critical regulation dynamics remains subject to further investigation.

    Source: DISCUSSION · p. 7

Abstract

from arXiv · show

Banks in the interbank network can not assess the true risks associated with lending to other banks in the network, unless they have full information on the riskiness of all the other banks. These risks can be estimated by using network metrics (for example DebtRank) of the interbank liability network which is available to Central Banks. With a simple agent based model we show that by increasing transparency by making the DebtRank of individual nodes (banks) visible to all nodes, and by imposing a simple incentive scheme, that reduces interbank borrowing from systemically risky nodes, the systemic risk in the financial network can be drastically reduced. This incentive scheme is an effective regulation mechanism, that does not reduce the efficiency of the financial network, but fosters a more homogeneous distribution of risk within the system in a self-organized critical way. We show that the reduction of systemic risk is to a large extent due to the massive reduction of cascading failures in the transparent system. An implementation of this minimal regulation scheme in real financial networks should be feasible from a technical point of view.

THE MODEL

The model links banks, firms, and households in a closed system where interbank borrowing helps banks meet firm-loan needs. Defaults can trigger cascades through interbank creditors.

  • At each timestep, each of B firms requests a random-sized loan from its main bank, which borrows interbank funds if reserves are insufficient.A bank unable to raise the full amount does not provide the firm-loan.Source: THE MODEL · p. 3
  • Households redistribute firm receipts through bank deposits and consumption, while firms use returned funds to repay loans.Households are modeled as one aggregated agent.Source: THE MODEL · p. 3
  • A firm default makes its bank write off outstanding credits; a bank default triggers events for its interbank creditors and may start a cascade.There is no recovery for interbank loans, and the model is a closed system without cash inflows or outflows.Source: THE MODEL · p. 3

The normal mode

In the normal mode, banks manage liquidity by requesting interbank loans from connected banks in random order. They accept partial funding and continue contacting neighbors until requirements are met.

  • A bank contacts neighbors when it needs liquidity for a firm-loan request or its own interbank repayments.Source: The normal mode · p. 3
  • The bank asks connected neighbors in random order.Source: The normal mode · p. 3
  • If a neighbor can provide only part of the requested loan, the bank takes that amount and continues asking other neighbors until its liquidity needs are satisfied.Source: The normal mode · p. 3

The transparent IB mode

The transparent mode orders potential interbank lenders by inverse DebtRank, favoring less risky neighbors. Banks' rankings are computed from network information and updated at the start of each timestep.

  • The model computes systemic-risk metrics from the interbank liability network and banks’ equity, including DebtRank and Katz rank.Rank 1 denotes the riskiest bank and rank B the least risky.Source: The transparent IB mode · pp. 3–4
  • The caption compares normal random selection, transparent inverse-DebtRank ordering, and fast mode across losses, cascade sizes, and interbank transaction volume.The simulations use a fully connected graph.Source: Figure 2 · p. 4
  • Before requesting interbank loans, a bank orders its connected neighbors by inverse DebtRank and asks the least risky first.Risk rankings are computed at the beginning of each timestep; risky banks are last in the order and practically never asked.Source: The transparent IB mode · p. 4
  • Central Banks may be able to support this transparency because many already hold the data needed to compute DebtRank.Source: The transparent IB mode · p. 4

Transparent IB market – fast mode

The fast mode recalculates DebtRank after every interbank-market transaction rather than only at the beginning of the day.

RESULTS

The transparent and fast modes sharply reduce extreme bank losses and default cascades compared with the normal mode. Transparency also spreads systemic risk more evenly, while interbank transaction volume increases and efficiency remains near one.

RESULTS

  • The simulations run for 500 timesteps, and reported results average 10,000 identical runs.Source: RESULTS · p. 4
  • No losses exceed 50 units in transparent mode or 40 in fast mode, while the normal mode retains a heavy-tailed loss distribution.Losses do not disappear entirely because firms still bring credit risk into the banking system.Source: RESULTS · p. 4
  • Normal-mode cascades can reach 80% of banks, compared with maximum cascade sizes of 40 banks in transparent mode and about 30 in fast mode.The likelihood of contagion is greatly reduced in transparent mode.Source: RESULTS · p. 4
  • Transparent and fast modes have higher interbank transaction volume, while the firm-loan efficiency measure E remains approximately 1 in every mode.The higher volume indicates that liquidity is channeled more effectively from banks with excess funds to those without.Source: RESULTS · p. 4
  • At timestep 100, the transparent mode spreads systemic risk impact more evenly across banks than the normal mode.Banks are ordered from most risky on the left to safest on the right; the figure averages 1,000 ER-network simulations.Source: RESULTS · pp. 4–5, Figure 3 · p. 5
  • At matched average connectivity, the scale-free BA network produces a slightly riskier loss situation than the ER network in both modes.The ER network uses γ = 0.115 and the shared average connectivity is ⟨k⟩ = 11.5.Source: RESULTS · p. 5
  • Time-to-first-default distributions are practically Gaussian; typically, the first default is a firm default and is largely independent of interbank-market conditions.The reported distributions have kurtosis ∼3.3 and skewness ∼0.4.Source: RESULTS · p. 5
  • DebtRank and Katz rank produce practically identical loss results, with no noticeable difference reported for cascade size or transaction-volume distributions.The loss comparison uses the same simulation parameters as the preceding figure.Source: Figure 4 · p. 5, RESULTS · p. 5

DebtRank

DebtRank measures the fraction of network economic value potentially affected by a node or set of distressed nodes. It recursively tracks distress through the interbank liability network.

DebtRank

  • DebtRank measures the fraction of total network economic value potentially affected by a node or set of distressed nodes.Source: DebtRank · p. 5
  • A bank's economic value is its interbank liabilities divided by the total interbank liabilities in the network.Source: DebtRank · p. 5
  • Recursive impact calculations account for effects on neighbors and nodes at distance two or greater.Source: DebtRank · p. 5
  • The alternative distress dynamics use continuous distress levels and discrete undistressed, distressed, or inactive states to prevent impact exceeding one in networks with cycles.Initial distress is assigned to the nodes in set Sf; the DebtRank of a single node measures its systemic impact.Source: DebtRank · pp. 5–6

Katz rank

Katz centrality is used to capture contagion risk in interbank networks. Banks are ranked by their Katz centrality, which incorporates loan sizes and network connections.

Katz rank

  • Katz centrality is used to capture the risk of contagion in interbank networks.Source: Katz rank · p. 6
  • The highest-centrality bank receives Katz rank 1 and the lowest-centrality bank receives rank B.Source: Katz rank · p. 6
  • Borrow-only banks can have nonzero Katz centrality, whereas banks that only provide loans have zero centrality.Loan sizes and a bank's neighbors and their neighbors are included in the centrality.Source: Katz rank · p. 6

Systemic Risk measures

Systemic risk is measured using time to first default, cascade size, and total losses. Figure 5 compares loss distributions across network types and operating modes.

Systemic Risk measures

  • The model measures systemic risk using time to first bank default, cascade size, and total losses following a default or cascade.Source: Systemic Risk measures · p. 6
  • Figure 5 presents loss distributions for normal and transparent modes, comparing ER networks (red) and scale-free (SF) networks (blue), both with the same average connectivity of 11.5.Source: Figure 5 · p. 6

Efficiency measures

The paper assesses banking-system efficiency by comparing firms' requested loans with loans paid out, and also measures interbank transaction volume.

Efficiency measures

DISCUSSION

The proposed transparency and incentive scheme reduces systemic risk while preserving financial-network efficiency. Its mechanism redistributes risk, and the authors suggest a Central Bank implementation while leaving a market-based route for the same dynamics to further investigation.

DISCUSSION

  • The scheme significantly reduces systemic risk without affecting network efficiency, redistributing risk rather than reducing interbank trading volume.Risky nodes low in DebtRank are barred from lending excess reserves; less risky banks can take more risk and earn more profits.Source: DISCUSSION · p. 7
  • Borrowing from a systemically dangerous node can transfer risk to the borrower and raise overall systemic risk, whereas lending to one need not increase the lender’s systemic importance.The scheme therefore has borrowers choose their lenders according to lender risk.Source: DISCUSSION · p. 7
  • The scheme’s performance is insensitive to the centrality measure and to scale-free versus random network topology, provided average connectivity remains in sensible regions.The authors suggest that more even risk distribution practically eliminates cascading failures.Source: DISCUSSION · p. 7
  • Central Banks could compute DebtRank regularly, share it with banks, and monitor interbank loans to enforce the regulation.A more market-based mechanism producing the same self-organized-critical dynamics remains for further investigation.Source: DISCUSSION · p. 7
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