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### Direct contagion via the solvency channel
- Definition and mechanics
  - Direct links connect borrowers and lenders (examples: loan exposures in the interbank market, leveraged investment funds’ debt-like liabilities held by other financial institutions, and banks’ loans to non-financial firms).
  - Occurs when a borrower is in distress (for example because it defaults) and is unable to repay its liabilities to counterparties, transmitting distress via counterparty risk.
- Role within contagion taxonomy
  - One of two broad direct contagion mechanisms (the other: funding-liquidity channel). Indirect channels operate via market-liquidity risk and overlapping portfolios.
- Key survey insights and model sensitivity
  - Estimated solvency contagion losses in banking systems tend to be small when models are calibrated to current balance sheets and interbank exposures.
  - Small estimated losses reflect:
    - the post-Global Financial Crisis build up in equity capital in the banking system, and
    - the reduction in the scale of interbank exposures.
  - Usable buffers of capital and liquidity materially affect loss estimates; assumptions about buffer usability are crucial.
  - Model outcomes are highly sensitive to modelling assumptions and parameters; point estimates should be interpreted with caution. Models are most useful to explore scenarios and policy interventions.
- Theoretical framework and extensions
  - Eisenberg and Noe (2001): clearing payment vector exists and is unique under mild conditions; assumes full face value of remaining assets distributed pro-rata on default.
  - Extensions:
    - Elsinger et al. (2009): cross-holdings of equity and seniority structure → equity and debt values become endogenous.
    - Rogers and Veraart (2013): non-zero bankruptcy costs → rescue incentives and lender-of-last-resort coordination.
    - Elliott et al. (2014): discontinuous losses at failure thresholds; cascades depend on network integration/diversification.
- Network structure insights
  - Integration increases exposures (can increase cascade likelihood) but can decrease likelihood of first failure.
  - Diversification increases interdependencies (can enable cascades) but reduces sensitivity to any single counterparty; system most susceptible when integration is intermediate and firms are partly diversified.
  - Vulnerability depends on shock location: shocks at large, highly leveraged, highly connected banks are more damaging (Glasserman and Young (2015)).
  - Policy responses include Basel Committee leverage ratio requirements and limits on large exposures.
- Pre-default contagion
  - Default-only models miss valuation changes before default. Extensions (DebtRank; non-linear probability-of-default mappings) show pre-default contagion can amplify impacts; allowing pre-default contagion leads to worse or at best equal stress test outcomes versus default-only models.
- Empirical evidence using regulatory exposure data
  - Consensus: solvency contagion risk in interbank markets has fallen since the Global Financial Crisis due to higher capital ratios and smaller interbank exposures.
  - Selected findings and calibrations:
    - Recovery rate values referenced: 0.550, 0.4, 0.6, 0.80.
    - Bardoscia et al. (2019) calibration with 2008 data: Aggregate contagion losses reach 140£billions under zero recovery rate, for an initial 70% equity shock; under a recovery rate of 0.8, losses are more than five times smaller.
  - Examples of reported contagion losses (select entries from Table 1):
    - Hüser et al. (2018): [0,0.2%] decrease in other banks’ CET1 ratio.
    - Fink et al. (2016): 0.5% of total CET1.
    - Bardoscia et al. (2019): ∼0£bn in 2016, [20,140] £bn in 2008.
    - Souza et al. (2015): 24% of total interbank assets in 2012, 47% of total interbank assets in 2008.
- Policy implications for stress testing
  - Pre-default contagion should be included in stress tests to avoid under-estimating losses.
  - Recovery rates and bank capitalisation materially affect contagion magnitude.
  - Strengthening capital and liquidity, limits on large exposures, and lender-of-last-resort facilities can mitigate solvency contagion risks.

### Indirect contagion via the market-liquidity channel (fire sales and price-mediated effects)
- Mechanism and pre-conditions
  - Fire sales occur when institutions must sell assets at distressed prices; requires mark-to-market accounting and imperfect market absorption.
  - Amplification increases with higher leverage, larger liquidity mismatch, and substantial cross-holdings of similar assets.
- Modeling components and choices
  - Core elements: (a) trigger causing initial sale; (b) liquidation strategy; (c) price reaction to sales.
  - Most models simulate ex-post asset management; ex-ante optimization approaches also exist.
- Representative model findings (stylized)
  - Cifuentes et al. (2005): joint clearing vector of payments and prices; fire-sale mechanism can trigger dramatic cascades; systemic risk non-monotonic in interconnectedness; threshold of liquid asset holdings above which contagion does not occur.
  - Greenwood et al. (2015): leverage targeting; calibrated shock = 50% write-off in GIIPS sovereign debt; fire sale channel increases losses of the average bank in the system by 302%.
  - Duarte and Eisenbach (2013): aggregate vulnerability (percentage of system-wide equity at risk) ≈ 12% in 2001, peaking at 38.3% in 2007.
  - Cont and Schaanning (2017): leverage-threshold deleveraging → under same shocks as Greenwood et al. (2015), average bank loss three times smaller than constant leverage targeting but still sizable.
  - Coen et al. (2019): solvency shocks → total fire sale losses (%CET1) under solvency shock: [0,10%]; under funding shock: [0,37%].
- Empirical calibration features (select data and shock/loss entries)
  - Greenwood et al. (2015): EU 90 largest banks, time period 2011, shock: 50% write-off of sovereign debt of all GIIPS, total fire sale losses (%CET1): 245.
  - Cont and Schaanning (2017): EU 51 banks, time period 2016, shocks: [0-20] (% CET1), total fire sale losses (%CET1): [0-50].
  - Duarte and Eisenbach (2013): US 100 largest banks, time period 1999 - 2016, shocks: 1% shock all assets, total fire sale losses (%CET1): 22 (average across time).
  - Coen et al. (2019): UK 7 major banks, time period 2016, shocks: Solvency shock: [25%,50%] CET1; Liquidity shock: [0%,22%] (outflows % b.s.), total fire sale losses (%CET1): see above.
- Policy-relevant diagnostics
  - Severity depends on accounting rules, market depth heterogeneity, banks’ leverage policies, liquidation strategies, and initial system liquidity.
  - Funding liquidity shocks (outflows) can be more damaging than pure solvency shocks.
  - Strategic complementarities can amplify selling; calibration choices materially affect estimated spillovers and aggregate losses.

### Interaction of direct and indirect contagion
- Co-existence and cross-amplification
  - Direct (solvency/funding) and indirect (fire sales/overlapping portfolios) channels interact, generating amplification loops; adding indirect channels can amplify or preserve robust-yet-fragile properties depending on setup.
- Multi-layer and three-channel models
  - Montagna and Kok (2016): three-layer agent-based model → simultaneous propagation across layers can produce contagion larger than sum of each layer.
  - Aldasoro and Faia (2016): runs on liabilities, interconnected debt defaults, and fire sales interact; liquidity freezes ↔ fire sales form amplification loops.
  - Covi et al. (2021): calibrated to euro area banks → credit risk losses dominate funding and liquidity via fire sales, but illiquidity-driven defaults outweigh insolvency-triggered defaults; funding-risk concentration suggests limits on funding concentration.
- Empirical and supervisory-dataset findings
  - Caccioli et al. (2015): adding overlapping-portfolio linkages to direct-exposure data strongly amplifies contagion.
  - Roncoroni et al. (2019): non-linear relationship between diversification, shock size, and interbank contagion losses; diversification to real sectors helps, diversification of interbank counterparties can increase spreading.
  - Aldasoro et al. (2022): interbank exposures explain minor share of contagion losses; common exposures (fire sales, synchronous price dislocations) account for bulk of contagion.
- Collateral and margin channels (emerging evidence)
  - Collateral channels amplify losses and funding demands via margin calls and rehypothecation; existing models often study these channels in isolation.
  - Research gap: need models integrating collateral channels with fire sales and unsecured interbank contagion.

### Price-mediated contagion, dynamic hedging, and NBFI examples (section highlights)
- Price-mediated contagion and hedging
  - Dynamic hedging (e.g., options sellers hedging as prices fall) can amplify price moves; historical examples include portfolio insurance (1987) and PRDC notes (2008).
  - Agent-based models can capture price deviations and unstable dynamics; traditional asset-price models struggle with fire-sale/hedging dynamics.
- Contagion involving collateral, margins, and securities financing
  - Collateral: initial margin (haircuts) and variation margin; failure to pay variation margin usually treated as default.
  - Collateral reduces solvency contagion but raises funding-liquidity and market-liquidity risks.
- Historical NBFI stress episodes
  - March 2020 “dash for cash”, September 2022 gilt event, Archegos (early 2021) with realised bank losses ≈ $10 billion, Long Term Capital Management (1998), AIG derivatives exposures, CCP failures (Hong Kong CCP 1987 bailout $1 billion).
- Modelling and data gaps
  - Trade repository data used increasingly; simulation models for margin-triggered flows exist but system-wide stress tests capturing cross-sector contagion remain limited.

### Fund stress testing (4.3.1) — typical scenarios, ingredients, and empirical findings
- Typical scenario
  - Starts with an exogenous redemption shock → fund liquidates assets → price impacts → further losses and redemptions → potential contagion to banks and MMFs via funding liquidity shortages.
- Shock calibration methods
  - Historical approach; event study; expert judgment; macro-financial scenario approach.
  - Macro approaches: directly estimate flows–macro relationships or use two-step flow-performance approach.
- Flow-performance factor estimates (selected exact estimates)
  - Fricke and Fricke (2021): 0.3 (Lagged returns).
  - ECB (2017): 0.5 (Benchmark indices).
  - van der Veer et al. (2017): 0.04 (Lagged returns and flows, leverage, size).
  - Morris et al. (2017): 0.4 (global EME international government bond funds), 0.9 (global EME corporate bond funds) (Lagged returns, change in lagged VIX).
  - Goldstein et al. (2017): 0.85 (corporate bond funds), 0.41 (equity funds) (Lagged negative returns).
  - Mirza et al. (2020): 0.2 (equity funds), 0.39 (bond funds), 0.13 (hedge funds), 0.99 (money market funds) (Lagged flows and returns).
  - Arora et al. (2019): 0.4 (Change in NAV; estimation strategy as in Cetorelli et al. (2016)).
- Liquidation strategies modelled
  - Slicing approach (proportional sales across portfolio): preserves composition but may force sales of illiquid assets.
  - Waterfall approach (sell most liquid assets first): reduces price impact but may distort portfolio and create first-mover advantage.
- Price impact and second-round effects
  - Price impact models used: linear price impact; Amihud illiquidity measure.
  - Second-round channels: funding liquidity (withdrawals at banks/MMFs) and market liquidity (sales depress prices → further redemptions).
- Empirical/model outcomes (selected exact findings)
  - Cetorelli et al. (2016): spillover losses would be 22 cents per dollar of initial loss.
  - Fricke and Fricke (2021): for a 5% shock on asset values, aggregate vulnerability (AV) = 1.3%.
  - ESMA (2019): redemption shock calibrated using ExpectedShortfall at 1%, 3% and 5% level.
  - Fiedor et al. (2019): sales of limited-liquidity asset classes could move prices by 150 to 300 bps.
  - Baranova et al. (2017a): weekly redemptions = 1% of total net assets → investment-grade corporate bond spreads ≈ +40 basis points; redemptions = 1.3% → spreads ≈ +70 basis points; second-round redemptions account for ≈ half of overall spread change.
- Modeling other sectors’ reactions
  - Including banks, broker-dealers, long-term investors, hedge funds can amplify price impacts through demand-side dynamics and financing constraints.

### CCP stress testing (high-level)
- Standard framework: “Cover-2” — CCPs assess sufficiency of initial margin + default fund to cover failure of two largest counterparties.
- Limitations: does not capture network propagation, more-than-two-member defaults, or amplification across markets.
- Network-aware approaches (selected findings)
  - Poce et al. (2018): network effects can substantially increase CCP member vulnerability.
  - Paddrik and Young (2021): conventional approaches may underestimate CCP vulnerability in CDS markets.

### Sector-specific approaches — cross-cutting observations
- Fund stress testing is the most advanced in NBFI sphere; CCP stress testing is evolving toward network-aware methods.
- Key modelling choices affecting outcomes: shock calibration, flow-performance parameter, liquidation strategy, price impact specification, inclusion of other sectors and second-round channels.
- Data constraints: lack of granular asset-holding and interlinkage data impedes disaggregated system-wide modelling.

### Incorporating macrofinancial feedbacks into macroprudential stress testing models (5.3)
- Overview and trade-offs
  - Three broad modelling approaches: DSGE, semi-structural econometric (SVAR/GVAR), and network models.
  - Trade-offs:
    - DSGE: strong microfoundations but stylised balance sheets and limited heterogeneity.
    - Semi-structural: adaptable to data and policy questions; many specifications lack explicit time-varying bank asset-mix modelling.
    - Network: rich interconnections and balance-sheet detail but rely on reconstruction/behavioural assumptions.
- DSGE representative quantitative magnitudes
  - Typical: a 5 percent fall in intermediary net worth → ≈ 0.5 percent fall in GDP.
  - Specific reported effects:
    - Christiano et al. (2010): risk news accounts for 26-47% of output variance; 0.3-1.5pp contribution to US GDP fall during crisis attributed to bank funding channel.
    - Meh and Moran (2010): 5% bank capital shock → 0.5% peak fall in output.
    - Gerali et al. (2010): 5% bank capital shock → 0.5% fall in output at year 3.
    - Gertler and Karadi (2011): 1% decline in intermediary net worth → 0.15% peak fall in output.
    - Clerc et al. (2015): 1std shock to bank risk → 0.5% fall in GDP; 1std shock to housing/physical capital values → nearly 1.5% fall in GDP.
- Semi-structural econometric models (SVAR/GVAR) findings
  - Gray (2013): 664bps shock to Italian banking expected loss → 0.5 percent fall in Italian GDP.
  - Krznar and Matheson (2017): 1 percent fall in bank capital → 6 percent fall in credit and 0.5 percent fall in GDP.
  - Budnik et al. (2020): allowing feedbacks from excessive deleveraging → euro area output falls by an additional 1.6 pp on top of original 2.4% shock.
- Network models: amplification and limits
  - Network-model amplification typically reported in range 2-10 times initial shock (dependent on assumptions and reconstruction methods).
  - Limitations include reliance on reconstructed networks and ad-hoc behavioural responses.
- Policy-relevant modelling priorities
  - Incorporate bank heterogeneity, estimate bank capital sensitivity to asset-class shocks, account for borrower net worth/collateral channels, avoid double-counting historical deleveraging when designing initial shocks.
  - Data enablers: counterparty-level data (trade repositories), empirical estimation of market-impact and behavioural parameters.

### Balance sheet-based indicators (6.1)
- Network measures (entity-specific and network-specific)
  - Centrality examples: PageRank; Eigenvector Centrality — captures firms’ position, suited to identify key players.
  - Concentration examples: Weighted degree; HH index — measure market concentration and “too-big-to-fail”.
  - Connectivity example: Network density — captures structure (core-periphery); relationship with instability is non-monotonic.
- Model-based measures (selected)
  - DebtRank: recursive impact of institution distress; high DebtRank → systemic importance.
  - Aggregate Vulnerability (AV): fraction of system equity capital lost due to fire-sales under constant-leverage assumption; decomposable by bank contributions.
  - Indirect Contagion Index: assesses indirect price-mediated contagion via fire sales; computable from portfolio holdings.
  - Capital at Risk (CaR) and Conditional Capital at Risk (CCaR): 1-year ahead expected and tail losses conditional on current conditions; decomposable by country/sector/channel.
  - Liquidity at Risk: forward-looking liquidity resources required under stress; Liquidity shortfall = Liquidity at Risk − liquid assets available.
  - Systemic Risk Probability; Average Bank Default Probability: probabilistic systemic risk measure; systemic event defined as 1.5 per cent of banks in distress/default concurrently.
- Observations
  - Many entity-specific contagion/vulnerability indicators useful for microprudential supervision; macroprudential system-level indicators are less common.
  - Decomposable outputs useful for identifying contagion sources and policy diagnostics.

### Lessons for policymakers and supervisory stress test design (7.1)
- Scope of current supervisory stress tests
  - Supervisory frameworks focus on direct losses from credit, market, operational, and litigation risks.
  - Macroprudential literature identifies non-linear propagation channels: solvency risk (including pre-default valuation effects), market liquidity risk, funding liquidity risk.
  - Supervisory progress examples:
    - 2017 Bank of England ACS applied three feedback models: solvency contagion, wholesale funding cost, and fire sales.
    - Bank of England’s 2023 system-wide exploratory scenario will investigate bank and NBFI behaviours post-shock.
- Determinants of amplification
  - For a given shock, impact depends on:
    - (a) size of capital and liquidity buffers,
    - (b) liquidation strategies adopted,
    - (c) financial network topology.
  - Buffer usability:
    - Whether buffers are treated as usable is a key modelling assumption; assumptions explain substantial variance across studies.
    - Models assuming maintenance of leverage ratios (treating buffers as non-usable) find larger shock effects.
  - Liquidation strategies and fund behaviour:
    - Selling liquid assets first generally lowers price impact versus vertical slicing, but can create first-mover incentives and investor-protection versus systemic-stability trade-offs.
  - Regulatory constraints and binding constraints:
    - Which regulatory constraint binds (risk-based capital vs leverage) affects liquidation choices and spillover magnitudes.
- Network topology
  - Systemic risk is a non-linear function of network structure; no simple generalizable policy prescriptions from topology alone.
- Research priorities for model developers (three high-return directions)
  1. Greater focus on amplification in the non-bank financial system:
     - Key questions on asset managers, insurers, pension funds, CCP margin procyclicality, and dealer liquidity provision.
     - Need granular, high-frequency data on fund flows, holdings, and leverage.
  2. Analyse interconnectedness across the system as a whole:
     - Build multi-sectoral models of NBFI to analyse liquidity supply/demand under stress.
  3. Incorporate comprehensive two-way macro-financial interactions:
     - Permit banks’ reactions to stress to affect credit supply and economic activity, which feed back to asset performance and financial stability.

_Italic: Source: wpiea2023173-print-pdf._

### 3.1    Direct contagion via the solvency channel   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  

### 3.1    Direct contagion via the solvency channel

### Definition and mechanics
- Direct links connect borrowers and lenders; examples include loan exposures in the interbank market, leveraged investment funds’ debt-like liabilities held by other financial institutions, and banks’ loans to non-financial firms.
- Direct contagion via the solvency channel occurs when a borrower is in distress (for example because it defaults) and is unable to repay its liabilities to counterparties.
- Because these liabilities are other agents’ assets, the counterparties may then become distressed, potentially triggering a default cascade.
- This channel operates via counterparty risk: the borrower cannot pay back the lender.

### Role within the taxonomy of contagion channels
- The solvency channel is one of two broad direct contagion mechanisms; the other is direct contagion via the funding-liquidity channel (where lender distress leads to reduced lending or funding withdrawals).
- Indirect contagion channels (for contrast) operate via market-liquidity risk and overlapping portfolios (price-mediated effects, including fire sales).

### Key insights from the survey relevant to solvency contagion
- Estimates of solvency contagion losses in the banking system tend to be small when models are calibrated to current balance sheets and the current configuration of interbank exposures.
- The relatively small estimated losses reflect:
  - the post-Global Financial Crisis build up in equity capital in the banking system, and
  - the reduction in the scale of interbank exposures over the same period.
- Usable buffers of capital and liquidity are important for mitigating the scale of contagion losses; assumptions about buffer usability materially affect loss estimates.
- Model sensitivity:
  - Model outcomes are highly sensitive to modelling assumptions and parameters (for example, market liquidity of specific asset classes), which are often hard to calibrate.
  - Point estimates should be interpreted with caution; the models are most useful for exploring scenarios and policy interventions that could prevent severe contagion.

### Questions for policy analysis using solvency-contagion models
- Are there reasonable calibrations of key parameters where severe solvency contagion occurs?
- What shocks, balance sheet positions, or market liquidity conditions would be required for such severe outcomes?
- Which policy interventions would be most successful at steering the system away from dire outcomes?

*Source: wpiea2023173-print-pdf - 3.1    Direct contagion via the solvency channel*

### 3.1    Direct contagion via the solvency channel

### 3.1    Direct contagion via the solvency channel

### Modelling framework and key theoretical developments
- Eisenberg and Noe (2001)
  - Introduced a modelling framework for analysing direct contagion via the solvency channel in the interbank market.
  - Analysed a network of firms with interfirm debt claims and the vector of clearing payments that occur upon the default of one firm.
  - When a bank cannot repay its debt in full it defaults, potentially triggering cascades as creditors unable to receive payments fail to pay their own creditors.
  - Showed that a clearing payment vector always exists and, under mild conditions, is unique.
  - Strong simplifying assumption: when a bank defaults, the full face value of its remaining assets is distributed to creditors pro-rata (no legal costs, no delays, no seniority differences).

- Extensions relaxing Eisenberg and Noe assumptions
  - Elsinger et al. (2009): account for cross holdings of equity and detailed seniority structure of debt; equity and debt values become endogenously determined; equity values are not necessarily convex and debt values not necessarily concave in the exogenous income as in Eisenberg and Noe (2001).
  - Rogers and Veraart (2013): allow for non-zero bankruptcy costs; when a bank defaults it realizes only a fraction of asset value. Introducing default costs:
    - generates incentives for rescue consortia (benefit for solvent banks to rescue insolvent ones),
    - but practical challenges mean a lender of last resort is required as coordination mechanism.
    - non-zero bankruptcy costs can create incentives for a bank to increase its failure costs to improve negotiating power (also discussed in Elliott et al. (2014)).
  - Elliott et al. (2014): accounts for discontinuous losses when banks’ value falls below the failure threshold; analyses how cascades depend on network structure (integration and diversification).

### Network structure, integration versus diversification trade-offs
- Integration and diversification effects
  - Increasing integration increases exposures and can increase likelihood of a cascade after an initial failure, but can decrease the likelihood of the first failure.
  - Diversification increases interdependencies enabling contagion to cascade, but also makes firms less sensitive to any single counterparty’s failure.
  - After a threshold, further increases in diversification reduce widespread contagion likelihood; a system is most susceptible to widespread contagion when integration is intermediate and firms are partly diversified.
- Additional considerations affecting the connectivity trade-off
  - Errors in the structure of the contract network (Battiston et al. (2016)): imperfect information about number and identity of counterparties can make higher diversification reduce precision in estimating systemic default probabilities.
  - Size of the initial shock matters: Acemoglu et al. (2015) finds diversified networks are less fragile for relatively small shocks, but for larger shocks more interconnected networks can facilitate contagion and become more fragile.
  - Robust-yet-fragile property (Haldane (2009)) and related findings (Georg (2013))—optimal network resilience depends on other factors including shock size and endogenous balance-sheet optimization.
- Vulnerability depends on where shock originates
  - Glasserman and Young (2015): solvency contagion losses are limited on average, but network is more vulnerable when the shock originates at a bank that is large, highly leveraged and highly connected.
- Policy responses
  - Post-crisis policy measures targeted to reducing network vulnerabilities include Basel Committee leverage ratio requirements and limits on large exposures.

### Pre-default contagion (valuations before outright default)
- Limitations of default-only contagion models
  - Eisenberg and Noe (2001) assumes no ex-ante uncertainty about a bank’s ability to repay; losses cannot crystallise before maturity.
  - In practice, outside creditors observe deteriorations in creditworthiness and value exposures accordingly, so distress can propagate pre-default.
- Model extensions capturing pre-default contagion
  - Battiston et al. (2012): DebtRank, a measure of systemic importance accounting for fraction of economic value potentially affected by a bank’s distress; initial shocks can generate impacts larger than the shocks themselves even when no bank defaults initially.
  - Bardoscia et al. (2016): extends probability-of-default mapping to be non-linear in relative equity loss.
  - Other approaches:
    - Fink et al. (2016): heuristic rules for counterparty risk valuations.
    - Barucca et al. (2020): valuations grounded in functions derived from a clearing mechanism.
    - Veraart (2020): allows different functional forms for counterparty valuations, enabling a wide range of shapes with few parameters.
- Policy implication from modelling pre-default contagion
  - Allowing for pre-default contagion leads to worse or at best equal stress test outcomes compared to models with contagion only at default; ignoring pre-default contagion can under-estimate losses from this channel.

### Empirical evidence using detailed regulatory exposure data
- Improvement in data availability since the Global Financial Crisis has permitted more accurate analyses of solvency contagion in interbank networks. Prior to the crisis, studies relied on estimated or partial bilateral exposures (e.g., Wells (2004), Furfine (2003), Upper and Worms (2004)), yielding divergent conclusions in part due to data constraints.
- Common empirical conclusion across studies using detailed regulatory data: solvency contagion risk in the interbank market has fallen significantly since the Global Financial Crisis era, driven by higher capital ratios and reduced scale of interbank exposures.
  - Bardoscia et al. (2019) (UK): contagion risk fell due to increases in banks’ capital ratios and decreases in interbank exposures.
  - Nier et al. (2007): better capitalised banks make the system more resilient against contagious defaults; effect is non-linear.
  - Abduraimova and Nahai-Williamson (2021): confirm Bardoscia et al. (2019) findings for the UK.
  - Souza et al. (2015): similar findings for the Brazilian interbank market.
  - Hüser et al. (2018): similar findings for the Euro Area when considering direct contagion risk related to bail-in of banks issuing securities.

### Role of recovery rates and calibration evidence
- Recovery rate at default plays an important role in the size of contagion losses.
  - Bardoscia et al. (2019): shows recovery rate has significant implications. Example calibration with 2008 data:
    - Aggregate contagion losses reach 140£billions under zero recovery rate, for an initial 70% equity shock.
    - Under a recovery rate of 0.8, everything else equal, losses are more than five times smaller.
- Recovery rate values referenced in empirical models (Table 1): 0.550, 0.4, 0.6, 0.80.

### Summary of models with empirical applications using detailed interbank exposures (select entries from Table 1)
- Models compared across dimensions (selected fields preserved verbatim)
  - Initial shock:
    - Hüser et al. (2018): Idiosyncratic shock to a bank’s assets (1%−12% of total assets)
    - Fink et al. (2016): Shock to real estate sector (15 pp change in loss given mortgage default)
    - Bardoscia et al. (2019): Equity shock (30%,50%,70%)
    - Souza et al. (2015): Fictitious initial default of a single institution
  - Solvency contagion trigger:
    - Hüser et al. (2018): Bail-in (write-down and recapitalization)
    - Fink et al. (2016): Increase in probability of default
    - Bardoscia et al. (2019): Increase in probability of default
    - Souza et al. (2015): Default
  - Recovery rate entries: Dependent on seniority of exposure (the write-down can be complete or partial); 0.550, 0.4, 0.6, 0.80
  - Banking systems and data:
    - Hüser et al. (2018): EU 26 largest euro area banking groups (ESCB and ECB datasets), Time period 2015
    - Fink et al. (2016): Germany 1710 banks (Deutsche Bundesbank’s credit register), Time period 2013
    - Bardoscia et al. (2019): UK 7 major banks (Bank of England regulatory data), Time period 2008-2016
    - Souza et al. (2015): Brazil 265 banks, credit unions or cooperatives, brokers/dealers (Brazilian supervisory exposure data), Time periods 2008 and 2011, 2012
  - Contagion losses reported:
    - Hüser et al. (2018): [0,0.2%] decrease in other banks’ CET1 ratio
    - Fink et al. (2016): 0.5% of total CET1
    - Bardoscia et al. (2019): ∼0£bn in 2016, [20,140] £bn in 2008
    - Souza et al. (2015): 24% of total interbank assets in 2012, 47% of total interbank assets in 2008

### Implications for stress testing and policy
- Accounting for pre-default contagion is important in stress testing; models that consider only post-default contagion can under-estimate losses.
- Recovery rates and bank capitalisation materially affect contagion magnitude; higher capital ratios and higher recovery rates reduce contagion losses.
- Policy measures that strengthen capital and liquidity (e.g., Basel III LCR and leverage requirements, limits on large exposures) and interventions such as lender-of-last-resort facilities can mitigate contagion risks identified by the literature.

*Italic: Source: 3.1    Direct contagion via the solvency channel (from wpiea2023173-print-pdf).*

### 3.3    Indirect contagion via the market-liquidity channel

### 3.3    Indirect contagion via the market-liquidity channel

### Mechanism and pre-conditions
- Banks suffering large losses may be forced to sell assets at distressed or fire sale prices, forcing revaluation of similar assets held by other banks and potentially triggering cascades of further fire sales.
- Two necessary pre-conditions for fire sale contagion:
  - mark-to-market accounting (assets valued at current market prices).
  - imperfect market absorption of asset sales so disposals depress market prices in the short run (e.g., natural buyers constrained, sales to non-specialised investors, constrained arbitrageurs).
- Amplification of losses from this channel increases with higher leverage, larger liquidity mismatch, and substantial cross-holdings of similar assets.

### Modeling components and choices
- Three main components across fire sale models:
  - (a) the trigger that causes the initial sale;
  - (b) the liquidation strategy (what assets are sold);
  - (c) the reaction of asset prices to sales.
- Models take banks’ initial balance sheets and connections as given and simulate ex-post asset management following shocks (most papers). An ex-ante approach exists (Awiszus et al. (2022)) that characterizes distributions of holdings that maximize market efficiency accounting for fire sales.

### Representative models and stylized findings
- Cifuentes et al. (2005)
  - Extends Eisenberg and Noe (2001) framework to include endogenous equilibrium price from intersection of downward-sloping market demand and vertical supply for a single marketable illiquid asset.
  - Shows existence of a joint clearing vector of payments and prices with interbank liabilities and fire sale dynamics.
  - Simulations: fire sale mechanism can trigger dramatic cascades; key determinants of contagion scale are system liquid asset holdings and interconnectedness.
  - Systemic risk is non-monotonic in interconnectedness: systemic risk lowest when average counterparties is either very low or very high.
  - Existence of a threshold level of liquid asset holdings above which fire sale contagion does not occur.
- Greenwood et al. (2015)
  - Motivated by leverage targeting evidence, assumes banks sell assets proportionately to holdings to maintain fixed leverage targets; price impact linear and proportional to total asset sales; homogeneous market depth across assets.
  - Calibrated to European banking system asset holdings in 2011.
  - Shock: 50% write-off in banks’ holdings of Greek, Italian, Irish, Portuguese and Spanish sovereign debt.
  - Finding: fire sale channel increases losses generated by shock; losses of the average bank in the system jump by 302%.
- Duarte and Eisenbach (2013)
  - Banks have a latent, time-varying leverage target with varying speeds of adjustment.
  - Aggregate vulnerability measure (percentage of system-wide equity capital at risk due to fire sale spillovers): around 12% in 2001, peaking at 38.3% in 2007.
- Cont and Schaanning (2017)
  - Non-linear deleveraging: banks sell only when leverage crosses a threshold (captures regulatory or voluntary buffers); allows heterogeneous market depths.
  - Calibrated to European banking system: conditional on same shocks as Greenwood et al. (2015), loss for the average bank is three times smaller than under constant leverage targeting, but still sizable.
- Coen et al. (2019), Braouezec and Wagalath (2018, 2019)
  - Refine liquidation strategies with optimisation under risk-based capital, leverage and liquidity constraints.
  - Findings: solvency shocks typically trigger modest fire sale losses; funding liquidity shocks (e.g., depositor and wholesale outflows) can generate significant losses.
  - Strategic complementarities: banks have incentives to liquidate more when others increase fire sale volumes, yielding Nash equilibria with amplified selling.

### Empirical calibration features (summary table elements preserved)
- Models surveyed differ across these dimensions (examples):
  - Sales trigger:
    - Greenwood et al. (2015): Leverage Target
    - Cont and Schaanning (2017): Leverage Threshold
    - Duarte and Eisenbach (2013): Partial adjustment to target leverage
    - Coen et al. (2019): Solvency and Liquidity constraints
  - Liquidation rule:
    - Greenwood et al. (2015): Proportional
    - Cont and Schaanning (2017): Proportional
    - Duarte and Eisenbach (2013): Proportional
    - Coen et al. (2019): Optimal (loss minimizing)
  - Marketable assets considered:
    - Greenwood et al. (2015): All assets
    - Cont and Schaanning (2017): Corporate and Sovereign exposures (bonds, equities, derivatives)
    - Duarte and Eisenbach (2013): Most assets (loans, bonds, equities and other securities)
    - Coen et al. (2019): Corporate and Sovereign exposures (bonds and equities)
  - Price impact assumptions:
    - Greenwood et al. (2015): Homogeneous across all assets (Impact of 10 bn is 10 bp)
    - Cont and Schaanning (2017): Heterogeneous (based on ADV) (Impact of 10 bn ranges from 1.8 to 1355 bp)
    - Duarte and Eisenbach (2013): Heterogeneous (based on NSFR haircut) (5−100%)
    - Coen et al. (2019): Heterogeneous (based on ADV) (Impact of 10 bn ranges from 1 to 720 bp)
  - Banking system and data:
    - Greenwood et al. (2015): EU 90 largest banks (EBA data), time period 2011, shocks: 50% write-off of sovereign debt of all GIIPS, total fire sale losses (%CET1): 245
    - Cont and Schaanning (2017): EU 51 banks (EBA data), time period 2016, shocks: [0-20] (% CET1), total fire sale losses (%CET1): [0-50]
    - Duarte and Eisenbach (2013): US 100 largest banks (Federal Reserve Board data), time period 1999 - 2016, shocks: 1% shock all assets, total fire sale losses (%CET1): 22 (average across time)
    - Coen et al. (2019): UK 7 major banks (BoE regulatory data), time period 2016, shocks: Solvency shock: [25%,50%] CET1; Liquidity shock: [0%,22%] (outflows % b.s.), total fire sale losses (%CET1): Losses under solvency shock: [0,10%]; Losses under funding shock: [0,37%]
- Note: ADV stands for average daily volumes.

### Policy-relevant implications and diagnostics
- Fire sale contagion severity depends critically on:
  - accounting rules (mark-to-market),
  - market depth and heterogeneity of price impacts,
  - banks’ leverage policies (fixed targets vs. thresholds vs. partial adjustment),
  - liquidation strategies and optimization under multiple constraints,
  - initial system liquidity (liquid asset holdings) and interbank interconnectedness.
- Threshold effects: there may exist levels of liquid asset holdings beyond which fire sale contagion does not occur.
- Funding liquidity shocks (outflows) can be more damaging than pure solvency shocks in producing significant fire sale losses.
- Strategic interactions in liquidation choices can amplify fire sales; anticipating others’ behaviour matters.
- Calibration choices (homogeneous vs. heterogeneous market depth, proportional vs. optimal liquidation) materially affect estimated spillovers and aggregate losses.

*Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023173-print-pdf.pdf*

### 3.5    Interaction of direct and indirect contagion

### 3.5    Interaction of direct and indirect contagion

### Co-existence and cross-amplification of channels
- Direct and indirect contagion co-exist and interact in the financial system, producing cross-amplification effects.
- Early simulated-interbank-network studies combined direct contagion via the solvency channel with indirect contagion from fire sales (Cifuentes et al., 2005; Nier et al., 2007; Gai and Kapadia, 2010).
  - These studies subject networks to an idiosyncratic shock hitting one bank’s assets; default transmits losses to creditors (direct contagion) and asset liquidations depress market prices (indirect contagion).
  - Cifuentes et al. (2005): allowing endogenous fire-sale prices can amplify initial shocks to produce potentially large effects.
  - Gai and Kapadia (2010): adding an indirect channel does not alter the robust-yet-fragile property of the original network.
  - Nier et al. (2007): market liquidity risk increases default cascades for any level of connectivity; illiquid asset holdings make concentrated systems especially fragile because default of a large bank forces liquidation of large asset amounts.

### Multi-layer and three-channel models
- Montagna and Kok (2016) build an agent-based model with three layers: short-term interbank exposures, long-term interbank exposures, and indirect exposures via overlapping portfolios.
  - Finding: simultaneous shock propagation across multiple network layers can generate contagion effects substantially larger than the sum of losses from each layer considered individually.
- Aldasoro and Faia (2016) model optimizing banks with contagion on both sides of balance sheets:
  - Channels: runs on short-term liabilities and liquidity hoarding (funding-liquidity channel), interconnected debt defaults (solvency channel), and fire sales (asset channel).
  - Interaction: liquidity freezes can lead to fire sales; fire-sale losses can in turn trigger funding runs — generating amplification loops.
- Covi et al. (2021) model credit and funding shocks together with fire sales, calibrated to euro area banks’ large exposures and balance sheet/regulatory data.
  - Findings:
    - Losses due to credit risk dominate those due to funding and liquidity risk via fire sales.
    - Illiquidity-driven defaults outweigh by far those triggered due to insolvency.
    - Funding risk relative to credit risk is concentrated on a few large exposures whose defaults may trigger liquidity default events.
    - Policy implication suggested: it may be prudent to impose limits on the concentration of funding since some small and medium-sized banks are exposed on the liability side to few large banks.
- Covi et al. (2020) apply the Montagna and Kok (2016) multi-layer framework to European banks, defining systemic risk as the probability of a large number of banks defaulting at a given time conditional on prior information.
  - Key determinants of systemic risk identified: the correlation of economic shocks and fire sales.

### Empirical and supervisory-dataset based findings
- Caccioli et al. (2015) use Austrian supervisory direct-exposure data and show:
  - The system is resilient to the failure of a single bank if counterparty risk is the only contagion mechanism.
  - Adding overlapping-portfolio (common-asset) indirect linkages strongly amplifies contagion, producing much larger cascading failures.
- Roncoroni et al. (2019) study 26 large euro area banks using ECB datasets, considering direct exposures (interbank loans and banks’ exposures to non-financial corporate and retail clients) and indirect exposures (overlapping asset classes).
  - Findings:
    - A strongly non-linear relationship exists between diversification of exposures, shock size, and interbank contagion losses.
    - Diversification of exposures to real economic sectors helps contain contagion.
    - Diversification of counterparties in the interbank market can increase spreading of contagion losses.
- Aldasoro et al. (2022) provide an accounting-based stress-testing framework for a banking sector connected by direct interbank exposures and common asset holdings; applied to detailed micro-financial euro area data:
  - Interbank exposures account for only a minor share of overall contagion losses.
  - Common exposures that make banks vulnerable to fire sales and synchronous price dislocations account for the bulk of distress contagion.

### Collateral and margin channels — emerging evidence and gaps
- Collateral channels are a relatively newer strand and have mostly been studied in isolation to date.
  - Gai et al. (2011) combine direct and indirect contagion from collateral where the shock originates from collateral but contagion plays out in the interbank market.
  - Cont et al. (2020) account for increased liquidity needs from margin calls that can lead to fire sales, but their model has only one bank and does not explicitly model contagion across multiple institutions.
  - Ghamami et al. (2022) study collateral fire sales and show that price-mediated collateral channels amplify losses beyond the direct effect of missed payments.
- Research gap and recommendation:
  - Future research could build on these collateral-channel models to account for interaction of collateral channels with fire sales and with direct contagion channels in unsecured interbank markets.

*Source: wpiea2023173-print-pdf - 3.5    Interaction of direct and indirect contagion*

### section 4.3.1 for a detailed discussion of fund stress testing and Tables 5 and 6 for overviews of key papers).

### wpiea2023173-print-pdf - section 4.3.1 for a detailed discussion of fund stress testing and Tables 5 and 6 for overviews of key papers)

### Price-mediated contagion, fire sales, and dynamic hedging
- Fire sales can occur when institutions need to raise cash at any cost (for example, to meet a margin call and avoid default), or to reduce exposure to potential falls in asset value (for example, when taking ownership of collateral or unwinding a hedge following a counterparty default).
- In non-banks, fire sales usually result from the use of secured leverage or derivatives; they can also arise from highly correlated trading strategies or “crowded trades” that are unwound simultaneously (example: the “Quant Meltdown” of 2007 as described in Khandani and Lo (2008)).
- Dynamic hedging activity can amplify price moves: institutions that sell options and hedge dynamically may buy as prices rise and sell as prices fall, potentially amplifying price moves when liquidity is thin or actions are unanticipated. Historical instances include:
  - Portfolio insurance hedging is said to have amplified the 1987 stock market crash.
  - Hedging of Power Reverse Dual Currency (PRDC) notes is widely thought to have amplified volatility in Asian FX markets in 2008.
- Convexity hedging in the US can amplify price moves when long term interest rates approach certain levels; this hedging is driven by the non-linear relationship between interest rates and the value of mortgage servicing rights. The authors note they are not aware of published models that capture these dynamics in a stress testing context.
- Modelling price impact of asset sales is crucial for stress tests that capture this channel. Traditional asset price models can struggle to capture fire sales and hedging because these dynamics appear to create low-risk arbitrage opportunities that contradict the efficient-markets hypothesis.
- Agent-based models (ABMs) are a developed strand of research that allow prices to deviate from fundamentals due to trading pressures and can generate multiple equilibria or unstable dynamics. Survey reference: LeBaron (2006). Seminal paper: Farmer and Joshi (2002) shows how combinations of trading strategies can amplify noise and cause excess / clustered volatility.
- The mechanisms here relate to broader risks from procyclicality on longer timescales, including macroeconomic feedback effects; suggested further reading (not covered here): Minsky (1977), Bijlsma and Vermeulen (2016), Rudolph (2011), Haldane (2014).

### Contagion involving collateral, margins, and securities financing
- Most financial institutions engage in securities financing transactions (repo / reverse-repo) and use derivatives collateralised with initial and variation margin.
- Derivatives link assets and liabilities to underlying prices; counterparty exposure can increase as market prices change. A growing liability, if unhedged, can become difficult for a counterparty to repay.
- Post-2008 practice increased the use of collateral to reduce counterparty credit risk. Two broad collateral types:
  - Initial margins (haircuts): overpayment of collateral to cover potential price changes following default.
  - Variation margin: collateral flows triggered by market price changes of collateral or the derivative contract. Failure to pay a collateral call is usually treated as a default.
- Collateral reduces solvency contagion but introduces funding-liquidity risk (need to raise funds to meet margin calls) and market-liquidity risk after a default (counterparties sell collateral).

### Historical examples of non-bank financial intermediation (NBFI) distress involving collateral
- Liability-driven investment (LDI) strategies used by defined benefit pension funds and life insurers in the UK involve leverage and derivatives to manage duration risk. Margin calls during the March 2020 “dash for cash” (Czech et al. (2021)) and the September 2022 gilt market event led institutions, including LDI funds, to draw down cash buffers and redeem from money market funds, crystallising liquidity mismatch risk and forcing sales in distressed and illiquid markets.
- Archegos Capital Management (early 2021): a highly leveraged hedge fund used derivatives (total return swaps) to gain leveraged equity exposures. Price falls triggered margin calls the fund could not meet; bank counterparties sold hedging assets, moved prices further, and some banks incurred realised losses totalling around $10 billion. (See ESMA (2022) account.)
- Long Term Capital Management (1998): a highly leveraged hedge fund arbitraging US treasury securities faced margin falls following market stress after a sovereign default and the Asian financial crisis; counterparties entered a “standsill agreement” to take over financing and hold positions to maturity rather than close them out immediately. (See Lowenstein (2001) account.)
- AIG and general insurers (2000s): selling credit risk protection using derivatives added a new layer of contagion risk to business models that otherwise might not contribute to systemic risk. (See Commission et al. (2011) account.)
- CCP failures: several past CCP failures, including the Hong Kong Futures Guarantee Corporation in 1987, illustrate contagion via margin shortfalls. The Hong Kong CCP was bailed out by the Hong Kong government for $1 billion.

### Modelling, data, and gaps in stress testing
- Trade repository data is increasingly used to analyse systemic risk potential in derivatives markets (example: Ali et al. (2016) pilot study using CDS data).
- Bardoscia et al. (2019) describes a model simulating stress in derivatives markets where shocks to market prices trigger variation margin calls and payment flows between financial institutions. If margin calls exceed liquidity buffers, institutions wait for incoming payments or borrow in the interbank market to fund shortfalls.
- Such models could be building blocks for system-wide contagion models. However, the authors state they are not aware of any stress testing models that attempt to capture these mechanisms that spread distress from one sector to another.

*Source: wpiea2023173-print-pdf - section 4.3.1 for a detailed discussion of fund stress testing and Tables 5 and 6 for overviews of key papers).*

### 4.3    Sector-specific approaches

### 4.3    Sector-specific approaches

### 4.3.1    Fund stress testing
- Typical scenario:
  - Starts with an exogenous redemption shock; fund liquidates assets to cover redemptions.
  - Asset sales affect prices via the market liquidity channel, triggering further losses and potentially further redemptions.
  - If funds withdraw deposits at banks or redeem MMF shares, this can lead to funding liquidity shortages at banks and MMFs.
  - Both market liquidity and funding liquidity channels may lead to contagion to other financial institutions.

- Common model ingredients and implementations (high-level synthesis of Tables 5–7):
  - Shock calibration methods:
    - Historical approach (example: ESMA (2019) uses a pure redemption shock calibrated using historical data).
    - Event study.
    - Expert judgment.
    - Macro-financial scenario approach (two main methodologies):
      - Directly estimate relationship between flows and macro-financial variables (e.g., VIX, VSTOXX, spreads, term premium).
      - Two-step flow-performance approach: compute impact of shock on returns, then quantify net flows given projected returns (Cetorelli et al., 2016; Fricke and Fricke, 2021; Arora et al., 2019).

- Flow-performance factor estimates (Table 7 — selected exact estimates):
  - Fricke and Fricke (2021): 0.3 (Lagged returns).
  - ECB (2017): 0.5 (Benchmark indices).
  - van der Veer et al. (2017): 0.04 (Lagged returns and flows, leverage, size).
  - Morris et al. (2017): 0.4 (global EME international government bond funds), 0.9 (global EME corporate bond funds) (Lagged returns, change in lagged VIX).
  - Goldstein et al. (2017): 0.85 (corporate bond funds), 0.41 (equity funds) (Lagged negative returns).
  - Mirza et al. (2020): 0.2 (equity funds), 0.39 (bond funds), 0.13 (hedge funds), 0.99 (money market funds) (Lagged flows and returns).
  - Arora et al. (2019): 0.4 (Change in NAV; estimation strategy as in Cetorelli et al. (2016)).

- Liquidation strategies modelled:
  - Slicing approach:
    - Funds sell securities proportionally across portfolio (horizontal slicing by asset class is common).
    - Used in Cetorelli et al. (2016); Fiedor et al. (2019); Fricke and Fricke (2021).
    - Pros: preserves portfolio composition; treats remaining and redeeming investors equally.
    - Cons: forces sales of less liquid asset classes proportionally, raising price-impact and financial stability concerns.
    - Vertical slicing (by liquidity degree) is less common (examples: Arora et al., 2019; Baranova et al., 2017a).
  - Waterfall approach:
    - Sell most liquid assets first (pecking order: cash, investment grade sovereign bonds, investment grade corporate bonds, high yield sovereign bonds, equities, high yield corporate bonds).
    - Pros: may reduce price impact and financial stability risk.
    - Cons: distorts portfolio structure and may create first-mover advantage for redeeming investors.

- Price impact and second-round effects:
  - Price impact estimations used in reviewed models:
    - Linear price impact (Cetorelli et al., 2016; ESMA, 2019; Fiedor et al., 2019).
    - Amihud illiquidity measure (Fricke and Fricke, 2021).
  - Second-round amplification channels:
    - Funding liquidity channel: cash used to meet redemptions can come from deposit withdrawals at banks or redemption of MMF shares, causing funding shortages at debtors.
    - Market liquidity channel: sales depress prices, generate losses for holders, trigger additional redemptions and sales; flow-performance relationship often used to quantify this amplification (Baranova et al., 2017a).

- Empirical and model outcomes (selected exact findings from Tables 5–6):
  - Cetorelli et al. (2016): spillover losses would be 22 cents per dollar of initial loss.
  - Fricke and Fricke (2021): In response to a 5% shock on asset values, aggregate vulnerability (AV, the fraction of equity wiped out due to the fire sale mechanism, relative to total equity) is 1.3%.
  - ESMA (2019): Redemption shock calibrated using the ExpectedShortfall at 1%, 3% and 5% level.
  - Fiedor et al. (2019): For asset classes with more limited liquidity (high yield bonds and emerging market bonds), fund sales could have a material impact, ranging from 150 to 300 bps, and generate material second round effects.
  - Baranova et al. (2017a) (European corporate bond market): weekly redemptions equal to 1% of total net assets would result in an increase in European investment-grade corporate bond spreads of around 40 basis points; redemptions of 1.3% of total net assets could increase spreads by around 70 bp. Second-round investor redemptions amplify initial market moves materially, accounting for around half of the overall change in spreads.
  - Arora et al. (2019) and others: estimated flow-performance parameters example values reported (see Flow-performance factor estimates above).

- Modeling other sectors’ reactions:
  - Some models include reactive behaviour of other sectors (e.g., banks, broker-dealers, long-term investors, hedge funds) to fund sales; these reactions can amplify price impacts via demand-side dynamics and financing constraints (examples summarized in Table 6).

### 4.3.2    CCP stress testing
- Standard CCP stress test framework:
  - Typically assesses whether CCPs have sufficient funds to cover the event that their two largest counterparties fail to meet their clearing obligations.
  - CCP funds comprise initial margin and default fund contributions.
  - This approach is known as “Cover-2” (CFTC, 2016).
  - Limitation: does not account for amplification via network spillovers, contagion effects, or the possibility that more than two members could default (Heath et al., 2016).

- System-wide perspectives on CCP stress testing (selected findings):
  - Poce et al. (2018): propose methodology that accounts for propagation and amplification of distress through network of bilateral exposures between clearing members; case study of an Italian CCP finds network effects substantially increase vulnerability of clearing members.
  - Paddrik and Young (2021): propose methodology for estimating vulnerability to default by a CCP in the credit default swaps market by studying direct and indirect effects of non-payment through the full network of exposures; indicate conventional stress testing approaches may underestimate potential vulnerability of the main CCP for this market.

### Cross-cutting observations and modelling challenges
- Fund stress testing literature is the most advanced among non-bank sectors; CCP stress testing literature remains in its infancy but evolving toward network-aware approaches.
- Key modelling choices materially affect outcomes: shock calibration method, flow-performance parameter, liquidation strategy (slicing vs waterfall), price impact specification (linear vs Amihud), inclusion of other sectors and second-round channels.
- Data and modelling complexity constraints:
  - System-wide models face a trade-off between aggregation (tractability, intuition) and disaggregation (identifying pockets of risk).
  - Lack of granular data on asset holdings and interlinkages is a main obstacle for granular system-wide modelling.

*Source: wpiea2023173-print-pdf — 4.3    Sector-specific approaches.*

### 5.1    Theory

### 5.1    Theory

### Financial intermediation frictions and channels
- Financial intermediation is subject to frictions such as informational asymmetries and misaligned incentives between borrowers and lenders (Stiglitz and Weiss, 1981; Holmstroem and Tirole, 1997).
- These frictions can be exacerbated by falls in the net worth of lenders or borrowers.
- A strand of literature examines declines in borrowers’ resilience (net worth or collateral value) — akin to the solvency channel:
  - Bernanke and Gertler (1989): financial accelerator model.
  - Kiyotaki and Moore (1997): model of credit cycles.
  - Bernanke et al. (1999): embeds a financial accelerator mechanism in a new-keynesian DSGE model.
  - Mechanism: falls in borrowers’ net worth or collateral value lead to a reduction in the quantity of finance banks offer or an increase in the cost of accessing finance.19
- Other literature emphasizes banks’ financial resilience and funding liquidity channels:
  - Diamond and Dybvig (1983): depositors may withdraw funding due to solvency concerns, causing withdrawal of bank lending and drops in economic output.
  - Gertler and Kiyotaki (2010) and Gertler and Karadi (2011): banks face an incentive constraint or market discipline condition to maintain a given leverage ratio; an exogenous decline in solvency causes deleveraging.
  - Regulatory constraints (capital requirements) can affect supply of finance (Repullo and Suarez (2013); Bridges et al. (2014)).
  - Related literature on “leverage cycles” (Geanakoplos (2003) and others).
- Footnotes and surveys referenced:
  - For an excellent recent survey, see Claessens and Kose (2018).17
  - Classic work linking balance-sheet effects and macroeconomics: Fisher (1933) and Minsky (1982).18
  - Quint and Rabanal (2014) examines macroprudential policy’s role in damping financial accelerator effects by influencing the spread between lending and deposit rates.19

### 5.2    Empirical evidence

### Purpose
- Provide a brief overview of empirical studies quantifying the importance of the channels described above, to inform which channels are most important for macroprudential stress testing models.

### 5.2.1    The bank resilience channel
- Earlier studies find a statistically significant but relatively small relationship between bank solvency and loan supply (Bernanke et al., 1991; Berrospide and Edge, 2010).
- More recent work refines when this channel is larger or smaller:
  - Jiménez et al. (2012):
    - Use micro data on loan applications to disentangle bank balance-sheet effects on loan supply from borrower balance-sheet effects on loan demand.
    - Find that higher short term interest rates or lower GDP growth reduce the supply of credit.
    - Effects are stronger for banks with weaker capital or liquidity positions, and are quantitatively important.
  - Carlson et al. (2013):
    - Find a significant relationship between capital ratios and bank lending.
    - Document a stronger relationship between capital ratios and loan growth for banks which are deleveraging than banks which are expanding.
    - Relationship stronger for banks with lower capital ratios.
  - Kashyap et al. (2010):
    - Show that the steady state impact of increases in capital requirements on lending spreads is likely to be negative but modest under normal circumstances.
  - Bahaj et al. (2016):
    - Find empirical support for a model where the response of lending to changes in capital requirements is ambiguous in sign, depending on prospects for profitability and lending growth.
  - Studies on lending composition following capital shocks:
    - Bidder et al. (2021): bank lending overall may not decrease following a negative capital shock, but composition may shift towards lower risk weighted loans.
    - Degryse et al. (2021): composition may shift towards more collateralised lending.

### 5.2.2    The borrower resilience channel
- Empirical literature on this channel is more recent and more sparse than for bank resilience.
- Household evidence:
  - Mian et al. (2013):
    - Document a higher marginal propensity to consume out of housing wealth for households that are more levered or have lower incomes, using US data at the zip-code level.
    - Note this could be driven by several channels, including increased credit constraints as housing wealth (collateral value) falls.
    - Find changes in indicators of credit constraints are larger for households with higher leverage or lower income for a given fall in housing wealth.
- Corporate/SME evidence:
  - Fazzari and Petersen (1993):
    - Show corporate investment is highly correlated with cash flows, particularly for small firms, indicating financial imperfections and balance-sheet strength matter for investment.
  - Joseph et al. (2020):
    - Document a positive relationship between SME cash holdings and investment, consistent with borrowing constraints playing a role in investment decisions for such firms.

*Source: wpiea2023173-print-pdf - 5.1    Theory*

### 5.3    Incorporating  macrofinancial  feedbacks  into  macroprudential  stress  testing

### 5.3    Incorporating macrofinancial feedbacks into macroprudential stress testing models

### Overview: scope, classification, and trade-offs
- Literature is relatively nascent compared with inter-bank and financial sector contagion modelling; relatively few papers incorporate financial frictions into models with a fully fledged banking system where bank and borrower resilience interact to produce feedbacks.
- Three broad modelling approaches reviewed: DSGE models, semi-structural econometric models (structural and global VARs), and network models.
- Table 9 (in source) summarises pros/cons and next steps; key cross-cutting messages:
  - DSGE: strong microfoundations and ability to capture macro-financial feedbacks, but tractability forces highly stylised balance sheets, representative bank agents, limited heterogeneity, and limited capacity to model aggregate default responses.
  - Semi-structural: flexible and adaptable to available data and policy questions; can incorporate banking sector interactions with macro variables; many specifications lack explicit modelling of changes in banks’ asset mix or quality over time.
  - Network: well suited to interconnections and richer balance sheets; often rely on reconstruction or strong behavioural assumptions; useful for qualitative amplification/contagion patterns but parameter dependence limits precise quantitative policy use.
- Suggested next steps across approaches include: introduce heterogeneous banking agents (capital positions, shock sensitivity), estimate sensitivity of bank capital to shocks at the asset-class level, and exploit increasing availability of counterparty-level data to build richer network models.

### DSGE models: features, examples, and limits
- Common strengths:
  - Microfounded: responses of agents grounded in optimising and rational behaviour.
  - Able to capture a variety of macro-financial feedback effects.
- Common limitations:
  - Requirement for tractability → highly stylised balance sheets and behavioural assumptions.
  - Typically include banking sector as single representative agent → cannot capture bank heterogeneity or interconnections.
  - Many models either rule out default in equilibrium or do not allow aggregate default rates to fluctuate, limiting usefulness for severe-shock stress testing.
  - Many models are calibrated rather than fully estimated; parameter uncertainty remains.
- Empirical/quantitative findings from representative DSGE studies (as reported):
  - General magnitude: typically a 5 percent fall in intermediary (or bank) net worth produces a fall in GDP of around half a percent.
  - Christiano et al. (2010): news about riskiness of entrepreneurial returns accounts for 26-47% of output variance depending on frequency and country; model attributes between 0.3-1.5pp of the total fall in US GDP growth during the crisis to the bank funding channel (with overall bank funding channel generally of limited importance outside crisis).
  - Meh and Moran (2010): a bank capital shock of 5% produces 0.5% peak fall in output relative to steady state.
  - Gerali et al. (2010): a bank capital shock of 5% results in a fall in output of 0.5% at year 3 (under a ‘high’ penalty for deviation from target capital ratio).
  - Darracq-Paries et al. (2011): a 1pp bank capital shock leads to higher loan spreads and a small but persistent impact on GDP (at lower end of empirical range 0.1 to 1pp).
  - Gertler and Karadi (2011): a 1% decline in intermediary net worth produces a peak 0.15% fall in output relative to steady state.
  - Clerc et al. (2015): under baseline parameterisation, a 1std shock to bank risk produces a 0.5% fall in GDP; a 1std shock to housing and physical capital values produces a nearly 1.5% fall in GDP.
- Development priorities for DSGE approaches:
  - Introduce heterogenous banking agents with different starting capital positions and shock sensitivities.
  - Improve estimation/calibration of key parameters (where currently calibrated rather than estimated).
  - Consider Heterogenous Agent New Keynesian (HANK) frameworks (work cited: Hedlund et al. (2017) and Kaplan et al. (2020)) to capture distributional channels and richer effects of financial frictions.

### Semi-structural econometric models (SVAR/GVAR and variants)
- Conceptual structure:
  - Real economy GVAR/SVAR blocks augmented with an explicit banking sector block.
  - Banking sector profits depend on macro variables (GDP, interest rates); banking sector affects macro outcomes via aggregate quantity and pricing of loans.
- Strengths:
  - Adaptable to data and specific policy questions (e.g., effectiveness of countercyclical buffers).
  - Best near-term promise for providing a platform for macroprudential stress testing robust enough to inform quantitative policy.
- Common limitations:
  - Many models do not include explicit time-varying bank asset mix/quality; such changes are captured only gradually via parameter influence.
  - Some models assume banks can restore capital by improving net profits without adverse knock-on effects (limits realism).
  - Panel estimation may force parameter commonality across banks, limiting heterogeneity in behavioral responses.
- Representative models and quantitative findings:
  - Gray (2013): GVAR across 16 countries; a 664bps shock to the Italian banking sector expected loss variable (with correlated shocks) results in a 0.5 percent fall in Italian GDP.
  - Gross et al. (2016): 28 countries and 42 banks; model can include quantity and price of credit and be run under different capital-shock identifying assumptions; GDP responses vary substantially across countries and assumptions.
  - Krznar and Matheson (2017) (Brazil): six individual banks; a 1 percent fall in bank capital results in a 6 percent fall in credit and 0.5 percent fall in GDP.
  - Budnik et al. (2020) (euro area, 19 countries, 91 banks): detailed balance sheet by asset classes and geography; allowing for feedbacks from excessive deleveraging, euro area output falls by an additional 1.6 pp (on top of original 2.4% shock in original scenario).
  - Catalan and Hoffmaister (2020) (Indonesia, 12 banks): allowing for deleveraging results in much smaller (roughly 5pp) peak fall in aggregate capital ratio, but real GDP undershoots the quasi-static simulation by a substantial (5%) gap by end of horizon.
- Important modelling and policy design considerations:
  - Historical shock scenarios implicitly already include some degree of bank deleveraging; when integrating macrofeedback-capable models, one must account for this to avoid double-counting or misattributing amplification. Example: Budnik et al. (2019) assume only the non-linear component of deleveraging is not already captured in initial shocks and examine the effects of that ‘excessive’ deleveraging.
  - Including feedbacks can change distribution of losses across banks substantially even when aggregate losses or macro outcomes are calibrated to be similar — relevant for micro vs macroprudential trade-offs.
  - Tension between micro and macroprudential objectives: under some scenarios deleveraging reduces aggregate capital ratio falls but at the cost of larger output declines; under others, deleveraging increases some banks’ vulnerability.

### Network models: structure, strengths, and caveats
- Strengths:
  - Ideally suited to examine interconnections between financial and real sectors and propagation/amplification via network structure.
  - Able to model richer and more detailed balance sheets in principle.
  - Useful to demonstrate qualitative amplification and contagion mechanisms; reported amplification factors in surveyed studies typically range from 2-10 times the initial shock.
- Common limitations:
  - Often rely on network reconstruction methods due to lack of counterparty-level balance sheet data.
  - Behavioural responses typically governed by ad-hoc assumptions; most models analyse exposures at a single point in time.
  - Heavy reliance on assumed parameters limits quantitative policy use; better suited for qualitative insights.
- Representative findings and examples:
  - Anand et al. (2013): detailed network with domestic banks, overseas banks, and domestic firms using probabilistic reconstruction; banks deleverage and fire-sell after losing half their capital; flexible and tractable to explore how loss distributions vary with initial shock and parameters, but many crucial parameters are fixed by assumption.
  - Castrén and Rancan (2014) and De Almeida (2015): cross-country sectoral network models where contagion occurs via falls in equity prices affecting sectoral balance sheets rather than agent-level behaviour.
- Future potential:
  - With increasing availability of counterparty-level data (e.g., trade repositories for derivatives), more detailed network models using actual data could be constructed and may eventually be usable as fully-fledged quantitative stress testing tools (data permitting).

### Other modelling approaches and innovations
- Game-theoretic stress testing (Halaj and Priazhkina (2021)):
  - Banks choose between reducing lending or selling securities by profit maximisation subject to regulatory constraints and bank characteristics.
  - Interactions occur through expected returns on new lending and securities holdings.
  - Market-impact parameters are empirically estimated rather than ad-hoc.
  - Limitation: model does not close the loop by feeding reductions in lending into macroeconomic outcomes (output, default). Extending the model to include macroeconomic consequences would make it promising for macroprudential stress testing.
- Agent-inspired/simple macrofinancial frameworks (Gross (2022)):
  - Simple, tractable set of equations inspired by agent-based modelling to reproduce stylised facts of interest.
  - Generate useful qualitative insights; robustness for quantitative policy-setting remains an open question.

### Key quantitative magnitudes and illustrative model outputs (as reported)
- Representative elasticities and shocks:
  - Typical DSGE scale: 5 percent fall in intermediary net worth → ~0.5 percent fall in GDP.
  - Specific reported effects:
    - Christiano et al. (2010): risk news accounts for 26-47% of output variance; 0.3-1.5pp contribution to US GDP fall attributed to bank funding channel during crisis.
    - Meh and Moran (2010): 5% bank capital shock → 0.5% peak fall in output.
    - Gerali et al. (2010): 5% bank capital shock → 0.5% fall in output at year 3.
    - Gertler and Karadi (2011): 1% decline in intermediary net worth → 0.15% peak fall in output.
    - Clerc et al. (2015): 1std shock to bank risk → 0.5% fall in GDP; 1std shock to housing and physical capital values → nearly 1.5% fall in GDP.
    - Gray et al. (2013): 664bps shock to Italian banking expected loss → 0.5 percent fall in Italian GDP.
    - Krznar and Matheson (2017): 1 percent fall in bank capital → 6 percent fall in credit and 0.5 percent fall in GDP.
    - Budnik et al. (2020): allowing for feedback from excessive deleveraging → euro area output falls by an additional 1.6 pp on top of original 2.4% shock.
    - Catalan and Hoffmaister (2020): allowing deleveraging → roughly 5pp smaller peak fall in aggregate capital ratio, but real GDP ends about 5% below the quasi-static simulation by the end of horizon.
- Network-model amplification:
  - Loss amplification often reported in range 2-10 times initial shock (dependent on assumptions and reconstruction methods).

### Policy-relevant implications and research priorities
- For practical macroprudential stress testing, models need to:
  - Incorporate heterogeneity across banks (capital positions, balance sheet composition, sensitivity to shocks).
  - Allow bank capital sensitivity to shocks to be estimated at the asset-class level and aggregated to bank level, enabling timely assessment of changes in balance sheet composition and resilience.
  - Account explicitly for borrower net worth and collateral channels where relevant (currently absent in many semi-structural models).
  - Carefully design initial shock scenarios to avoid implicit double-counting of historical deleveraging responses; identify the incremental or non-linear deleveraging effects that augmented models produce.
  - Recognise potential tensions between microprudential and macroprudential objectives when deleveraging or other defensive actions change loss distributions or macro outcomes.
- Data and modelling enablers:
  - Increased availability of counterparty-level data (e.g., trade repositories, product sales databases) could enable richer network models that use actual bilateral exposure data rather than reconstructions.
  - Empirical estimation of market-impact and behavioural parameters (rather than ad-hoc calibration) would materially improve model credibility for policy use.
  - Combining tractability with richer bank heterogeneity (potentially by abstracting from some nominal frictions) is a promising path for models usable in full macroprudential stress testing.

*Italic: Source — 5.3 Incorporating macrofinancial feedbacks into macroprudential stress testing models (extracted from source content).*

### 6.1    Balance Sheet-Based Indicators

### 6.1    Balance Sheet-Based Indicators

### 6.1.1    Network measures
- Purpose:
  - Network representation captures structural features of the banking system and summarizes the contribution of financial institutions to systemic risk.
  - Relationships represented via asset side (portfolio of loans and securities) or liability side (debt and equity issued; loans-deposits received, secured and unsecured).
- Uses:
  - Detect key players and inform micro-prudential and macro-prudential policy (example: calibration of GSIB buffer to tackle too-central-to-fail).
  - Monitor speed of shock transmissions and concentration risks.
- Indicator families and properties:
  - Centrality (Entity-Specific)
    - Examples: PageRank; Eigenvector Centrality.
    - Sources cited: Yun et al. (2019); Page et al. (1999).
    - Perspective: Micro.
    - Captures firms’ position in the network; treats asset and funding exposures equally; identifies key players.
  - Concentration (Entity-Specific)
    - Examples: Weighted degree; HH index of market share concentration.
    - Source cited: Minoiu and Reyes (2013).
    - Perspective: Micro.
    - Weighted degree captures total exposures lent (out) or borrowed (in); HHI ranges between 0 and 1 and measures market concentration; suitable for assessing “too big-too-fail”.
  - Connectivity (Network-Specific)
    - Example: Network density.
    - Sources cited: Georg (2013); Ladley (2013); Battiston et al. (2012); Nier et al. (2007).
    - Perspective: Macro.
    - Captures network structure (e.g., core-periphery with low density where high-centrality institutions provide liquidity to peripheral institutions).
    - Relationship with instability: non-monotonic — high interconnectivity stabilizes under small shocks but amplifies large shocks (Georg, 2013).

### 6.1.2    Model-based measures
- Scope and classification:
  - Model-based measures divided into microprudential (entity-specific) and macroprudential (system-level) indicators.
- Key model-based indicators and features:
  - DebtRank
    - Captures recursive impact of one or more institutions’ distress across the network.
    - High DebtRank = more central node; used to determine systemically important nodes.
    - Source: Battiston et al. (2012).
    - Perspective: Micro (Solvency/Credit Risk; Feedback Centrality).
  - Aggregate Vulnerability (AV)
    - Estimates fraction of system equity capital lost due to fire-sales spillovers under assumption of intermediaries maintaining constant leverage.
    - Additive and decomposable into each bank’s contribution; systemic importance of bank i = bank i’s contribution to AV.
    - Extensions/decompositions: Duarte and Eisenbach (2021) decompose AV into system size relative to outside buyers, leverage, average leverage adjustment speed, and illiquidity concentration.
    - Integration into stress-testing: Aldasoro et al. (2022) integrate AV into accounting-based stress-testing to compare contagion channels (direct interbank exposures vs indirect overlapping portfolios).
    - Sources: Greenwood et al. (2015); Duarte and Eisenbach (2021); Aldasoro et al. (2022).
    - Perspective: Micro and Macro (Solvency/Fire-Sales).
  - Indirect Contagion Index
    - Assesses indirect price-mediated contagion via fire sales.
    - Shows strong and positive relationship with fire sales losses; computable directly from portfolio holdings.
    - Source: Cont and Schaanning (2017).
    - Perspective: Micro (Solvency and Fire-sales).
  - Capital at Risk (CaR) and Conditional Capital at Risk (CCaR)
    - Quantify banks’ 1-year ahead expected and tail losses conditional on current economic and financial conditions.
    - Function of quarterly changes in banks’ exposures, counterparty default probabilities, loss given default parameters, and correlation structure of counterparty defaults.
    - Useful to rank banks by vulnerability and contagion potential; decomposable by country, sector, risk channels, and first vs second round effects.
    - Sources: Covi et al. (2022); Covi et al. (2021); Espinosa-Vega and Solé (2011).
    - Perspective: Micro and Macro (Solvency; Credit Risk and Market Risk).
  - Liquidity at Risk
    - Structural framework for joint stress testing of solvency and liquidity; quantifies liquidity resources required for an institution facing a stress scenario.
    - Output is function of external solvency shocks and endogenous liquidity shocks.
    - Net liquidity outflow is a function of: maturing liabilities; net scheduled outflows; net outflow of variation margin; credit-contingent cash outflows.
    - Liquidity shortfall = Liquidity at Risk − liquid assets available.
    - Contrast with Liquidity Coverage Ratio (LCR): LCR estimated from historical data on margin calls or average runoff rates; Liquidity at Risk is portfolio-specific and forward-looking.
    - Source: Cont et al. (2020).
    - Perspective: Micro (Liquidity/Funding Risk).
  - Systemic Risk Probability; Average Bank Default Probability
    - Probabilistic systemic risk measure modeling stochastic banks’ credit risk losses from correlated corporate defaults and augmenting via financial contagion channels in the interbank network.
    - Systemic event defined as event in which 1.5 per cent of all banks in the system enter into distress or default within the same time period.
    - Final output = ratio between number of systemic events and overall number of simulations/scenarios.
    - Decomposes systemic risk sources into correlated economic shocks and financial contagion (credit, liquidity, market risks); computes entity-specific default probabilities and average default probability.
    - Source: Covi et al. (2020).
    - Perspective: Macro (Solvency and Liquidity; Credit Risk and Fire-sales).
- Observations on the literature:
  - Many studies produce entity-specific contagion and vulnerability indicators suited for microprudential supervision.
  - Macroprudential indicators measuring system-level risk are less common, possibly due to definitional choices and triggering event selection (exogenous macro scenario vs exogenous bank default).
  - Models can perform counterfactual policy exercises by modifying banks’ balance-sheet components to test lower capital and liquidity requirements or other regulatory changes.
  - Decomposable outputs help identify sources of contagion and vulnerability for monitoring and policy purposes.

*Source: wpiea2023173-print-pdf - 6.1    Balance Sheet-Based Indicators*

### 7.1    Lessons for policymakers and for the design of supervisory stress tests

### 7.1    Lessons for policymakers and for the design of supervisory stress tests

### Scope and focus of current supervisory stress tests
- Current supervisory stress testing frameworks (examples: the Federal Reserve’s CCAR, the Bank of England’s Annual Cyclical Scenario (ACS), and the EBA stress test) are mainly focused on quantifying direct losses from credit, market, operational and litigation risks.
- Recent macroprudential stress testing literature has identified and modelled non-linear propagation channels that amplify shocks across the financial system, centred on contagion via:
  - solvency risk (including pre-default credit valuation adjustment channels),
  - market liquidity risk,
  - funding liquidity risk.
- Examples of supervisory progress cited:
  - the 2017 Bank of England ACS applied three feedback models: a solvency contagion model, a wholesale funding cost model, and a fire sales model.
  - the Bank of England’s 2023 system-wide exploratory scenario will investigate the behaviours of banks and non-bank financial institutions following a shock and their potential for shock amplification.

### Determinants of amplification
- For a given-sized shock, eventual system-wide impact depends on:
  - (a) the size of financial institutions’ capital and liquidity buffers,
  - (b) the liquidation strategies financial institutions adopt when they need to raise cash,
  - (c) the topology of the financial network.
- Capital and liquidity buffer usability:
  - Buffer usability is defined as the quality that allows losses or funding withdrawals to be absorbed without triggering asset sales, liquidity hoarding or tightening of credit conditions.
  - Papers generate starkly different results depending on whether buffers are assumed usable. In fire sale contagion models, variance in impacts is substantially explained by differing implicit assumptions about buffer usability.
  - Models that assume banks attempt to maintain leverage ratios following shocks and hence do not view capital buffers as usable find significantly larger effects from shocks.
  - Attention to buffer usability is noted as an international regulatory focus.
- Liquidation strategies and fund behaviour:
  - Selling behaviour by asset managers to meet redemptions affects the scale of fire sale losses.
  - Selling most liquid assets first typically produces significantly smaller asset price impact than selling a “vertical slice” of assets under management, thus muting the feedback between redemptions and asset price declines.
  - Trade-off: a “liquid assets first” policy may heighten investors’ incentives to redeem to avoid being left with a less liquid pool, creating a micro-prudential/investor-protection versus macro-prudential/systemic-stability trade-off.
  - Vertical slicing avoids favouring redeeming investors but may involve sales of illiquid assets and greater spillovers to others holding similar assets.
- Regulatory constraints and binding constraints:
  - System vulnerability to fire sale losses may depend on which post-GFC regulatory constraint is binding.
  - Example: a bank facing a binding risk-based capital constraint versus a binding leverage constraint will choose liquidation strategies that trade-off liquidation losses against alleviating the constraint.
  - A binding risk-based capital constraint may generate stronger incentives to sell illiquid risky assets first if they have higher risk weights, implying larger spillovers than when leverage binds.

### Network topology
- Systemic risk is a non-linear function of network structure, with fragility highest when connectedness is either very low (little diversification) or very high (greater potential for distant shocks to spread).
- There are no straightforward, generalizable policy implications from network topology; little attention has been paid to the influence of network structure in driving stress testing model results.

### Lessons for researchers developing macroprudential stress testing models (from 7.2)
- Progress made:
  - Models have advanced in capturing new propagation channels and sophisticated behaviour under stress.
  - There has been substantial progress grounding models in empirical balance sheet data of network interconnections.
- Remaining research priorities (three high-return directions highlighted, informed by March 2020 stress episode):
  1. Greater focus on amplification in the non-bank financial system:
     - The non-bank sector has grown rapidly as a source of credit and was the epicentre of stress during the March 2020 “dash for cash” crisis.
     - Priority research questions include:
       - Under what conditions can asset managers contribute materially to systemic stress via feedback loops between redemptions, asset sales and asset prices?
       - What drives insurance companies’ and pension funds’ behaviour in stress and under what conditions do they stabilise markets versus exacerbate stress?
       - How resilient are central counterparties to pronounced market stress and what is the most efficient way of reducing procyclicality in their margin requirements?
       - What influences market intermediaries’ (e.g., broker dealers) capacity to provide liquidity in stress, and where regulatory constraints (e.g., the leverage ratio) impinge on this capacity, is there scope to redesign constraints without impairing resilience?
     - Researchers will need more granular and high-frequency data on fund flows, asset holdings and leverage.
  2. Analyse interconnectedness across the system as a whole:
     - The March 2020 episode highlights that many fault-lines require a wide-lens view of sector interactions to analyse propagation via redemptions, margin calls, repo market conditions, and asset fire sales.
     - Building multi-sectoral models of the non-bank financial system is a substantial research challenge but essential to analyse overall demand and supply of liquidity under stress.
  3. Incorporate comprehensive two-way macro-financial interactions:
     - Stress testing models need to permit examination of banks’ reactions to stress, knock-on implications for credit supply and economic activity, and resulting impacts on asset performance—i.e., integrate with macroeconomic models with financial frictions (e.g., Gertler and Kiyotaki (2015)).
     - Models with macro-financial feedbacks would provide better grounded estimates of channels and allow systematic examination of macroeconomic implications of liquidity dry-ups and policy options.

*wpiea2023173-print-pdf - 7.1    Lessons for policymakers and for the design of supervisory stress tests*

### References

### References

### Major research themes represented
- Systemic risk and contagion in financial networks
  - Acemoglu, D., Ozdaglar, A., and Tahbaz-Salehi, A. (2015). Systemic risk and stability in financial networks. American Economic Review, 105(2):564–608.
  - Allen, F. and Gale, D. (2000). Financial contagion. Journal of political economy, 108(1):1–33.
  - Eisenberg, L. and Noe, T. H. (2001). Systemic risk in financial systems. Management Science, 47(2):236–249.
  - Glasserman, P. and Young, H. P. (2015). How likely is contagion in financial networks? Journal of Banking & Finance, 50:383–399.
  - Glasserman, P. and Young, H. P. (2016). Contagion in financial networks. Journal of Economic Literature, 54(3):779–831.

- Liquidity, fire sales, and price-mediated contagion
  - Adrian, T. and Shin, H. S. (2010). Liquidity and leverage. Journal of financial intermediation, 19(3):418–437.
  - Shleifer, A. and Vishny, R. (2011). Fire sales in finance and macroeconomics. Journal of Economic Perspectives, 25(1):29–48.
  - Diamond, D. W. and Rajan, R. G. (2011). Fear of fire sales, illiquidity seeking, and credit freezes. The Quarterly Journal of Economics, 126(2):557–591.
  - Duarte, F. and Eisenbach, T. M. (2013). Fire-sale spillovers and systemic risk. FRB of New York Staff Report, 645.
  - Bardoscia, M., Caccioli, F., Perotti, J. I., Vivaldo, G., and Caldarelli, G. (2016). Distress propagation in complex networks: the case of non-linear debtrank. PloS one, 11(10):e0163825.

- Stress testing, scenario simulation, and macroprudential frameworks
  - Adrian, T., Morsink, J., Schumacher, L. B., et al. (2020). Stress testing at the imf. International Monetary Fund Departmental Paper, (20/04).
  - Anderson, R., Danielsson, J., Baba, C., Das, M. U. S., Kang, M. H., and Basurto, M. A. S. (2018). Macroprudential stress tests and policies: Searching for robust and implementable frameworks. International Monetary Fund Working Paper, 2018/197.
  - Budnik, K. B., Balatti, M., Covi, G., Dimitrov, I., Groß, J., Hansen, I., Kleemann, M., Reichenbachas, T., Sanna, F., Sarychev, A., et al. (2019). Macroprudential stress test of the euro area banking system.
  - Greenlaw, D., Kashyap, A. K., Schoenholtz, K. L., and Shin, H. S. (2012). Stressed out: Macroprudential principles for stress testing. Chicago Booth Research Paper, (12-08).
  - Glasserman, P. and Young, H. P. (2016). Contagion in financial networks. Journal of Economic Literature, 54(3):779–831.

- Interbank networks, multilayer models, and exposure estimation
  - Eisenberg, L. and Noe, T. H. (2001). Systemic risk in financial systems. Management Science, 47(2):236–249.
  - Montagna, M. and Kok, C. (2016). Multi-layered interbank model for assessing systemic risk. ECB Working Paper, 1944.
  - Minoiu, C. and Reyes, J. A. (2013). A network analysis of global banking: 1978–2010. Journal of Financial Stability, 9(2):168–184.
  - Upper, C. (2011). Simulation methods to assess the danger of contagion in interbank markets. Journal of Financial Stability, 7(3):111–125.
  - Upper, C. and Worms, A. (2004). Estimating bilateral exposures in the german interbank market: Is there a danger of contagion? European economic review, 48(4):827–849.

- Investment funds, money market funds, and market-based finance vulnerabilities
  - Bouveret, A. (2017). Liquidity stress tests for investment funds: A practical guide. International Monetary Fund.
  - Goldstein, I., Jiang, H., and Ng, D. T. (2017). Investor flows and fragility in corporate bond funds. Journal of Financial Economics, 126:592–613.
  - Baranova, Y., Coen, J., Lowe, P., Noss, J., and Silvestri, L. (2017a). Simulating stress across the financial system: the resilience of corporate bond markets and the role of investment funds. Bank of England.
  - ESMA (2019). Stress simulation for investment funds. European Securities and Markets Authority.
  - Bouveret, A., Martin, A., and McCabe, P. E. (2022). Money market fund vulnerabilities: A global perspective.

- Central counterparties, clearinghouses, and derivatives market stability
  - CFTC, U. (2016). Supervisory stress test of clearinghouses. A report by staff of the US Commodity Futures Trading Commission.
  - Heath, A., Kelly, G., Manning, M., Markose, S., and Shaghaghi, A. R. (2016). Ccps and network stability in otc derivatives markets. Journal of financial stability, 27:217–233.
  - Paddrik, M., Rajan, S., and Young, H. P. (2020). Contagion in derivatives markets. Management Science.
  - Paddrik, M. and Young, H. P. (2021). How safe are central counterparties in credit default swap markets? Mathematics and Financial Economics, 15(1):41–57.

- Macro-financial linkages, feedback loops, and DSGE/macro models with financial frictions
  - Bernanke, B. and Gertler, M. (1989). Agency costs, net worth, and business fluctuations. American Economic Review, 79(1):14–31.
  - Christiano, L. J., Motto, R., and Rostagno, M. (2010). Financial factors in economic fluctuations. ECB Working Paper, (1192).
  - Gertler, M. and Kiyotaki, N. (2010). Handbook of Monetary Economics, volume 3, chapter Financial intermediation and credit policy in business cycle analysis, pages 547–599. Elsevier.
  - Krznar, M. I. and Matheson, M. T. D. (2017). Towards macroprudential stress testing: Incorporating macro-feedback effects. IMF working paper, (17/149).
  - Catalan, M. and Hoffmaister, A. (2020). When banks punch back: macrofinancial feedback loops in stress tests. IMF Working Paper, (20/72).

- Measurement, ranking, and systemic importance methods
  - Diebold, F. X. and Yılmaz, K. (2014). On the network topology of variance decompositions: Measuring the connectedness of financial firms. Journal of Econometrics, 182(1):119–134.
  - Battiston, S., Puliga, M., Kaushik, R., Tasca, P., and Caldarelli, G. (2012). Debtrank: Too central to fail? financial networks, the fed and systemic risk. Scientific reports, 2(1):1–6.
  - Page, L., Brin, S., Motwani, R., and Winograd, T. (1999). The pagerank citation ranking: Bringing order to the web. Technical report, Stanford InfoLab.
  - Yun, T.-S., Jeong, D., and Park, S. (2019). “too central to fail” systemic risk measure using pagerank algorithm. Journal of Economic Behavior & Organization, 162:251–272.
  - Gandy, A. and Veraart, L. A. (2017). A bayesian methodology for systemic risk assessment in financial networks. Management Science, 63(12):4428–4446.

### Methodological approaches and modeling tools emphasized
- Network models, multi-layered and overlapping-portfolio models
  - Anand, K., Gai, P., Kapadia, S., Brennan, S., and Willison, M. (2013). A network model of financial system resilience. Journal of Economic Behavior & Organization, 85:219–235.
  - Caccioli, F., Farmer, J. D., Foti, N., and Rockmore, D. (2015). Overlapping portfolios, contagion, and financial stability. Journal of Economic Dynamics and Control, 51:50–63.
  - Montagna, M. and Kok, C. (2016). Multi-layered interbank model for assessing systemic risk. ECB Working Paper, 1944.

- Agent-based models and computational approaches
  - Bookstaber, R., Paddrik, M., and Tivnan, B. (2018). An agent-based model for financial vulnerability. Journal of Economic Interaction and Coordination, 13:433–466.
  - Farmer, J. D. and Joshi, S. (2002). The price dynamics of common trading strategies. Journal of Economic Behavior & Organization, 49(2):149–171.
  - LeBaron, B. (2006). Agent-based computational finance. Handbook of computational economics, 2:1187–1233.

- Empirical stress episodes and case studies (e.g., Covid-19, September 2019)
  - Anbil, S., Anderson, A. G., and Senyuz, Z. (2021). Are repo markets fragile? Evidence from September 2019. FEDS Working Paper, 2021-28.
  - Eren, E., Schrimpf, A., and Sushko, V. (2020). US dollar funding markets during the Covid-19 crisis - the money market fund turmoil. Bank for International Settlements, BIS Bulletin No 14.
  - Schrimpf, A., Shin, H. S., and Sushko, V. (2020). Leverage and margin spirals in fixed income markets during the Covid-19 crisis. Bank for International Settlements, BIS Bulletin No 2.
  - Cunliffe, J. (2020). Financial system resilience: Lessons from a real stress. Speech given by Sir Jon Cunliffe, Deputy Governor Financial Stability, Investment Association Webinar, London Tuesday 9 June 2020.

### Policy and regulatory topics covered
- Capital requirements, countercyclical buffers, and macroprudential calibration
  - Bahaj, S., Bridges, J., Malherbe, F., and O’Neill, C. (2016). What determines how banks respond to changes in capital requirements? Bank of England Working Paper, (593).
  - FED(2016). The federal reserve board’s framework for implementing the u.s. basel iii countercyclical capital buffer. Technical report.
  - Van Oordt, M. (2022). Calibrating the magnitude of the countercyclical capital buffer using market-based stress tests. Journal of Money, Credit and Banking, First Online:1–37.
  - Bennani, T., Couaillier, C., Devulder, A., Gabrieli, S., Idier, J., Lopez, P., Piquard, T., and Scalone, V. (2017). An analytical framework to calibrate macroprudential policy. (648). Banque de France Working Paper.

- Regulatory reform impacts on market liquidity and dealer intermediation
  - Baranova, Y., Liu, Z., Shakir, T., et al. (2017b). Dealer intermediation, market liquidity and the impact of regulatory reform. Bank of England, 665.
  - Heavily cited work on CCPs, rehypothecation, and shadow banking vulnerabilities (e.g., FSB (2017); Pozsar et al. (2010)).

*References section from wpiea2023173-print-pdf.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023173-print-pdf.pdf_