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### I. WHAT ARE MACROPRUDENTIAL STRESS TESTS?
- Definition:
  - Stress testing: technique of subjecting portfolios or balance sheets to numerical simulations of hypothetical “shocks” to selected variables and assessing impacts on profits, capital, or ability to meet obligations.
- Historical and regulatory context:
  - J.P. Morgan’s RiskMetrics methodology used Value at Risk (VaR) to measure market risk (Zangari 1996).
  - Basel II required stressed VaR tests for market risk and, in some cases, credit risk (Pillar 1); additional stress tests could be required under Pillar 2 (BCBS 2005).
- Microprudential vs macroprudential focus:
  - Microprudential tests: assess likelihood of failure of an individual institution; objective is ensuring soundness of each institution via capital requirements.
  - Critique: ensuring each institution’s soundness is neither necessary nor sufficient for system-wide stability; collective responses (e.g., simultaneous asset shrinkage) can amplify economic damage (Crockett 2000; Borio 2003; Kashyap and Stein 2004).
- Post-crisis shift:
  - Global financial crisis highlighted systemic risk and liquidity/funding market importance; calls for widening regulators’ “field of vision” (Bernanke 2008).
- Distinctive macroprudential features:
  - Introduce general equilibrium dimensions: outcomes depend on shock, institution buffers, behavioral responses, and interactions with other agents.
  - Focus shifts from individual institution soundness to resilience of the system as a whole and its ability to provide financial intermediation services.
- Four research and practitioner strands:
  - Integrating solvency and liquidity risks (IMF 2008; Gorton and Metrick 2009; Afonso et al. 2010; BCBS 2013).
  - Aggregate/systemic metrics and marginal contributions: distress dependence, risk budgeting, CoVaR, SRISK (Segoviano and Goodhart 2009; Huang et al. 2009; Adrian and Brunnermeier 2011; Acharya et al. 2013).
  - Principles for macroprudential stress tests (Greenlaw et al. 2012; Borio et al. 2012; IMF 2012a).
  - U.S. Federal Reserve emphasis on common exposures, fire sales, funding access, and horizontal (across-banks) analysis (Bernanke 2013; Tarullo 2014).
- Scope caveats of the paper:
  - Focuses on frameworks used by supervisors, authorities, and international organizations (not an academic macrofinancial modeling survey).
  - Focuses solely on macroprudential aspects of stress testing; scenario selection, shock calibration, transparency, and policy follow-up are excluded.

### II. IMPLEMENTING MACROPRUDENTIAL STRESS TESTS: PROGRESS SO FAR
- Overarching rationale:
  - Systemic risk arises from banks’ behavioral responses and interconnectedness (fire-sale dynamics, network contagion, imperfect information, bailout incentives).
  - Partial equilibrium microprudential tests are limited: they treat shocks exogenously, often separate liquidity and market risks, ignore interactions among banks and macro feedback, and assume static balance sheets (acceptable for one-year horizons but problematic for 3–5 year horizons).

- Two broad approaches to introduce general equilibrium dimensions:

  - Balance sheet–based models (use detailed supervisory bank data; integrate solvency, liquidity, behavior, interconnections).
    - Representative models and features:
      - Barnhill and Schumacher (2011): joint modeling of systemic liquidity and solvency; runs modeled as reaction to asset-value-induced capital breaches.
      - Bank of England RAMSI (Alessandri et al. 2009; Aikman et al. 2009): integrates credit, market, and liquidity risk; uses scoring to map market losses to funding cost increases; allows asset composition changes.
      - Kapadia et al. (2012): funding distress as function of solvency, liquidity profile, and confidence indicators.
      - Oesterreichische Nationalbank ARNIE (Feldkircher et al. 2013; Puhr and Schmitz 2013): detailed cash-flow model distinguishing contractual and behavioral flows; channels linking solvency and liquidity; dynamic balance sheets under assumptions.
      - ECB model (Henry et al. 2013): optimization framework with mean-variance portfolio choice, risky funding, regulatory limits; one-period, highly stylized.
      - Bank of Canada MFRAF: three modules (credit losses, liquidity risk, network spillovers); finding: considering liquidity and network spillovers with credit losses yields an additional 20 percent aggregate capital decline (Anand et al. 2014).
      - Bank of Korea SAMP and Bank of Japan FMM: integrate solvency, funding risks, fire sales, liquidity withdrawals, and macro feedback; Bank of Japan uses three-year horizon FMM (Kitamura et al. 2014).
      - Hong Kong Monetary Authority model (Wong and Hui 2009): integrates solvency and liquidity with Merton-type market-value-of-assets default modeling.
      - Variable hurdle-rate approach: hurdle rates above regulatory minima to capture funding-cost sensitivity to capital (Aymanns et al. 2015 found a significant negative relationship between solvency and funding cost using ~10,000 U.S. banks over 21 years and 2,700 global banks over 10 years).
    - Benefits:
      - Tractability in tracing shock impacts through explicitly modeled channels; enables attribution of effects and measurement of cross-institution contagion.
    - Limitations:
      - Captures only explicitly modeled general equilibrium effects; models differ in chosen features.
      - Analytical and computational complexity and data requirements escalate quickly; modular implementations can be slow and cumbersome, limiting high-frequency monitoring.
      - Dependence on availability and quality of supervisory balance sheet data; gaps due to OTC derivatives and shadow banking; accounting vs economic measure reconciliation challenges.
      - Limited reproducibility if supervisory data are non-public.
      - Weak microfoundations: behavioral rules-of-thumb often replace integrated optimizing-agent frameworks; liability optimization often absent.

  - Market price–based approaches (use market data/statistical techniques to capture interlinkages).
    - Two main subclasses:
      - Distress dependence / multivariate density extraction:
        - Segoviano and Goodhart (2009, 2010): estimate individual probabilities of distress; use CIMDO non-parametric method to derive multivariate density; compute metrics like JPoD, probability of specific bank distress, banking stability index; time-varying, captures linear and non-linear dependence; inputs for PDs can be market or other data; used in IMF FSAPs.
      - Merton-type / Contingent Claims Analysis (CCA):
        - Equity as call option on firm assets; market-implied default probability from leverage, asset volatility, and asset price dynamics; risk-neutral probabilities convertible to real-world probabilities.
        - CCA constructs a “risk-adjusted” balance sheet; decline in asset value increases expected losses to creditors and affects market equity beyond book-loss aggregation; can estimate how capital levels affect borrowing costs and default probabilities.
        - Used in IMF FSAPs for Hong Kong SAR, Israel, Sweden, the UK, and the U.S.A.
    - Benefits:
      - Broad metric capturing multiple vulnerability sources; market perceptions can incorporate self-fulfilling run risks.
      - Computational simplicity and light data needs; suitable for high-frequency monitoring; public market data enables external replication.
      - Analytical rigor: distress dependence uses established statistical extraction; CCA grounded in standard finance theory.
      - Easier integration of non-bank institutions into same framework.
    - Pitfalls:
      - Reliance on market data: unavailable for unlisted banks or illiquid markets; market prices reflect traded items only; noisy signals that can misestimate fundamentals.
      - Summary metric combines multiple factors into implied PD/distress—limits decomposition of contributing factors without additional tools.
      - Potential backward-looking nature, but balance sheet–based tests suffer from data lag issues as well.

- Focusing stress tests on system-wide resilience (not just aggregation of individual shortfalls):
  - Principle: macroprudential stress tests should measure system resilience—ability to continue financial intermediation—not just individual bank soundness.
  - Two central problems with current practice:
    - Aggregation problem: sum of individual shortfalls is not a good proxy for systemic vulnerability due to non-additive interconnections and time-varying, non-linear dependence.
    - Robustness problem: a single severe scenario does not guarantee resilience to all shocks of the same probability; theoretically correct approach would evaluate a multidimensional region with a given probability mass (e.g., 95 or 99 percent) and find maximum loss across that region, but this is hard to implement and subject to technical pitfalls (dimensional dependence of maximum loss).
  - Promising model developments addressing aggregation and robustness:
    - Distress dependence extended to map system-level results to individual regulatory ratios (Segoviano et al. 2015): CIMDO → Monte Carlo systemic loss distribution → systemic expected shortfall → Shapley Value → Marginal Contribution to Systemic Risk (MCSR); compare MCSR to capital buffers.
    - Systemic CCA (Gray and Jobst 2011; Jobst and Gray 2013): generate risk-adjusted balance sheets → individual expected loss distributions assumed fat-tailed (GEV) → non-parametric multivariate dependence function → multivariate extreme value distribution (M-GEV) → systemic expected shortfall and marginal contributions to systemic loss.
    - Policy-focused optimization (Webber and Willison 2011): policymaker minimizes bank capital requirements subject to probabilistic systemic stability target; nested simplified Merton-type bank model; derives capital consistent with systemic solvency probability target.
    - Pritsker (2014): defines “system assets in distress” (SAD) as sum of banks’ intermediation capacities; sets constrained stress maximization (CSM) to choose bank capital so that P(SAD > θ) ≤ α (α is systemic risk target); uses Monte Carlo to estimate SAD density non-parametrically.
  - Practical challenge: hard to jointly measure systemic risk and translate into actionable individual bank requirements; models must be robust, explainable to supervisors and market participants, and adaptable across institutions and jurisdictions.

### III. THE WAY FORWARD FOR MACROPRUDENTIAL STRESS TESTS
- State of play:
  - Significant progress integrating general equilibrium effects into stress tests; much less progress in measuring system-wide resilience and making results actionable for policy.
- Key recommendations and practitioner priorities:
  1. Use a variety of models
     - Combine balance sheet–based and market price–based models, using the same shock scenarios, to exploit complementary strengths.
     - Balance high-frequency monitoring (market price–based) with detailed, less frequent balance-sheet analyses.
     - Recognize synthesis and communication challenges and avoid over-reliance on a single framework.
  2. Run more—and better—stress scenarios
     - Single or two-scenario exercises (baseline + adverse/severe) risk providing misleading signals due to the robustness problem.
     - Use multiple extreme-but-plausible scenarios and report distributions of results around main scenario forecasts.
     - Scenarios should include shocks originating inside the financial system, mild external shocks that tip a fragile system, and cross-border/regional/global shock channels.
     - International coordination on scenario design and calibration may be necessary for cross-border institutions.
  3. Expand coverage to non-bank financial entities
     - Include non-banks (especially insurance companies, asset managers, mutual funds, pension funds where relevant) in macroprudential stress frameworks as the boundary between banks and non-banks blurs.
     - Market price–based models are particularly well-suited for integrating banks and non-banks into a single framework.
     - Prioritize inclusion of sectors closely connected to banks by ownership or financial linkages.
  4. Explore agent-based models
     - Agent-based models capture heterogeneous, bounded-rational agents and state-contingent, endogenous network formation—features traditional neoclassical models miss.
     - Examples: CRISIS project for Europe; simpler agent-based implementations by Klinger and Teplý (2014) and Chan-Lau (2014).
     - Agent-based models can illuminate behavioral responses, evolving interactions, and emergent outcomes not predictable from past behavior.
     - Implementation requires new skills and approaches but offers promising insights for stress testing.
  5. Embed stress tests into the financial stability policy framework
     - Treat stress tests as one tool among many (early warning indicators, microprudential perspectives); avoid elevating their results to an over-determinative status.
     - Be cautious about public and political expectations: results are always subject to model risk, data limitations, and “unthinkable” outcomes.
     - Use stress tests to inform policy dialogue and decision-making rather than as sole mechanistic triggers for policy action.
- Overarching guidance:
  - Combine multiple models, multiple scenarios, broader sectoral coverage, and new modeling paradigms (agent-based) while maintaining humility about stress-test predictive power.
  - Tailor stress tests to business models and dominant transmission channels; set expectations that no single quantitative output should be mechanically linked to policy responses.

*Source: _wp15146 - References .............................................................................................................*

### References .............................................................................................................

### _wp15146 - References .............................................................................................................

### I. WHAT ARE MACROPRUDENTIAL STRESS TESTS?
- Stress testing: technique of subjecting portfolios or balance sheets to numerical simulations of hypothetical “shocks” to selected variables and assessing impacts on profits, capital, or ability to meet obligations.
- Historical milestones and regulatory context:
  - J.P. Morgan’s RiskMetrics methodology used Value at Risk (VaR) to measure market risk (Zangari 1996).
  - Basel II required stressed VaR tests for market risk and, in some cases, credit risk (Pillar 1); additional stress tests could be required under Pillar 2 (BCBS 2005).
- Microprudential vs macroprudential focus:
  - Microprudential tests assess likelihood of failure of an individual institution; objective is ensuring soundness of each institution via capital requirements.
  - Critique: ensuring each institution’s soundness is neither necessary nor sufficient for system-wide stability; collective responses (e.g., simultaneous asset shrinkage) can amplify economic damage (Crockett 2000; Borio 2003; Kashyap and Stein 2004).
- Post-crisis shift:
  - Global financial crisis highlighted systemic risk and liquidity/funding market importance; calls for widening regulators’ “field of vision” (Bernanke 2008).
- Distinctive features of macroprudential stress tests:
  - Introduce general equilibrium dimensions: outcomes depend on shock, institution buffers, behavioral responses, and interactions with other agents.
  - Shift focus from individual institution soundness to resilience of the system as a whole and its ability to provide financial intermediation services.
- Four research and practitioner strands referenced:
  - Integrating solvency and liquidity risks (IMF 2008; Gorton and Metrick 2009; Afonso et al. 2010; BCBS 2013).
  - Aggregate/systemic metrics and marginal contributions: distress dependence, risk budgeting, CoVaR, SRISK (Segoviano and Goodhart 2009; Huang et al. 2009; Adrian and Brunnermeier 2011; Acharya et al. 2013).
  - Principles for macroprudential stress tests (Greenlaw et al. 2012; Borio et al. 2012; IMF 2012a).
  - U.S. Federal Reserve emphasized common exposures, fire sales, funding access, and horizontal (across-banks) analysis (Bernanke 2013; Tarullo 2014).
- Caveats of the paper:
  - Focuses on frameworks used by supervisors, authorities, and international organizations (not academic macrofinancial modeling survey).
  - Focuses solely on macroprudential aspects of stress testing; scenario selection, shock calibration, transparency, and policy follow-up are excluded.

### II. IMPLEMENTING MACROPRUDENTIAL STRESS TESTS: PROGRESS SO FAR
#### A. Introducing General Equilibrium Dimensions in Stress Tests
- Rationale: systemic risk arises from banks’ behavioral responses and interconnectedness (fire-sale dynamics, network contagion, imperfect information, bailout incentives).
- Limitations of partial equilibrium microprudential tests:
  - Exogenous shock → losses on capital of individual banks with simplistic behavior assumptions.
  - Liquidity and market risks often treated separately; interactions among banks and macro feedback generally ignored.
  - Static balance sheet assumptions acceptable for one-year horizons but problematic for 3–5 year horizons.
- Two grouped approaches to introduce general equilibrium dimensions:
  1. Balance sheet-based models (use detailed bank data; integrate solvency, liquidity, behavior, interconnections).
     - Representative examples and key features:
       - Barnhill and Schumacher (2011): joint modeling of systemic liquidity and solvency; runs modeled as reaction to asset-value-induced capital breaches.
       - Bank of England RAMSI (Alessandri et al. 2009; Aikman et al. 2009): integrates credit, market, and liquidity risk; uses scoring to map market losses to funding cost increases; allows asset composition changes.
       - Kapadia et al. (2012): funding distress as function of solvency, liquidity profile, and confidence indicators.
       - Oesterreichische Nationalbank ARNIE (Feldkircher et al. 2013; Puhr and Schmitz 2013): detailed cash-flow model distinguishing contractual and behavioral flows; channels linking solvency and liquidity; dynamic balance sheets under assumptions.
       - ECB model (Henry et al. 2013): optimization framework with mean-variance portfolio choice, risky funding, regulatory limits; one-period, highly stylized.
       - Bank of Canada MFRAF: three modules (credit losses, liquidity risk, network spillovers); finding: considering liquidity and network spillovers with credit losses yields an additional 20 percent aggregate capital decline (Anand et al. 2014).
       - Bank of Korea SAMP and Bank of Japan FMM: integrate solvency, funding risks, fire sales, liquidity withdrawals, and macro feedback; Bank of Japan uses three-year horizon FMM (Kitamura et al. 2014).
       - Hong Kong Monetary Authority model (Wong and Hui 2009): integrates solvency and liquidity with Merton-type market-value-of-assets default modeling.
       - Variable hurdle-rate approach: hurdle rates above regulatory minima to capture funding-cost sensitivity to capital (Aymanns et al. 2015 found a significant negative relationship between solvency and funding cost using ~10,000 U.S. banks over 21 years and 2,700 global banks over 10 years).
     - Benefits:
       - Tractability in tracing shock impacts through explicitly modeled channels; attribution of effects and measurement of cross-institution contagion feasible.
     - Limitations:
       - Only captures explicitly modeled general equilibrium effects; many models differ in chosen features.
       - Analytical/computational complexity and data requirements escalate quickly; modular implementations can be slow and cumbersome, limiting high-frequency monitoring.
       - Dependence on availability and quality of supervisory balance sheet data; gaps due to OTC derivatives and shadow banking; accounting vs economic measure reconciliation challenges.
       - Limited reproducibility if supervisory data are non-public.
       - Weak microfoundations: behavioral rules-of-thumb often replace integrated optimizing-agent frameworks; liability optimization often absent.
  2. Market price-based approaches (use market data/statistical techniques to capture interlinkages).
     - Two main subclasses discussed:
       - Models extracting multivariate density for the banking system (distress dependence models).
         - Segoviano and Goodhart (2009, 2010): estimate individual probabilities of distress; use CIMDO non-parametric method to derive multivariate density; compute metrics like JPoD, probability of specific bank distress, banking stability index; time-varying, captures linear and non-linear dependence; inputs for PDs can be market or other data; used in IMF FSAPs.
       - Merton-type / Contingent Claims Analysis (CCA).
         - Equity as call option on firm assets; market-implied default probability from leverage, asset volatility, and asset price dynamics; risk-neutral probabilities convertible to real-world probabilities.
         - CCA constructs a “risk-adjusted” balance sheet; decline in asset value increases expected losses to creditors and affects market equity beyond book-loss aggregation; can estimate how capital levels affect borrowing costs and default probabilities.
         - Used in IMF FSAPs for Hong Kong SAR, Israel, Sweden, the UK, and the U.S.A.
     - Benefits:
       - Broad metric capturing multiple vulnerability sources; market perceptions can incorporate self-fulfilling run risks.
       - Computational simplicity and light data needs; suitable for high-frequency monitoring; public market data enables external replication.
       - Analytical rigor: distress dependence uses established statistical extraction; CCA grounded in standard finance theory.
       - Easier integration of non-bank institutions into same framework.
     - Pitfalls:
       - Reliance on market data: unavailable for unlisted banks or illiquid markets; market prices reflect traded items only; noisy signals that can misestimate fundamentals.
       - Summary metric combines multiple factors into implied PD/distress—limits decomposition of contributing factors without additional tools.
       - Potential backward-looking nature, but balance sheet-based tests suffer from data lag issues as well.

#### B. Focusing Stress Tests on the Resilience of the Financial System as a Whole
- Principle: macroprudential stress tests should measure system resilience—ability to continue financial intermediation—not just individual bank soundness.
- Current practice gap:
  - Many tests still focus on individual binary pass-fail outcomes and aggregate shortfalls, which raises two problems:
    - Aggregation problem: sum of individual shortfalls is not a good proxy for systemic vulnerability due to non-additive interconnections and time-varying, non-linear dependence.
    - Robustness problem: single severe scenario does not guarantee resilience to all shocks of the same probability; theoretically correct approach would evaluate a multidimensional region with a given probability mass (e.g., 95 or 99 percent) and find maximum loss across that region, but this is hard to implement and subject to technical pitfalls (dimensional dependence of maximum loss).
- Promising model developments addressing aggregation and robustness:
  - Distress dependence extended to map system-level results to individual regulatory ratios (Segoviano et al. 2015): use CIMDO to generate multivariate density → Monte Carlo systemic loss distribution → systemic expected shortfall → Shapley Value to calculate Marginal Contribution to Systemic Risk (MCSR); compare MCSR to capital buffers.
  - Systemic CCA (Gray and Jobst 2011; Jobst and Gray 2013): generate risk-adjusted balance sheets → individual expected loss distributions assumed fat-tailed (GEV) → non-parametric multivariate dependence function → multivariate extreme value distribution (M-GEV) → systemic expected shortfall and marginal contributions to systemic loss.
  - Policy-focused optimization (Webber and Willison 2011): policymaker minimizes bank capital requirements subject to probabilistic systemic stability target; nested simplified Merton-type bank model; provides a way to derive capital consistent with systemic solvency probability target.
  - Pritsker (2014): defines “system assets in distress” (SAD) as sum of banks’ intermediation capacities; sets constrained stress maximization (CSM) to choose bank capital so that P(SAD > θ) ≤ α (α is systemic risk target); uses Monte Carlo to estimate SAD density non-parametrically.
- Practical challenges:
  - Hard to jointly measure systemic risk and translate into actionable individual bank requirements; models must be robust, explainable to supervisors and market participants, and adaptable across institutions and jurisdictions.

### III. THE WAY FORWARD FOR MACROPRUDENTIAL STRESS TESTS
- Summary of state: significant progress integrating general equilibrium effects into stress tests; much less progress in measuring system-wide resilience and making results actionable for policy.
- Key recommendations and priorities for practitioners:
  1. Use a variety of models
     - Combine balance sheet-based and market price-based models, using the same shock scenarios, to exploit complementary strengths.
     - Balance high-frequency monitoring (market price-based) with detailed, less frequent balance-sheet analyses.
     - Recognize synthesis and communication challenges and avoid over-reliance on a single framework.
  2. Run more—and better—stress scenarios
     - Single or two-scenario exercises (baseline + adverse/severe) risk providing misleading signals due to the robustness problem.
     - Use multiple extreme-but-plausible scenarios and report distributions of results around main scenario forecasts.
     - Scenarios should include shocks originating inside the financial system, mild external shocks that tip a fragile system, and cross-border/regional/global shock channels.
     - International coordination on scenario design and calibration may be necessary for cross-border institutions.
  3. Expand coverage to non-bank financial entities
     - The blurring between banks and non-banks and growth of shadow banking calls for including non-banks (especially insurance companies, asset managers, mutual funds, pension funds where relevant) in macroprudential stress frameworks.
     - Market price-based models are particularly well-suited for integrating banks and non-banks into a single framework.
     - Prioritize inclusion of sectors closely connected to banks by ownership or financial linkages.
  4. Explore agent-based models
     - Agent-based models capture heterogeneous, bounded-rational agents and state-contingent, endogenous network formation—features traditional neoclassical models miss.
     - Examples: CRISIS project for Europe; simpler agent-based implementations by Klinger and Teplý (2014) and Chan-Lau (2014).
     - Agent-based models can illuminate behavioral responses, evolving interactions, and emergent outcomes not predictable from past behavior.
     - Implementation requires new skills and approaches but offers promising insights for stress testing.
  5. Embed stress tests into the financial stability policy framework
     - Treat stress tests as one tool among many (early warning indicators, microprudential perspectives); avoid elevating their results to an over-determinative status.
     - Be cautious about public and political expectations: results are always subject to model risk, data limitations, and “unthinkable” outcomes.
     - Use stress tests to inform policy dialogue and decision-making rather than as sole mechanistic triggers for policy action.
- Overarching guidance:
  - Combine multiple models, multiple scenarios, broader sectoral coverage, and new modeling paradigms (agent-based) while maintaining humility about stress-test predictive power.
  - Tailor stress tests to business models and dominant transmission channels; set expectations that no single quantitative output should be mechanically linked to policy responses.

*Italic: Source: _wp15146 - References .............................................................................................................*

### REFERENCES

### _wp15146 - REFERENCES

### Systemic risk and stress testing
- Acharya, V. V., L. H. Pedersen, T. Philippon, and M. Richardson, 2010, “Measuring Systemic Risk,” Working Paper No. 10/02 (Cleveland: Federal Reserve Bank).  
- Acharya, V. V., R. Engle, and D. Pierret, 2013, “Testing Macroprudential Stress Tests: The Risk of Regulatory Risk Weights,” NBER Working Paper No. 18968 (Cambridge, MA: National Bureau of Economic Research).  
- Adrian, T. and M. K. Brunnermeier, 2011, “COVAR,” NBER Working Paper No. 17454 (Cambridge, MA: National Bureau of Economic Research).  
- Aikman, D., P. Alessandri, B. Eklund, P. Gai, S. Kapadia, E. Martin, N. Mora, G. Sterne, and M. Willison, 2009, “Funding Liquidity Risk in a Quantitative Model of Systemic Stability,” Bank of England Working Paper No. 372 (London: Bank of England).  
- Alessandri, P., P. Gai, S. Kapadia, N. Mora, and C. Puhr, 2009, “Towards a Framework for Quantifying Systemic Stability,” International Journal of Central Banking, Vol. 5, No. 3, pp. 47–81.  
- Basel Committee on Banking Supervision, 2013, “Liquidity Stress Testing: A Survey of Theory, Empirics and Current Industry and Supervisory Practices,” Basel Committee on Banking Supervision Working Paper No. 24 (Basel: Bank for International Settlements).  
- Borio, C., M. Drehmann, and K. Tsatsaronis, 2012, “Stress Testing Macro Stress Testing: Does it Live Up to Expectations?” BIS Working Paper No. 369 (Basel: Bank for International Settlements).  
- Greenlaw, D., Kashyap, A. K., Schoenholtz, K., and H. S. Shin, 2012, “Stressed Out: Macroprudential Principles for Stress Testing,” Booth School of Business Working Paper No. 71(Chicago: The University of Chicago).  
- Henry, J., C. Kok, A. Amzallag, P. Baudino, I. Cabral, M. Grodzicki, M. Gross, G. Halaj, M. Kolb, M. Leber, C. Pancaro, M. Sydow, A. Voulidis, M. Zimmermann, and A. Zochowski, 2013, “A Macro Stress testing Framework for Assessing Systemic Risks in the Banking Sector,” ECB Occasional Paper No. 152 (Frankfurt: European Central Bank).  
- Jobst, A. A. and D. F. Gray, 2013, “Systemic Contingent Claims Analysis—Estimating Market-Implied Systemic Risk,” IMF Working Paper 13/54 (Washington DC: International Monetary Fund).  
- Segoviano, M. A., S. Malik, P. Lindner, and F. Cortes, 2015, “Systemic Risk and Interconnectedness (SyRin): A Comprehensive Multi-Sector Framework,” IMF Working Paper (forthcoming), (Washington DC: International Monetary Fund).  

### Liquidity, funding, and interconnectedness
- Afonso, G., A. Kovner, and A. Shoar, 2010, “Stressed, Not Frozen: The Federal Funds Market in the Financial Crisis,” Federal Reserve Bank of New York Staff Report No. 437 (New York: Federal Reserve Bank).  
- Barnhill, T. and L. Schumacher, 2011, “Modeling Correlated Systemic Liquidity and Solvency Risks in a Financial Environment with Incomplete Information,” IMF Working Paper 11/263 (Washington DC: International Monetary Fund).  
- Bolton, P., T. Santos, and J. Scheinkman, 2009, “Market and Public Liquidity,” American Economic Review, Vol. 99, pp. 594–599.  
- Heider, F., M. Hoerova, and C. Holthausen, 2009, “Liquidity Hoarding and Interbank Market Spreads: The Role of Counterparty Risk,” ECB Working Paper No. 1126 (Frankfurt: European Central Bank).  
- Kapadia, S., M. Drehmann, J. Elliott, and G. Sterne, 2012, “Liquidity Risk, Cash-Flow Constraints and Systemic Feedbacks,” Bank of England Working Paper No. 456 (London: Bank of England).  
- Diamond, D. W. and R. G. Rajan, 2011, “Fear of Fire Sales, Illiquidity Seeking, and Credit Freezes,” Quarterly Journal of Economics, Vol. CXXVI, issue 2, pp. 557–591.  
- Puhr, C. and S. W. Schmitz, 2013, “A View from the Top—The Interaction Between Solvency and Liquidity Stress,” Journal of Risk Management in Financial Institutions, Vol. 7, No. 1, pp. 38–51.  
- Pierret, D., 2014, “Systemic Risk and the Solvency-Liquidity Nexus of Banks,” mimeo, NYU Stern School of Business.  

### Models, methodologies, and measurement tools
- Acharya, V. V. and T. Yorulmazer, 2008, “Cash-in-the-Market Pricing and Optimal Resolution of Bank Failures,” Review of Financial Studies, Vol. 21, pp. 2705–2742.  
- Altman, E. I., 1968, “Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy,” Journal of Finance, Vol. 23, No. 4, pp. 589–609.  
- Altman, E. I. and E. Hotchkiss, 2006, Corporate Financial Distress and Bankruptcy, 3rd edition, (New Jersey: John Wiley & Sons, Inc.).  
- Black, F. and M. Scholes, 1973, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, Vol. 81, No. 3, pp. 637-654.  
- Merton, R. C., 1974, “On the Pricing of Corporate Debt: the Risk Structure of Interest Rates,” Journal of Finance, Vol. 29, No. 2, pp. 449–470.  
- Breuer, T., 2008, “Overcoming Dimensional Dependence of Worst Case Scenarios and Maximum Loss,” Journal of Risk, Vol. 11, No. 1, pp. 79–92.  
- Breuer, T., M. Jandačka, K. Rheinberger, and M. Summer, 2009, “How to Fund Plausible, Severe, and Useful Stress Scenarios,” International Journal of Central Banking, Vol. 5, No. 3, pp. 205–224.  
- Segoviano, M. A., 2006, “Consistent Information Multivariate Density Methodology,” Financial Markets Group, London School of Economics Discussion Paper No. 557 (London: London School of Economics).  
- Segoviano, M. A. and C. Goodhart, 2009, “Banking Stability Measures,” IMF Working Paper 09/4 (Washington DC: International Monetary Fund).  
- Segoviano, M. A. and C. Goodhart, 2010, “Distress Dependence and Financial Stability,” in Financial Stability, Monetary Policy, and Central Banking, ed. by Alfaro (Santiago: Central Bank of Chile).  
- Glasserman, P., C. Kang, and W. Kang, 2015, “Stress Scenario Selection by Empirical Likelihood,” Quantitative Finance, Vol. 15, no. 1, pp. 25-41.  
- Klinger, T. and P. Teplý, 2014, “Systemic Risk of the Global Banking System—An Agent-Based Network Model Approach,” Prague Economic Papers, Vol. 1, pp. 24–41.  
- Bookstaber, R., 2012, “Using Agent-Based Models for Analyzing Threats to Financial Stability,” Office of Financial Research Working Paper No. 0003 (Washington DC: U.S. Department of the Treasury).  
- Chan-Lau, J. A., 2013, Systemic Risk Assessment and Oversight, (London: Risk Books).  
- Chan-Lau,  J.A., 2010, “Regulatory Capital Charges for Too-Connected to Fail Institutions,” Financial Markets, Institutions, and Instruments, Vol. 19, No. 5, pp. 355 – 79.  
- Crosbie, P. and J. Bohn, 2003, Modeling Default Risk: Modeling Methodology (New York: Moody’s KMV).  
- Dwyer, D. W., A. E. Kocagil, and R. S. Stein, 2004, Moody’s KMV Riskcalc™ v3.1 Model (New York: Moody’s KMV).  
- Zangari, P., 1996, “Statistical and Probability Foundations,” RiskMetricTM—Technical Document, 4th edition, Ch. 4, pp. 45–74 (New York: Morgan Guaranty Trust Company of New York).  

### Macroprudential frameworks, regulation, and policy guidance
- Borio, C., 2003, “Towards a Macroprudential Framework for Financial Supervision and Regulation?” BIS Working Paper No. 128 (Basel: Bank for International Settlements).  
- Crockett, A. D., 2000, “Marrying the Micro- and Macro-Prudential Dimensions of Financial Stability,” remarks before the Eleventh International Conference of Banking Supervisors, Basel, 20-21 September 2000 (Basel: Bank for International Settlements).  
- Basel Committee on Banking Supervision, 2005, “International Convergence of Capital Measurement and Capital Standards: A Revised Framework,” Technical Report (Basel: Bank for International Settlements).  
- Basel Committee on Banking Supervision, 2009, Revisions to the Basel II Risk Framework (Basel: Bank for International Settlements).  
- Board of Governors of the Federal Reserve System, 2014, Comprehensive Capital Analysis and Review 2015: Summary Instructions and Guidance (Washington DC: Federal Reserve).  
- Federal Reserve System, 2013, “Policy Statement on the Scenario Design Framework for Stress Testing,” Federal Register, Vol. 78, No. 230, pp. 71435–71448.  
- Tarullo, D. K., 2014, “Stress Testing after Five Years,” remarks at the Federal Reserve Third Annual Stress Test Modeling Symposium (Boston: Federal Reserve Bank).  
- Webber, L. and M. Willison, 2011, “Systemic Capital Requirements,” Bank of England Working Paper No. 436 (London: Bank of England).  

### Country reports, IMF and central bank applications
- Aymanns, C., C. Caceres, C. Daniel, and L. Schumacher, 2015, “Bank Solvency and Funding Cost,” IMF Working Paper (forthcoming), (Washington DC: International Monetary Fund).  
- Bank of England, 2013, “A Framework for Stress Testing the UK Banking System,” Bank of England Discussion Paper, October (London: Bank of England).  
- Bank of Korea, 2012, “Systemic Risk Assessment Model for Macroprudential Policy (SAMP),” Financial Stability Report, October (Seoul: Bank of Korea).  
- Feldkircher, M., G. Fenz, R. Ferstl, G. Krenn, B. Neudorfer, C. Puhr, T. Reininger, S. W. Schmitz, M. Schneider, C. Siebenbrunner, M. Sigmund, and R. Spitzer, 2013, “ARNIE in Action: the 2013 FSAP Stress Tests for the Austrian Banking System,” Financial Stability Report, No. 26, pp. 100–118.  
- International Monetary Fund, 2008, Global Financial Stability Report, October 2008 (Washington DC: International Monetary Fund).  
- International Monetary Fund, 2010, “United States: Financial Sector Assessment Program Documentation—Technical Note on Stress Testing,” IMF Country Report No. 10/244. Available at http://www.imf.org/external/pubs/ft/scr/2010/cr10244.pdf.  
- International Monetary Fund, 2011a, “Sweden: Technical Note on Contingent Claims Analysis to Measure Risk and Stress Test the Swedish Banking Sector,” IMF Country Report No. 11/286. Available at http://www.imf.org/external/pubs/ft/scr/2011/cr11286.pdf.  
- International Monetary Fund, 2011b, “United Kingdom: Technical Note on Stress Testing the Banking Sector,” IMF Country Report No. 11/227. Available at http://www.imf.org/external/pubs/ft/scr/2011/cr11227.pdf.  
- International Monetary Fund, 2012a, Macrofinancial Stress Testing: Principles and Practices, IMF Policy Paper. Available at http://www.imf.org/external/np/pp/eng/2012/082212.pdf.  
- International Monetary Fund 2012b, “Israel: Technical Note on Stress testing the Banking, Insurance and Pension Sectors,” IMF Country Report No. 12/88. Available at http://www.imf.org/external/pubs/ft/scr/2012/cr1288.pdf.  
- International Monetary Fund, 2014a, “Switzerland: Financial Sector Stability Assessment,” IMF Country Report No. 14/143. Available at http://www.imf.org/external/pubs/ft/scr/2014/cr14143.pdf.  
- International Monetary Fund, 2014b, “People's Republic of China––Hong Kong Special Administrative Region: Technical Note on Stress Testing the Banking Sector,” IMF Country Report No. 14/210. Available at http://www.imf.org/external/pubs/ft/scr/2014/cr14210.pdf.  
- International Monetary Fund, 2015, Global Financial Stability Report, April 2015 (Washington DC: International Monetary Fund).  
- Feldkircher, M., G. Fenz, R. Ferstl, G. Krenn, B. Neudorfer, C. Puhr, T. Reininger, S. W. Schmitz, M. Schneider, C. Siebenbrunner, M. Sigmund, and R. Spitzer, 2013, “ARNIE in Action: the 2013 FSAP Stress Tests for the Austrian Banking System,” Financial Stability Report, No. 26, pp. 100–118.  

### Additional theory, empirical and technical contributions
- Allen, F. and D. Gale, 2007, Understanding Financial Crises (New York: Oxford University Press).  
- Alfaro, R. and M. Drehmann, 2009, “Macro Stress Tests and Crises: What Can We Learn?” BIS Quarterly Review, December.  
- Anand, K., G. Bédard-Pagé, and V. Traclet, 2014, “Stress Testing the Canadian Banking System: A System-Wide Approach,” Financial System Review, June, pp. 61–68.  
- Borio, C., 2003, “Towards a Macroprudential Framework for Financial Supervision and Regulation?” BIS Working Paper No. 128 (Basel: Bank for International Settlements).  
- Gauthier, C., A. Lehar, and M. Souissi, 2010, “Macroprudential Regulation and Systemic Capital Requirements,” Bank of Canada Working Paper No. 2010–4 (Ottawa: Bank of Canada).  
- Goodhart, C., P. Sunirand, and D. Tsomocos, 2006, “A Model to Analyze Financial Fragility,” Economic Theory, Vol. 27, No. 1, pp. 107–142.  
- Gorton, G. and A. Metrick, 2009, “Securitized Banking and the Run on the Repo,” NBER Working Paper No. 15223 (Cambridge, MA: National Bureau of Economic Research).  
- Gray, D. F. and S. W. Malone, 2008, Macrofinancial Risk Analysis (Hoboken: John Wiley & Sons, Inc.).  
- Gray, D. F., 2010, “New Directions in Financial Sector and Sovereign Risk Management,” Journal of Investment Management, Vol. 8, No. 1, pp. 23–38.  
- Gray, D. F., and A. A. Jobst, 2011, “Modelling Systemic Financial Sector and Sovereign Risk,” Sveriges Riksbank Economic Review, No. 2, pp. 68–106.  
- Neyman, A., 2002, “Value of Games With Infinitely Many Players,” in Aumann, R.J. and S. Hart (eds.), Handbook of Game Theory with Economic Applications (Amsterdam: Elsevier).  
- Pritsker, M., 2014, “Enhanced Stress Testing and Financial Stability,” mimeo, The Federal Reserve Bank of Boston.  
- Solow, R., 2010, “Building a Science of Economics for the Real World,” in Statement at the Hearing of the House Committee on Science and Technology Subcommittee on Investigations and Oversight, U.S. House of Representatives, 111th Congress, July 20 (Washington DC: U.S. Government Printing Office).  
- Stein, J. and A. Kashyap, 2004, “Cyclical Implications of the Basel II Capital Standards,” Economic Perspectives, Vol. 28, Q1, pp. 18–31.  
- Tarashev, N., C. Borio, and K. Tsatsaronis, 2010, “Attributing Systemic Risk to Individual Institutions,” BIS Working Paper No. 308 (Basel: Bank for International Settlements).  
- Wong, E. and C. Hui, 2009, “A Liquidity Stress-Testing Framework with Interaction between Market and Credit Risks,” Hong Kong Monetary Authority Working Paper No. 06/2009 (Hong Kong: Hong Kong Monetary Authority).  
- Chan-Lau, J. A., 2014, “Regulatory Requirements and Their Implications for Bank Solvency, Liquidity, and Interconnectedness Risks: Insights from Agent-Based Model Simulations.” Available at SSRN: http://ssrn.com/abstract=2537124.  
- Glasserman, P., C. Kang, and W. Kang, 2015, “Stress Scenario Selection by Empirical Likelihood,” Quantitative Finance, Vol. 15, no. 1, pp. 25-41.  

*References list from _wp15146 - REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15146.pdf_