## stimfea

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### Purpose and role of IMF stress tests
- IMF staff use macroprudential stress tests to assess systemic risk as part of the IMF’s mandate to monitor global financial stability.
- Stress tests assess resilience of financial systems in IMF member countries and underpin policy advice primarily through the Financial Sector Assessment Program (FSAP).
- IMF staff provide technical assistance in stress testing to a large number of member countries.

### Definition and focus of IMF macroprudential stress tests
- An IMF macroprudential stress test: a methodology to assess financial vulnerabilities that can trigger systemic risk and the need for systemwide mitigating measures.
- Distinction:
  - Microprudential stress test:
    - Forward-looking supervisory tool assessing adequacy of individual banks’ capital (or liquidity) conditional on portfolio risks.
    - Supervisory focus on whether a bank “passes” the test and subsequent supervisory measures.
  - Macroprudential stress test:
    - Focuses on vulnerabilities that can trigger systemic risk (high leverage, mispricing, concentration of risk, liquidity mismanagement).
    - Final objective: assess whether identified vulnerabilities can compromise financial stability for the whole economy.
    - Results by institution are not published; used with authorities to support FSAP recommendations.

### Policy implications and typical recommendations
- Recommendations based on IMF stress tests can include:
  - Need to boost capital cushions.
  - Adoption of borrower-based measures (debt to income and loan to value ratios).
  - Implementation of surcharges (countercyclical or risk specific surcharges).
  - Application of liquidity requirements.

### Concept of systemic risk and broader goals
- IMF, FSB, and BIS (2009) definition: systemic risk as disruptions to the provision of financial services caused by impairment of all or parts of the financial system with potential serious negative consequences for the real economy.
- IMF stress testing historically focused on vulnerabilities leading to financial crisis; more recently also on vulnerabilities that create downside risks to growth (“growth at risk”).
- Current goals:
  - Assess risk of systemic failures of significant financial institutions.
  - Identify financial vulnerabilities that can create risks for sustainable economic growth, even absent a full financial crisis.

### Coverage, scope, and operational approach
- Primary coverage: depository intermediaries, particularly systemically important banks (global or domestic).
- Nonbank testing: included when specific systemic risk sources identified (insurance, asset management, nonfinancial firms, households) using different methodologies (not described in this paper).
- Operational constraints and reach:
  - IMF conducts stress tests as part of financial stability assessments in 12–14 different financial systems each year.
  - IMF helps develop authorities’ stress-testing capacity in about 18 different financial systems each year.
- Typical approach: combination of top-down (IMF staff) and bottom-up (financial institutions) stress tests based on agreed methodology and scenarios.

### Structure of IMF stress-testing work program (paper coverage)
- The paper provides:
  - Brief history of IMF stress-test evolution.
  - Key steps of an IMF staff stress test.
  - Discussion of use of stress test results for policy advice.
  - Identification of remaining challenges and overview of IMF staff work program.

### Origins and methodological evolution
- Stress testing emerged prominently after the 1997–98 Asian crisis; FSAP inaugurated in 1999.
- Early IMF approaches: spreadsheet-based, one-year credit-risk horizon, instantaneous market-risk shocks; scenario design often used worst historical developments.
- Methodological developments:
  - Monte Carlo simulations, Credit Risk Plus, entropy risk measures, adoption of Basel II inputs (PDs, LGDs, EaDs).
  - Post-2008 shift from microprudential bank-by-bank analysis to macroprudential systemic-risk focus; expanded coverage to sovereign, funding, market liquidity risks, contagion models, nonbanks, amplification mechanisms.

### FSAP coverage mandates
- 2010 decision: 25 jurisdictions deemed systemically important.
- 2013 review: number increased to 29.

### Key steps in IMF staff stress-testing approach
- Initial assessment of vulnerabilities using financial indicators and Growth-at-Risk (GaR); define perimeter and data issues.
- Scenario design: choice of shocks and calibration of macro-financial variables guided by FSAP Risk Assessment Matrix (RAM) and Global RAM; GaR used to calibrate scenario severity consistently.
- Stress tests of solvency, liquidity, and contagion: satellite models translate adverse scenario variables into balance-sheet items, profits and losses, and stressed liquidity inflows/outflows; contagion models assess network propagation.
- Risk amplification mechanisms: integrate modules to assess interactions among risk types and amplification channels (work in progress).

### Assessment of vulnerabilities and role of Growth-at-Risk (GaR)
- Systemic vulnerabilities include leverage, maturity transformation, interconnectedness, complexity leading to feedback loops, asset fire-sales, and reduced credit supply.
- GaR measures downside risk to GDP growth and informs selection and calibration of stress-test scenarios and severity.
- Vulnerability categories:
  - Cyclical: credit growth, credit-to-GDP gap, loan-to-deposit ratio, volatile funding.
  - Structural: dependence on international capital inflows, high dollarization, high interconnectedness, concentration of funding or asset exposures, high NPL shares.
  - Institutional: weak AML-CFT frameworks that could trigger blacklisting or loss of correspondent services.

### Scenario design, severity benchmarks, and simulation tools
- Minimum scenarios: baseline (WEO projections) and at least one adverse scenario; risk horizon typically spans three to five years.
- Scenario requirements: forward-looking, severe, consistent, robust; severity often anchored by fall in real GDP below baseline or cumulative fall in real GDP growth.
- Historical rule of thumb: shocks to GDP growth at least two historical standard deviations from the mean over first two to three years; GaR currently used as a minimum severity benchmark conditional on cyclical phase.
- Simulation models:
  - Global Macrofinancial Model (GFM): structural DSGE, quarterly, covering 40 economies.
  - Flexible System of Global Models (FSGM): semi-structural, annual, covering 24 economies.
  - Structural VARs or authorities’ macro models for developing economies.
  - MASS: Macro-Financial System Simulator enabling full distributions of institutions’ capital positions and worst-case scenario search.

### Stress testing banks: solvency framework and presentation
- Basic modules: solvency, liquidity, contagion; advanced integrated framework combines risks.
- Solvency tests: compare actual capital under stress (initial capital plus net losses) to stressed capital requirements.
- Income statement forecasting under stress includes net interest income, provisions, trading losses, fee income, operational expenses, taxes; satellite models map macro-financial changes to these components over the risk horizon.
- Hurdle/passing rates:
  - For Basel III jurisdictions include Pillar 1 and Pillar II, capital conservation buffers, institution-specific countercyclical capital buffers, buffers for systemically important banks, systemic risk buffers (countercyclical buffer may be excluded).
  - Leverage ratios increasingly used as supplementary hurdle rates.
  - Asset maintenance ratio used for systemically important branches on occasion.
- Results: granular bank-level outputs produced for authorities; public releases present aggregated vulnerabilities and policy recommendations while preserving confidentiality.

### Leverage ratios and presentation elements
- Example presentation elements (Figure 5, Country A Bank 1):
  - Total Capital Adequacy Ratio (Percent) with time labels Dec. 2014; Dec. 15; Dec. 16; Dec. 17; Dec. 18; Dec. 19; Dec. 20 and vertical axis markers 0 through 10.
  - Capital Needs presented with time labels Jan. 2014 through Jan. 20 and vertical axis markers 0; 100; 200; …; 900 and secondary axis markers –1,500; –1,000; –500; 0; 500; 1,000; 1,500.
  - Net Profit Components vertical markers 50; 52; 54; …; 68 and secondary vertical markers 0.0; 0.5; 1.0; 1.5; 2.0; 2.5.
  - Contribution to Change of Capitalization Ratio (Percent) section included.

### Liquidity stress testing: objectives, design, and time buckets
- Objectives: assess capacity to withstand extreme but plausible funding shocks (funding-liquidity) and/or large declines in value of assets (market-liquidity).
- Two complementary approaches:
  - Cash-flow stress test (IMF staff): customized parameters, includes all unencumbered marketable securities, simulates inflows/outflows over multiple time buckets, explicit exchange-rate evolution assumptions.
  - Liquidity Coverage Ratio (LCR): ensures stock of HQLA to meet liquidity needs in a 30-day horizon; internationally harmonized parameters.
- Rationale: cash-flow test addresses illiquidity that can last more than 30 days and cliff effects at end of 30 days.
- Time buckets explicitly listed:
  - next 24 hours
  - 2 to 7 days
  - up to 30 days
  - 31–60 days
  - 61–90 days
  - 91–120 days
  - 121–150 days
  - 151–180 days
  - 181 days–1 year
  - 1–3 years
  - beyond 3 years
- Failure criterion: a bank fails the test when only emergency liquidity assistance (ELA) would allow it to continue fulfilling obligations; before ELA, counterbalancing capacity and standard central bank facilities are considered.

### Contagion analysis: scope and methods
- Contagion assessed at interbank, cross-sectoral, and cross-border levels.
- Methods:
  - Exposure-based domino-effect analyses (Espinosa-Vega and Solé (2010) approach).
  - Market-based indicators and asset-price codependence measures for indirect linkages and common exposures.
  - Combined exposure and market-based approaches where data permit.
- Cross-border: uses exposure frameworks and BIS locational/consolidated data; qualitative assessment of cross-border relations supplements quantitative models.

### Risk amplification mechanisms captured
- Key amplification channels included in FSAPs:
  - Interconnectedness (interbank, cross-sectoral, cross-border).
  - Solvency–liquidity interaction (funding-cost/solvency loop, sovereign-bank nexus).
  - Market liquidity channel (asset fire sales, reduced counterbalancing capacity).
  - Real–financial feedbacks (funding-cost pass-through to lending rates, deleveraging effects on GDP).
- Implementation notes (summary points):
  - Bank-solvency nexus: implemented in most FSAPs.
  - Funding channel: implemented in the Euro Area FSAP and in most FSAPs, granularity dependent on data.
  - Market liquidity channel: implemented when data available.
  - PD impact, NPL channel, liquidity dry-out channel: implemented in most FSAPs with ad hoc variants as needed.
  - Counterparty credit risk and derivatives inflows: implemented in specific FSAPs.

### Funding cost–solvency empirical links and IMF implementation
- Empirical findings:
  - A 100 basis point increase in regulatory capital ratios is associated with a decrease of bank funding costs of about 105 basis points (Schmitz, Sigmund, and Valderrama (2017) result).
  - A 100 basis point increase of funding costs reduces CAR by 32 basis points on average (Schmitz, Sigmund, and Valderrama (2017) result).
  - Nonlinearities: interbank funding cost more sensitive to solvency during stress and at lower solvency levels.
- IMF implementation examples (Japan, New Zealand, United Kingdom, Poland, euro area, Switzerland):
  - Integrated solvency–funding feedback via sequential iteration: solvency outputs update funding-cost projections year-by-year until convergence.
  - Funding costs projected at bank, instrument, and contract level; modeling elements include interest expenses to interest-earning liabilities ratio, bank-specific capital sensitivity terms, and Markov regime-switching components for base rates and liquidity premia.

### Equity valuation, sovereign–bank nexus, and market-valuation choices
- Equity-market effects: stressed equity valuations can trigger rating downgrades and higher funding costs; methodologies such as Merton-based/Bloomberg DRSK used to quantify amplification.
- Sovereign–bank nexus:
  - Regulatory frameworks may give low/zero risk-weights for sovereign bonds held to maturity; investors focus on market value of bank equity.
  - IMF stress tests sometimes assume market-valuation losses on sovereign bonds (including held-to-maturity) depending on sovereign debt sustainability assessment.

### Solvency factors in liquidity testing and liquidity dry-out scenarios
- Solvency factors in liquidity tests: PD estimates affect haircuts and revaluation of counterbalancing capacity; NPLs reduce interest-income inflows; solvency deterioration implies higher collateral requirements and reduced secured funding.
- Liquidity dry-out scenarios: ad hoc variants include asymmetric reduction of funding at longer horizons, shutdowns of funding for a quarter, or deprivation of significant wholesale funding.

### Banks’ reactions, macro-financial feedbacks, and modeling advances
- Typical calibration: impact of funding-cost increases on lending rates (reference rate + client spread) affects loan demand and GDP; many tests assume aggregate bank lending supply is maintained to avoid capital-ratio improvements via deleveraging.
- Limitations: assuming no change in credit supply is unrealistic; crises show procyclical deleveraging and funding constraints.
- Emerging modeling efforts to endogenize bank responses and second-round effects include agent-based models, semi-structural macroeconomic models embedding bank-level frameworks, and macro-financial ABMs.

### Using stress-test results for policy and macroprudential advice (examples)
- Policy tools informed by stress tests:
  - Additional capital cushions and buffers.
  - Borrower-based limits (LTV, DSTI/DTI).
  - Regulatory floors for internal-model risk-weights.
- Examples from FSAPs:
  - 2019 Switzerland FSAP recommended borrower-based measures for residential property lending.
  - 2017 Netherlands and 2016 Ireland FSAPs used household microdata to inform macroprudential LTV limits.
  - 2016 Finland FSAP recommended regulatory floors for internal models.
  - 2016 Sweden FSAP recommended adding a cap on DTI.
  - 2018 Romania FSAP proposed a systemic risk buffer and calibrated a DSTI limit; PDs found highly sensitive around DSTI ratios of 50 percent.

### Climate risk as an emerging frontier
- Two main channels: physical risks (property damage) and transition risks (policy/technology shifts affecting asset valuations).
- Insured loss evidence:
  - Annual global weather-related insured losses increased from about US$10 billion in the 1980s to about US$50 billion in the last decade and US$138 billion in 2017.
- Transition-risk example: top US coal producers’ market valuation fell by 95 percent between 2010 and 2017.
- Challenges: transition risks are large, nonlinear, irreversible, and partly unforeseeable; comprehensive climate stress testing requires improved disclosures and taxonomies.
- IMF plans: broaden physical-risk stress tests beyond nonlife insurance; pilot and expand transition-risk assessments; engage with central banks, supervisors, and the Central Banks and Supervisors Network for Greening the Financial System (observer).

### Annex: Perimeter of stress tests — coverage and data challenges
- Nonbank coverage:
  - Insurance companies stressed in about 15 percent of IMF stress tests (examples: Sweden, Japan, Belgium).
  - Asset management sector included in liquidity stress tests when large source of bank funding (examples: United States, Luxembourg, Sweden, Brazil).
  - Nonfinancial corporates and households: tests of corporates (debt at risk) and estimates of DSTI for households when data available.
    - Debt at risk: percent of total corporate debt of firms whose interest coverage ratio (ICR) is less than 1.5.
    - ICR defined as earnings before interest and depreciation divided by total interest payments.
    - ICR < 1 implies firm is not generating sufficient revenues to pay interest without adjustments.
- Data challenges:
  - Data nonexistence: funding and liquidity data historically absent; proxies used in absence of pricing time series.
  - Underdeveloped markets: lack of term structures or market-based measures in developing countries; dollarized economies may lack domestic securities term structures in US dollars.
  - Insufficient time series: short PD or NPL histories in many developing countries; regional or comparable-country approaches used.
  - Confidentiality: authorities provide data on a voluntary basis; Article VIII does not obligate data provision.
  - Heterogeneous sources: public information combined across sources; duration approaches and haircuts used when granular detail absent.
  - Technical notes on limitations are publicly available via the IMF website.

### Platform, tool design, and solvency measurement practices
- Core platform: Excel-based framework for transparency; organizes parameter estimates and supports comparison with authorities’ top-down and banks’ bottom-up results.
- Plans to translate Excel into a programming language with an Excel interface as complexity grows.
- Solvency measurement:
  - Credit risk: principal driver; follows prudential practice treating interest on NPLs as non-accruals.
  - Basel frameworks used:
    - Internal Risk-Based exposures: expected losses = PD × LGD × EAD; capital requirement at 99th percentile minus expected losses under ASFM calibration.
    - Standardized approach: provisions for NPLs (usually 90 days past-due) and risk-weights by exposure type/rating.
  - Granularity examples: Euro FSAP estimated clients’ default probabilities by country and asset class across 37 jurisdictions with 7 portfolio classes.
  - Econometric approaches: Newey-West HAC-robust standard errors, quantile regression, Bayesian Model Averaging (BMA); criteria for final projections ordered by out-of-sample performance, in-sample performance, goodness of fit, sign of coefficients, and expert judgment benchmarked to 2008 and 2012 crises.
  - LGD and EAD modeling: collateral values, legal/judiciary features, vintage LTV distributions, forced-sales discounts; EADs include credit lines and guarantees with percent triggers per year and assumption of no new credit lines during risk horizon.
  - Interest income decomposition: quantity effect and interest rate effect; two measures of interest-rate risk in banking book (earnings-based across 10 repricing buckets and valuation/duration approach).
  - Market risk: interest rate, credit spread, FX, equity, commodity risks; full revaluation when detailed portfolios available; reliance on banks’ estimates for large trading portfolios.

*Source: stimfea - 1. Introduction*

### 1. Introduction ........................................................................................................

### 1. Introduction

### Purpose and role of IMF stress tests
- IMF staff use macroprudential stress tests to assess systemic risk as part of the IMF’s mandate to monitor global financial stability.
- Stress tests help assess the resilience of financial systems in IMF member countries and underpin policy advice to preserve or restore financial stability.
- This assessment and advice are mainly provided through the Financial Sector Assessment Program (FSAP).
- IMF staff also provide technical assistance in stress testing to a large number of its member countries.

### Definition and focus of IMF macroprudential stress tests
- An IMF macroprudential stress test is a methodology to assess financial vulnerabilities that can trigger systemic risk and the need of systemwide mitigating measures.
- Distinction between microprudential and macroprudential stress tests:
  - Microprudential stress test:
    - A forward-looking supervisory tool that assesses the adequacy of individual banks’ capital (or liquidity) conditional on their portfolio risks.
    - Key to the supervisory purpose is the ability of the bank “to pass or not to pass the test” and subsequent supervisory measures if the bank does not pass.
  - Macroprudential stress test:
    - Focuses on financial vulnerabilities that can trigger systemic risk.
    - Financial vulnerabilities include high leverage, mispricing, concentration of risk, liquidity mismanagement, and others that amplify adverse shocks.
    - While assessing individual institutions is part of the work, the final objective is to assess whether identified vulnerabilities can compromise financial stability for the whole economy.
    - Results by institution are not published; they are discussed with authorities and used to support the financial stability assessment and recommendations in FSAP reports.

### Policy implications and possible recommendations
- Recommendations based on IMF stress tests can include:
  - Need to boost capital cushions.
  - Adoption of other macroprudential measures, such as measures targeting credit demand (debt to income and loan to value ratios).
  - Implementation of surcharges (countercyclical or risk specific surcharges).
  - Application of liquidity requirements.

### Concept of systemic risk and broader goals
- IMF, FSB, and BIS (2009) defines systemic risk at the onset of the global financial crisis as the risk of disruptions to the provision of financial services caused by an impairment of all or parts of the financial system, that had the potential to cause serious negative consequences for the real economy.
- Historically, IMF vulnerability analysis via stress testing focused on vulnerabilities that could lead to financial crisis.
- More recently, IMF work also identifies financial vulnerabilities that may not lead to a financial crisis but could create downside risks to growth through the operation of the financial system.
- Both systemic financial disruptions and milder reversals of financial vulnerabilities could create downside risks to growth (“growth at risk”) (IMF 2017a; see also Adrian, Boyarchenko, and Giannone 2019).
- Current goal of IMF financial surveillance and stress testing:
  - Assess risk of systemic failures of significant financial institutions.
  - Identify financial vulnerabilities that can create risks for sustainable economic growth, even if they may not lead to a financial crisis.

### Coverage: institutions and scope
- IMF stress tests primarily apply to depository intermediaries, particularly systemically important banks (whether globally or domestically systemic).
- Rationale: Banks are prone to behavior that can lead to systemic risk via maturity and liquidity transformation or credit risk channels.
- In many cases, following identification of specific systemic risk sources, IMF staff have included stress tests of nonbanks (insurance and asset management companies and nonfinancial firms) and estimates of stress for households.
- Note: Stress tests of nonbanks rely on methodologies and toolboxes different from those used for banks; their description is not included in this paper.

### Operational constraints and approach
- IMF stress testing is adapted to the diversity of its member countries:
  - IMF conducts stress tests as part of financial stability assessments in 12–14 different financial systems each year.
  - IMF helps develop country authorities’ capacity in stress testing in about 18 different financial systems each year through Financial Sector Stability Reviews and technical assistance missions.
- The diversity of membership imposes the need to adapt to different threats to financial stability, uneven data availability, and diverse complexity of financial systems.
- IMF stress testing typically combines:
  - Top-down stress tests (conducted by IMF staff, sometimes in collaboration with national supervisors).
  - Bottom-up stress tests (produced by financial institutions).
  - Both approaches are based on agreed-on methodology and scenarios with IMF staff.

### Structure of the paper
- The paper provides:
  - A brief history of the evolution of stress tests at the IMF.
  - The key steps of an IMF staff stress test.
  - A discussion of how IMF staff use stress test results for policy advice.
  - Identification of remaining challenges to make stress tests more useful for monitoring financial stability and an overview of IMF staff work program in that direction.

*Source: stimfea - 1. Introduction*

### Introduction

### Introduction

### Origins and evolution of risk management and stress testing
- Risk management traces to advances in option pricing in the 1970s and volatile financial events in the 1980s and 1990s, including the 1987 stock market crash, the savings and loans crisis in the US, and financial crises in major emerging market economies.
- JPMorgan’s portfolio Value-at-Risk frameworks: RiskMetrics for market risk in 1994 and CreditMetrics for credit risk in 1996 became field standards; the portfolio VaR measure was subsequently adopted in the market risk amendment of 1996 and later in Basel II in 2006.
- Stress testing emerged as an articulated risk management tool after the 1997–98 Asian crisis; the FSAP (Financial Sector Assessment Program) was inaugurated in 1999 by the IMF and World Bank.
- Early IMF staff stress tests were heterogeneous, often spreadsheet-based, with a one-year credit risk horizon and instantaneous shocks for market risks; scenario design often used worst historical developments.

### IMF methodological developments and tools
- Early portfolio and distributional approaches used by IMF teams:
  - 1999 South African FSAP: Monte Carlo simulation for multivariate projection of macro-financial variables and correlated market and credit risks, producing distributions of bank losses.
  - Use of Credit Risk Plus (developed 1997) in multiple FSAP stress tests.
  - Starting with 2006 Denmark FSAP: portfolio approach based on entropy risk measures (Segoviano 2006).
- Adoption of Basel II and the Basel formula for regulatory capital inputs (PDs, LGDs, EaDs) made stress testing methodology more uniform (Schmieder, Hasan, and Puhr 2011).
- Post-2008 GFC and European crisis: shift from microprudential, bank-by-bank analysis toward macroprudential and systemic risk-focused stress testing; expanded coverage to sovereign, funding, market liquidity risks, contagion models, nonbanks, and amplification mechanisms (interaction of solvency/liquidity and real economy feedback).

### FSAP coverage and mandatory assessments
- Following the crises, financial stability assessments under FSAP became mandatory for jurisdictions with systemically important financial sectors:
  - 2010 decision: 25 jurisdictions were deemed systemically important.
  - 2013 review: number increased to 29.

### Key steps in the IMF staff stress testing approach
- Initial assessment of vulnerabilities (Chapter 4) using financial indicators and Growth-at-Risk (GaR); defines perimeter and data issues.
- Scenario design (Chapter 5): choice of shocks and calibration of macro-financial variables, guided by the FSAP Risk Assessment Matrix (RAM) and the Global RAM; GaR used to calibrate scenario severity consistently across countries.
- Stress tests of solvency, liquidity, and contagion (Chapter 6): satellite models translate adverse scenario variables into balance sheet items, profits and losses, and stressed liquidity inflows/outflows; contagion models assess network propagation.
- Risk amplification mechanisms (Chapter 7): integrate modules to assess interactions among risk types and amplification channels; much of this module remains work in progress.

### Assessment of vulnerabilities and role of GaR
- Systemic vulnerabilities: imbalances and conditions that magnify shocks (leverage, maturity transformation, interconnectedness, complexity) and can lead to feedback loops, asset fire-sales, and reduced credit supply.
- Forward-looking tools:
  - GaR and stress testing both map vulnerabilities; GaR measures downside risk to GDP growth and helps identify vulnerabilities for granular stress tests.
  - The term structure of GaR provides information on horizon-dependent effects; loose financial conditions can mitigate short-term downside risks but raise medium-term risks (intertemporal trade-off).
- Categorization of vulnerabilities:
  - Cyclical vulnerabilities: position in the financial cycle; leverage is a key indicator (credit growth, credit-to-GDP gap, loan-to-deposit ratio, volatile funding).
  - Price-of-risk indicators and GaR inform timing and severity.
  - Structural vulnerabilities: examples include dependence on international capital inflows, high dollarization, high interconnectedness, concentration of funding or asset exposures, and high NPL shares.
  - Institutional vulnerabilities: e.g., weak AML-CFT frameworks that can trigger blacklisting, loss of correspondent services, or rating downgrades.

### Scenario design, severity, and simulation tools
- IMF stress tests use at least two scenarios: a baseline using WEO projections and at least one adverse scenario; risk horizon typically spans three to five years.
- Scenario requirements: forward-looking, severe, consistent, robust; severity often anchored by fall in real GDP below baseline or cumulative fall in real GDP growth.
- Historical rule of thumb: shocks to GDP growth representing at least two historical standard deviations from the mean over the first two to three years; currently GaR is used as a minimum severity benchmark, conditional on cyclical phase.
- Scenario design phases:
  - Selection of shocks aligned with identified vulnerabilities (country-specific or global, drawn from RAM).
  - Assessment of sufficient severity (GaR used for consistency across countries).
  - Simulation of complete macro-financial variable paths consistent with chosen severity.
- Simulation models:
  - Global Macrofinancial Model (GFM): structural macro econometric DSGE, quarterly frequency, covering 40 economies (Vitek 2018); includes bank and capital-market intermediation and international spillovers—preferred when macro-financial linkages and spillovers are important.
  - Flexible System of Global Models (FSGM): semi-structural macro-econometric, annual frequency, covering 24 economies (Andrle and others 2015); preferred when structural shifts are important.
  - For developing economies, staff use structural VARs or authorities’ macro models.
- Limitations and robustness:
  - GFM and FSGM are linear for computational feasibility; nonlinearities are sometimes captured through scenario calibration (discrete asset price adjustments, asymmetric default rate adjustments, effective lower bound restrictions).
  - Robustness may require multiple adverse scenarios or sensitivity tests, including layer-of-shocks approaches and failure tests of large exposures.
  - The Macro-Financial System Simulator (MASS) enables simulation of full distributions of institutions’ capital positions, captures macro-financial feedback and state-dependent nonlinear dynamics, and embeds a worst-case scenario search methodology (Gross, Leika, and Valderrama 2018).

### Stress testing banks: basic framework and solvency testing
- Basic framework modules: solvency, liquidity, contagion; advanced framework integrates all risks in a single exercise.
- Solvency stress tests assess resilience by comparing actual capital under stress (initial capital plus net losses under adverse scenario) to capital requirements under stress (e.g., regulatory capital calculations that reflect portfolio size and stressed credit risk parameters).
- Income statement forecasting under stress includes net interest income (interest rate and funding shock effects), provisions, trading losses, fee income, operational expenses, and taxes; satellite models map macro-financial changes to these components to project income statements, balance sheets, and capital ratios over the risk horizon.
- Hurdle/passing rates are used diagnostically and are based on the country’s regulatory approach:
  - For Basel III jurisdictions, hurdle rates include minimum capital requirement (Pillar 1) and supervisory review (Pillar II); capital conservation buffers, institution-specific countercyclical capital buffers, buffers for systemically important banks, and systemic risk buffers are considered (countercyclical buffer may be excluded as it can be used to absorb cyclical losses).
  - Leverage ratios increasingly used as supplementary hurdle rates for global banks.
  - Asset maintenance ratio used on occasion for systemically important branches (amount of local assets available to pay local deposits).
- Presentation of results:
  - IMF framework produces granular stress test outputs for each bank (income statements, balance sheets, capital ratios) but public releases present aggregated vulnerabilities and policy recommendations while preserving confidentiality.

*Source: stimfea - Introduction (IMF staff).*

### 2. Leverage Ratios

### 2. Leverage Ratios

### Presentation of Results of IMF Solvency Stress Tests
- Figure 5: Presentation of Results of IMF Solvency Stress Tests (Country A Bank 1: Graphs)

### Total Capital Adequacy Ratio (Percent)
- Time labels shown: Dec. 2014; Dec. 15; Dec. 16; Dec. 17; Dec. 18; Dec. 19; Dec. 20
- Vertical axis markers shown: 0; 1; 2; 3; 4; 5; 6; 7; 8; 9; 10

### Capital Needs (In currency and unit as chosen)
- Horizontal time labels shown: Dec. 2014; Dec. 15; Dec. 16; Dec. 17; Dec. 18; Dec. 19; Dec. 20
- Additional horizontal time labels shown: Jan. 2014; Jan. 15; Jan. 16; Jan. 17; Jan. 18; Jan. 19; Jan. 20
- Vertical axis markers shown: 0; 100; 200; 300; 400; 500; 600; 700; 800; 900
- Secondary vertical axis markers shown: –1,500; –1,000; –500; 0; 500; 1,000; 1,500

### Net Profit Components
- Vertical axis markers shown: 50; 52; 54; 56; 58; 60; 62; 64; 66; 68
- Secondary vertical axis markers shown: 0.0; 0.5; 1.0; 1.5; 2.0; 2.5

### Contribution to Change of Capitalization Ratio (Percent)
- Section title presented: Contribution to Change of Capitalization Ratio (Percent)

*Source: stimfea - 2. Leverage Ratios (PDF chapter/section)*

### 6. Probability of Default and Loss Given Default

### 6. Probability of Default and Loss Given Default

### Liquidity stress testing: objectives and design
- Purpose: assess capacity of individual banks and the banking system to withstand extreme but plausible funding shocks (funding-liquidity) and/or significant declines in the value of banks’ assets (market-liquidity).
- Two complementary approaches:
  - Cash-flow stress test (IMF staff): customized parameters, includes all unencumbered marketable securities, simulated behavior of inflows and outflows over multiple time buckets, explicit exchange-rate evolution assumptions.
  - Liquidity Coverage Ratio (LCR): ensures stock of high-quality liquid assets (HQLA) to meet liquidity needs in a 30-day horizon; parameters are internationally harmonized and predetermined.
- Rationale for cash-flow test vs LCR:
  - Historical experience shows illiquidity can last more than 30 days and cliff effects appear at end of 30 days.
  - Cash-flow test uses customized run-off/roll-over rates and haircuts that reflect local funding markets and treats all marketable assets as potential funding sources (with haircuts).

### Data, time buckets, and behavioral assumptions
- Data requirements: more granular and higher frequency than solvency stress tests; consistent with Basel liquidity monitoring tools for contractual maturity mismatches.
- Time buckets explicitly listed:
  - next 24 hours
  - 2 to 7 days
  - up to 30 days
  - 31–60 days
  - 61–90 days
  - 91–120 days
  - 121–150 days
  - 151–180 days
  - 181 days–1 year
  - 1–3 years
  - beyond 3 years
- Inflows/outflows: contractual items and behavioral assumptions (for example, demand deposits, callable bonds), plus contingent flows dependent on price changes or credit-rating downgrades.
- Calibration of adverse-scenario parameters (run-off rates, rollover rates, haircuts) uses combination of solvency-stress-test outputs, country characteristics, and literature; multiple scenarios with varying severity levels are recommended.

### Failure criteria and use of central bank facilities
- A bank fails the test when only emergency liquidity assistance (ELA) from the central bank would allow it to continue fulfilling obligations.
- Before ELA, banks can use counterbalancing capacity to obtain liquidity in secondary markets or standard central bank facilities; failure implies depletion of cash items and insufficient eligible collateral for standard facilities.

### Contagion analysis: scope and methods
- IMF teams assess contagion risks at three levels:
  - interbank
  - cross-sectoral (among different types of financial intermediaries)
  - cross-border
- Methodologies:
  - Exposure-based domino-effect analyses (Espinosa-Vega and Solé (2010) approach often used) capturing credit and funding shocks.
  - Market-based indicators and asset-price codependence measures to capture indirect linkages and common exposures.
  - Combined exposure and market-based approaches where data permit.
- Cross-border analysis:
  - Uses exposure frameworks and BIS locational/consolidated data to propagate shocks through networks; a banking system “fails” if losses exceed total Tier 1 or regulatory capital, triggering domino effects.
  - Complemented by qualitative assessment of cross-border relations (funding flows, liquidity rules, ringfencing, resolution modalities).

### Risk amplification mechanisms captured in FSAP stress tests
- Key amplification channels included in FSAPs:
  - Interconnectedness (interbank, cross-sectoral, cross-border) — domino effects via credit and funding channels.
  - Solvency–liquidity interaction — funding-cost/solvency loop and sovereign-bank nexus.
  - Market liquidity channel — asset fire sales reducing valuations and CBC (counterbalancing capacity).
  - Real–financial feedbacks — pass-through of funding costs to lending rates, portfolio reallocation, deleveraging effects on GDP.
- Implementation notes (Table 2 summary points preserved):
  - Bank-solvency nexus: implemented in most FSAPs.
  - Funding channel: implemented in the Euro Area FSAP and in most FSAPs, granularity dependent on data availability.
  - Market liquidity channel: implemented in FSAPs when data available.
  - PD impact: estimated PDs affect asset values/haircuts and implemented in most FSAPs.
  - NPL channel: NPLs stop making interest payments, affecting liquidity inflows; implemented in most FSAPs.
  - Liquidity dry-out channel: several ad hoc versions implemented in most FSAPs based on local funding structures.
  - Counterparty credit risk and derivatives inflows: implemented in specific FSAPs (for example, Switzerland FSAP).

### Funding cost and solvency: empirical links and implementation
- Empirical findings cited:
  - A 100 basis point increase in regulatory capital ratios is associated with a decrease of bank funding costs of about 105 basis points (Schmitz, Sigmund, and Valderrama (2017) result).
  - A 100 basis point increase of funding costs reduces CAR by 32 basis points on average (Schmitz, Sigmund, and Valderrama (2017) result).
  - Nonlinearities: interbank funding cost is more sensitive to solvency during periods of stress and at lower solvency levels.
- IMF implementation in recent FSAPs (Japan, New Zealand, United Kingdom, Poland, euro area, Switzerland):
  - Integrated solvency–funding feedback via sequential iteration: solvency test outputs update funding-cost projections year-by-year until convergence.
  - Funding costs projected at bank, instrument, and contract level; example for Japan: interest expenses to interest-earning liabilities ratio, bank-specific capital sensitivity term, and Markov regime-switching component for base rates and liquidity premia; funding costs in foreign currency modeled with Markov regime-switching for USD/JPY swap market liquidity premium.

### Equity valuation, sovereign-bank nexus, and market valuation choices
- Equity-market effects: stressed equity valuations can trigger rating downgrades and higher funding costs; Euro Area FSAP used a Merton-based/Bloomberg DRSK approach to quantify amplification from equity valuation to funding costs.
- Sovereign-bank nexus:
  - Regulatory frameworks often give low/zero risk-weights or low provisions for sovereign bonds held to maturity; investors focus on market value of bank equity.
  - IMF stress tests sometimes assume market-valuation losses on sovereign bonds (including those held to maturity) to reflect investor concerns and to assess capital ratios under stress; decision to include market valuation losses depends on IMF staff assessment of sovereign debt sustainability.

### Solvency factors in liquidity stress tests and liquidity dry-out
- Solvency factors incorporated into liquidity tests:
  - PD estimates affect haircuts and revaluation of counterbalancing capacity.
  - NPLs reduce interest income inflows.
  - Solvency deterioration implies higher collateral requirements and reduced secured funding.
- Liquidity dry-out:
  - Insolvency concerns can cause inability to raise funding at any cost (liquidity dry-out), exemplified by runs in repo markets during 2007–08.
  - IMF uses multiple ad hoc liquidity-dry-out scenarios, e.g., asymmetric reduction of funding at longer horizons, shutdowns of funding for a quarter, or deprivation of significant wholesale funding.

### Banks’ reactions and macro-financial feedbacks
- Typical IMF stress-test practice: calibrate impact of funding-cost increases on lending rates (reference rate + client spread), affecting loan demand and GDP; most tests assume aggregate bank lending supply is maintained in adverse scenarios to avoid capital-ratio improvements via deleveraging and to assess banks’ capacity to preserve economic growth.
- Limitations: assuming no change to credit supply is not realistic; banking crises exhibit procyclical deleveraging and market funding constraints that can cause credit freezes and asset fire sales.
- Emerging modeling efforts to endogenize bank responses and second-round effects:
  - Valderrama (forthcoming): agent-based dynamic portfolio optimization with endogenous credit provision.
  - Krznar and Matheson (2017): semi-structural macroeconomic model embedding bank-level stress-testing framework to capture deleveraging feedbacks.
  - Gross and others (2018): macro-financial Agent-Based Model (ABM) with housing market and detailed bank funding-cost dynamics to evaluate macroprudential policies.
  - Catalán and Hoffmaister (forthcoming): disaggregated banking sector embedded in macro SVAR to quantify dynamic feedbacks and banks’ heterogeneous contributions to systemic risk.

### Using stress-test results for policy and macroprudential advice
- Stress tests support microprudential and macroprudential recommendations, including:
  - Additional capital cushions and buffers.
  - Borrower-based limits (for example, loan-to-value (LTV) and debt-service-to-income (DSTI) or debt-to-income (DTI) caps).
  - Regulatory floors for internal-model risk-weights.
- Examples:
  - 2019 Switzerland FSAP recommended borrower-based measures to strengthen resilience in residential property lending based on mortgage-loss exposures from stress tests.
  - 2017 Netherlands and 2016 Ireland FSAPs used household microdata to inform macroprudential LTV limits.
  - 2016 Finland FSAP found weaknesses in banks’ risk parameter estimates and recommended regulatory floors for internal models.
  - 2016 Sweden FSAP recommended adding a cap on debt-to-income (DTI) ratio.
  - Austria (forthcoming) used semi-structural mortgage-loss projections to analyze LTV and DSTI policies.
  - 2018 Romania FSAP proposed a systemic risk buffer (SRB) calibrated to absorb interest-rate-related sovereign exposures identified in stress tests and calibrated a DSTI limit using loan-level PD modeling; PDs found highly sensitive around DSTI ratios of 50 percent.

### Climate risk: emerging frontier for stress testing
- Two main climate-risk channels for financial sector:
  - Physical risks from property damage.
  - Transition risks from policy/technology shifts change asset valuations.
- Observed insured losses:
  - annual global weather-related insured losses increased from about US$10 billion in the 1980s to about US$50 billion in the last decade and US$138 billion in 2017.
- Transition risks: examples include sharp valuation drops in “stranded assets” (e.g., top US coal producers’ market valuation fell by 95 percent between 2010 and 2017).
- Data and modeling challenges:
  - Transition risks are large, nonlinear, irreversible, and partly unforeseeable.
  - Comprehensive climate stress testing requires improved, comparable disclosures and taxonomies; IMF supports adoption of Task Force on Climate related Financial Disclosures recommendations.
- IMF plans:
  - Broaden physical-risk stress tests to capture macro-financial effects beyond nonlife insurance.
  - Pilot and expand transition-risk assessments (FSAP for an oil-producing advanced economy underway).
  - Engage with central banks, supervisors, and the Central Banks and Supervisors Network for Greening the Financial System (observer).

*Source: IMF staff.*

### Annex 1. Perimeter of Stress Tests

### Annex 1. Perimeter of Stress Tests

### Coverage of nonbanks
- Insurance companies:
  - Stress tests of insurance companies have been performed in about 15 percent of IMF stress tests; recent examples include Sweden (IMF 2016c, 2017b), Japan (IMF 2017d), and Belgium (IMF 2013b).
  - Rationale for inclusion: insurers may provide significant long-term funding to banks, the public sector, and the real economy; insurers are broadening investments and venturing into direct lending to corporates and households; the insurance sector can be highly interconnected with the banking sector via funding channels, (cross-)shareholdings, and joint distribution channels.
  - Inclusion decision weighs these aspects to decide whether to stress-test insurers.
- Asset management sector:
  - Included usually in liquidity stress tests when they represent a large source of funding for the banking sector (examples: United States [IMF 2015a], Luxembourg [IMF 2017g], Sweden [IMF 2016c, 2017b], Brazil [IMF 2018d] FSAPs).
  - Bank-sponsored off-balance sheet wealth management products were included in solvency stress tests in the China FSAP (IMF 2017h, Box 2, page 25) given multiple interlinkages with the banking sector.
- Nonfinancial corporates and households:
  - IMF stress tests comprise tests of nonfinancial corporations and estimates of debt-service to income (DSTI) ratios for households (Chow 2015).
  - Complete stress tests of nonfinancial corporates assess emerging market firms with increasing borrowings in foreign currency; tests are based on the share of corporate debt at risk, vulnerable to shocks to corporate earnings, interest rates, or exchange rates.
  - Footnote detail on "debt at risk":
    - The debt at risk for each country is computed as the percent of total debt from corporates whose interest coverage ratio (ICR) is less than 1.5.
    - The ICR is defined as the ratio of earnings before interest and depreciation to total interest payments.
    - An ICR of less than 1 implies that the firm is not generating sufficient revenues to pay interest on its debt without adjustments.
    - During the Asian Financial Crisis, countries whose corporate sector with median ICR below 1.5 were more vulnerable.
  - DSTI:
    - When household borrowings represent a vulnerability and data are available, staff also estimates DSTI ratios to assess the impact of rising interest rates and to support policy recommendation for maximum stressed DSTI limit for households.

### Data challenges in IMF stress tests
- Nature of solvency stress tests:
  - Primarily balance-sheet based and depend on very granular prudential data that in many cases are not available to IMF staff unless provided by the authorities.
- Types of data challenges:
  - Data does not exist:
    - Example: funding and liquidity data historically absent; ECB has only recently started collecting monthly price data on funding instruments by instrument and by bank.
    - In absence of pricing time series, proxies are used (for example, credit default swap spreads in advanced economies; spread of government’s issued securities).
  - Markets not developed:
    - Developing countries and emerging market economies may lack term structure of riskless and risky securities or publicly available market-based measures of risk; dollarized economies may lack term structures of domestic securities in US dollars.
  - Data exist but are not sufficient:
    - Time series of actual PDs or NPLs may be too short in many developing countries; teams may estimate asset quality using information from countries with similar risk factors or regional models (example: recent approach used in Namibia).
  - Authorities unable or unwilling to share confidential data:
    - Data are provided to IMF staff on a voluntary basis; Article VIII of the IMF’s Articles of Agreement does not include an obligation to provide related data.
  - Data obtained from different sources:
    - Publicly available information is combined from different sources (for example, estimating bank clients’ PDs by asset class and geography from asset prices such as stock indexes and sovereign spreads).
    - Repricing of bond portfolios when complete information is unavailable: duration approach applied to partly aggregated bond classes.
    - LGDs for mortgages under stress approximated by scenario’s decline in real estate prices when granular information is lacking.
    - All limitations are explained in technical notes publicly available via the IMF website, imf.org.

### Platform and tool design
- Core platform: Excel-based framework to provide transparent account of methodology to authorities.
  - Framework organizes estimates of parameters (sensitivity of bank asset quality or funding costs to macro-financial and bank-specific factors) which are calculated outside the framework.
  - Focus on comprehensive analysis of banking system and individual banks based on supervisory reporting to enable comparisons with authorities’ top down (TD) and banks’ bottom up (BU) results.
  - Granularity allows identification of sources of risk (credit, market, sovereign, funding, etc.) and bank-by-bank customization of feedback loops (market, funding liquidity, funding costs, credit growth, deleveraging, balance sheet composition).
  - As complexity grows, plans to translate the Excel sheet into a programming language with an Excel interface to facilitate user work.
- Example data source mention:
  - Moody’s Expected Default Frequency Data cited as an example for estimating PDs from asset prices.

### Solvency stress testing: measurement of risks and impacts
- Credit risk (principal driver of profits and capital requirements):
  - Stress tests follow prudential practice classifying interest payments on NPLs as non-accruals, affecting both profits (through provisions) and interest income.
  - Basel framework basis:
    - For Internal Risk-Based exposures: expected losses = PD × LGD × EAD; provisions projection depends on stressed PDs, stressed LGDs, and stressed EADs.
    - Minimum capital equivalent to losses at the 99th percentile of loss distribution calibrated by the Asymptotic Single Risk Factor (ASFM) chosen by the Basel Committee minus expected losses.
    - For Basel standardized approach: expected losses replaced by provisions for non-performing loans (usually defined as 90 days past-due); capital requirements based on risk weights depending on exposure type and rating.
    - FSAP teams project NPLs and may adjust risk-weighted assets assuming downgrading under the adverse scenario.
  - Granularity example:
    - Euro FSAP (IMF 2018c) estimated bank clients’ default probabilities by country and asset class across 37 jurisdictions (9 core euro area countries, 11 other EU countries, and 17 outside EU countries).
    - Asset classes comprised 7 portfolios (government, corporate, SME, specialized lending, retail, secured by real estate, other); valuation impact on sovereign exposures computed for 45 sovereign issuers.
    - Integration of market and credit risks via "satellite models" linking changes in interest rates or exchange rates to PDs, LGDs, and EADs.
  - Econometric and modelling approaches used to estimate PDs and address tail risk and model uncertainty:
    - Newey-West HAC-robust standard errors for heteroskedasticity/autocorrelation once regressors are stationary and ergodic.
    - Quantile regression to explore conditional drivers in higher tail of credit risk distribution; distribution divided into quartiles and deciles to explore cliff-effects.
    - Bayesian Model Averaging (BMA) to address uncertainty of drivers using a normal diffuse prior distribution; BMA advocated to take explicit control of model uncertainty and produce wide error bounds around scenario-conditional capital positions.
    - Combination of criteria to inform final projections in the following order: out-of-sample forecast performance; in-sample forecast performance for the overall period; goodness of fit; sign of coefficients according to theory; and expert judgment benchmarked against the 2008 financial crisis and the 2012 European sovereign debt crisis.
  - Modelling LGD and EAD under stress when data are available:
    - LGD for collateral loans related to collateral value; stress scenarios (for example, real estate prices) can be used to apply haircuts.
    - Legal and judiciary system features considered to estimate expected recovery fractions and timing; World Bank Doing Business Indicators sometimes used as a starting point.
    - Example: UK IMF stress tests (IMF 2016f) estimated mortgage LGDs using four parameters: distribution of original LTV ratios by vintage; outstanding value of each loan vintage net of amortization; house price fall assumed under the scenario; forced sales discount on the property’s market price under foreclosure.
    - EADs include credit lines and guarantees; framework allows choosing percent triggers per year of the risk horizon; assumes no new credit lines and guarantees are granted during the risk horizon.
    - Counterparty credit risk from derivatives estimated with the aid of discussions with banks.
- Net interest income:
  - Changes decomposed into quantity effect (changes in quantities assuming no interest rate changes; uses historical effective interest rate for each balance sheet item) and interest rate effect (losses/gains from changes in interest rates affecting exposures with different repricing times).
  - Interest rate effect includes banks’ sensitivity to higher funding costs.
  - Two measures of interest rate risk in the banking book estimated by significant currency:
    - Earnings-based measure: interest-sensitive assets and liabilities sorted into 10 time-buckets by repricing dates, with emphasis on repricing within the first year.
      - Given banks’ role in liquidity transformation, more assets tend to reprice early in the risk horizon than liabilities; positive shocks to interest rates can affect banks unless exposures are hedged.
      - Hedging instruments are included but sensitivity stress tests may assess losses if hedging markets fail.
    - Valuation approach: measures equity losses due to valuation effects in the banking book, estimated using a duration approach.
- Market risk and trading losses:
  - Framework considers interest rate risk and credit spread risk of corporate and sovereign instruments held for trading (HFT) or available for sale (AFS); foreign exchange risk in banking and trading books; equity and commodity risks.
  - Losses on HFT and AFS securities due to interest rate and credit spread risks assessed through full revaluation when detailed portfolio descriptions and prices are available.
  - Foreign exchange, equity, and commodity risks assessed based on potential losses of open positions when scenario shocks materialize.
  - For large trading portfolios, staff relies on banks’ estimates and engages discussions to form an opinion on nonlinear risks and models used by banks for market risk calibration.
  - Counterparty risk, credit valuation adjustment (CVA) losses, and securitization risks are discussed with banks and rely on a mix of staff and banks’ inputs.
  - Real estate price shocks:
    - Adverse scenarios typically feature a shock to real estate prices where household and corporate leverage is high.
    - Stressed real estate prices used to calibrate decline in banks’ collateral (increase in LGD).
    - Securities backed by real estate suffer haircuts estimated as a function of the decline in property prices.
    - PD or NPL models may include real estate prices as a key explanatory variable for forecasting asset quality deterioration in residential or commercial real estate loans.

*stimfea - Annex 1. Perimeter of Stress Tests*

### References

### References

### Stress testing methodologies, models, and theoretical frameworks
- Aymanns, Christoph, Carlos Caceres, Christina Daniel, and Liliana Schumacher. 2016. “Bank Solvency and Funding Cost.” IMF Working Paper 16/64, International Monetary Fund, Washington, DC.
- Barnhill, Theodore M., Panagiotis Papapanagiotou, and Liliana Schumacher. 2002. “Measuring Integrated Market and Credit Risks in Bank Portfolios: An Application to a Set of Hypothetical Banks Operating in South Africa.” Journal of Financial Markets Institutions & Instruments 11 (5).
- Barnhill, Theodore M., and Liliana B. Schumacher. 2011. “Modeling Correlated Systemic Liquidity and Solvency Risks in a Financial Environment with Incomplete Information.” IMF Working Paper 11/263, International Monetary Fund, Washington, DC.
- Brunnermeier, Markus K., Thomas Eisenbach, and Yuliy Sannikov. 2013. “Macroeconomics with Financial Frictions: A Survey.” Advances in Economics and Econometrics. New York: Cambridge University Press.
- Brunnermeier, Markus K., and Yuliy Sannikov. 2014. “A Macroeconomic Model with a Financial Sector.” American Economic Review 104 (2): 379–421.
- Čihák, Martin. 2007. “Introduction to Applied Stress Testing.” IMF Working Paper 07/59, International Monetary Fund, Washington, DC.
- Danielsson, Jon, Paul Embrechts, Charles Goodhart, Con Keating, Felix Muennich, Olivier Renault, and Hyunh Son Shing. 2001. “An Academic Response to Basel II.” FMG Special Papers, Financial Markets Group, London.
- Gray, Dale, and Andreas Jobst. 2013. “Systemic Contingent Claims Analysis.” IMF Working Paper 13/54, International Monetary Fund, Washington, DC.
- Gross, Marco, and Francisco Javier Población Garcia. 2017. “Implications of Model Uncertainty For Bank Stress Testing.” Journal of Financial Services Research 1–28.
- Gross, Marco, Bjorn Hilberg, Sander Van der Hoog, and Dirk Kohlweyer. 2018. “The Eurace 2.0 Model.” International Monetary Fund, Washington, DC.
- Gross, Marco, Mindaugas Leika, and Laura Valderrama. 2018. “Capital at Risk.” Unpublished.
- Han, Fei, and Mindaugas Leika. 2019. “Integrating Solvency and Liquidity Stress Tests: The Use of Markov Regime-Switching Models.” IMF Working Paper 19/250, International Monetary Fund, Washington, DC.
- Segoviano, Miguel. 2006. “Portfolio Credit Risk and Macroeconomic Shocks: Application to Stress Testing Under Data-Restricted Environment.” IMF Working Paper 06/283, International Monetary Fund, Washington, DC.
- Schmieder, Christian, Maher Hasan, and Claus Puhr. 2011. “Next Generation Balance Sheet Stress Testing.” IMF Working Paper 11/83, International Monetary Fund, Washington, DC.
- Valderrama, Laura. Forthcoming. “An Agent-Based Model for Stress Testing.” IMF Working Paper, Washington, DC.
- Vitek, Francis. 2018. “The Global Macrofinancial Model.” IMF Working Paper 18/81, International Monetary Fund, Washington DC.

### Liquidity, funding, and market resilience
- Baranova, Yuliya, Jamie Coen, Pippa Lowe, Joseph Noss, and Laura Silvestri. 2017. “Simulating Stress Across the Financial System: The Resilience of Corporate Bond Markets and the Role of Investment Funds.” Financial Stability Paper 42, Bank of England, London.
- Baranova, Yuliya, Zijun Liu, and Tamarah Shakir. 2017. “Dealer Intermediation, Market Liquidity and the Impact of Regulatory Reform.” Working Paper 665, Bank of England, London.
- Basel Committee on Banking Supervision (BCBS). 2013. “Liquidity Stress Testing: A Survey of Theory, Empirics and Current Industry and Supervisory Practices.” BCBS Working Paper No 24, Basel.
- BCBS. 2015. “Making Supervisory Stress Tests More Macroprudential: Considering Liquidity and Solvency Interactions and Systemic Risk.” BCBS Working Paper 29, Basel.
- BCBS. 2017. Basel III: Finalizing Post-Crisis Reforms. Basel.
- Goldstein, Itay, and Ady Pauzner. 2005. “Demand-Deposit Contracts and the Probability of Bank Runs.” Journal of Finance 60: 1293–327.
- Gorton, Gary, and Andrew Metrick. 2009. “Securitized Banking and the Run on Repo.” Journal of Financial Economics 104: 425–51.
- Puhr, Claus, and Stephan. W. Schmitz. 2013. “A View From The Top – The Interaction Between Solvency And Liquidity Stress.” Journal of Risk Management in Financial Institutions 7 (1).
- Schmitz, Stefan, Michael Sigmund, and Laura Valderrama. 2017. “Bank Solvency and Funding Cost: New Data and New Results.” IMF Working Paper 17/116, International Monetary Fund, Washington, DC.
- IMF. 2011. “How to Address the Systemic Part of Liquidity Risk” Global Financial Stability Report. Washington DC, April.
- IMF. 2015b “Market Liquidity—Resilient or Fleeting?” Global Financial Stability Report. Washington, DC, October.

### Macroprudential policy, counterscyclical tools, and financial stability guidance
- Basel Committee on Banking Supervision (BCBS). 2010. Guidance for National Authorities Operating the Countercyclical Capital Buffer. Basel.
- Drehmann, Mathias, Claudio Borio, and Costas Tsatsaronis. 2011. “Anchoring Countercyclical Capital Buffers: The Role of Credit Aggregates.” Bank for International Settlements Working Paper 355, Basel.
- Drehmann, Mathias, and Kostas Tsatsaronis. 2014. “The Credit-to-GDP Gap and Countercyclical Capital Buffers: Questions and Answers.” BIS Quarterly Review (March): 55–73.
- IMF. 2014. “Guidance on Macroprudential Policy.” Washington, DC.
- IMF. 2016a. “Staff Guidance Note on Macroprudential Policy.” Policy Paper Series, Washington, DC.
- Lipinsky, Fabian, and Mirela Miescu. Forthcoming. “Capital Gaps, Risk Dynamics and the Macroeconomy—A Macro-Financial Framework for Macroprudential Policy Analysis and Stress Testing.” IMF Working Paper, International Monetary Fund, Washington, DC.
- Nier, Erlend, Radu Popa, Maral Shamloo, and Liviu Voinea. “Debt Service and Default: Calibrating Macroprudential Policy Using Micro Data.” IMF Working Paper 19/182, International Monetary Fund, Washington, DC.
- Stein, Jeremy. 2014. “Incorporating Financial Stability Considerations into a Monetary Policy Framework.” Remarks at the International Research Forum on Monetary Policy, Board of Governors of the Federal Reserve System, Washington, DC.

### Systemic risk, interconnectedness, and contagion analysis
- Bricco, Jana, and TengTeng Xu. 2019. “Interconnectedness and Contagion Analysis: A Practical Framework.” IMF Working Paper 19/220, International Monetary Fund, Washington, DC.
- Catalán, Mario, and Alexander Hoffmaister. Forthcoming. “When Banks Punch Back: Macrofinancial Feedback Loops in Stress Tests.” IMF Working Paper, International Monetary Fund, Washington, DC.
- Cont, Rama, Artur Kotlicki, and Laura Valderrama. Forthcoming. “Liquidity at Risk: Joint Stress Testing of Solvency and Liquidity.” IMF Working Paper, International Monetary Fund, Washington, DC.
- Cortes, Fabio, Peter Lindner, Sheheryar Malik, and Miguel Segoviano. 2018. “A Comprehensive Multi-Sector Tool for Analysis of Systemic Risk and Interconnectedness (SyRIN).” IMF Working Paper 18/14, International Monetary Fund, Washington, DC.
- Diebold, Francis X., and Kamil Yilmaz. 2008. “Measuring Financial Asset Return and Volatility Spillovers, With Application to Global Equity Markets.” NBER Working Paper 13811, National Bureau of Economic Research, Cambridge, MA.
- Espinosa-Vega, Marco A., and Juan Solé. 2010. “Cross-Border Financial Surveillance: A Network Perspective.” IMF Working Paper 10/105, International Monetary Fund, Washington, DC.
- Malik, Sheheryar, and TengTeng Xu. 2017. “Interconnectedness of Global Systemically-Important Banks and Insurers.” IMF Working Paper 17/210, International Monetary Fund, Washington, DC.
- IMF, Financial Stability Board, and Bank for International Settlements (IMF, FSB, BIS). 2009. “Guidance to Assess the Systemic Importance of Financial Institutions, Markets and Instruments: Initial Considerations.” Report to the G-20 Finance Ministers and Central Bank Governors, Washington, DC, and Basel.

### Empirical applications, country assessments, and technical notes
- Bank of England. 2015. The Bank of England’s Approach to Stress Testing the UK Banking System. London.
- Baranova, Yuliya, Jamie Coen, Pippa Lowe, Joseph Noss, and Laura Silvestri. 2017. “Simulating Stress Across the Financial System: The Resilience of Corporate Bond Markets and the Role of Investment Funds.” Financial Stability Paper 42, Bank of England, London.
- Broszeit, Timo, Andreas A. Jobst, and Nobuyasu Sugimoto. 2014. “Macroprudential Solvency Stress Testing of the Insurance Sector.” IMF Working Paper 14/133, International Monetary Fund, Washington, DC.
- Chow, Julian. 2015. “Stress Testing Corporate Balance Sheets in Emerging Economies.” IMF Working Paper 15/216, International Monetary Fund, Washington, DC.
- Corbacho, Ana, and Peiris, Shanaka J. 2018. The ASEAN Way: Sustaining Growth and Stability. Washington, DC: International Monetary Fund, 201–06.
- Dees, Stephane, Filippo de Mauro, M. Hashem Pesaran, and Vanessa Smith. 2007. “Exploring the International Linkages of the Euro Area: A Global VAR Analysis.” Journal of Applied Economics 22 (1): 1–38.
- Geithner, Timothy. 2014. Stress Test. Reflections on Financial Crises. New York: Crown Publishers.
- Gilchrist, Simon, and Egon Zakrajšek. 2012. “Credit Spreads and Business Cycle Fluctuations.” American Economic Review 102 (4): 1692–720.
- Gross, Marco, Mindaugas Leika, and Laura Valderrama. 2018. “Capital at Risk.” Unpublished.
- IMF: country and technical notes cited include titles on Singapore, Belgium, Finland, Sweden, Ireland, United Kingdom, Japan, New Zealand, Netherlands, Luxembourg, People’s Republic of China, Peru, Armenia, Euro Area, Brazil, Poland, Romania, Switzerland, and a forthcoming Austria technical note (various years and technical note types as listed).
- Ong, Li Lian, and Ceyla Pazarbasioglu. 2013. “Credibility and Crisis Stress Testing” IMF Working Paper 13/178, International Monetary Fund, Washington, DC.
- Puhr, Claus, and Stephan. W. Schmitz. 2013. “A View From The Top – The Interaction Between Solvency And Liquidity Stress.” Journal of Risk Management in Financial Institutions 7 (1).
- Segoviano, Miguel, and Charles Goodhart. 2009. “Banking Stability Measures.” IMF Working Paper No 09/04, International Monetary Fund, Washington DC.
- US Federal Reserve Board. 2014. “Policy Statement on the Scenario Design Framework for Stress Testing.” Washington DC.
- Xu, TengTeng, Kun Hu, and Udaibir S. Das. 2019. “Bank Profitability and Financial Stability.” IMF Working Paper 19/5, International Monetary Fund, Washington, DC.

*Source: stimfea - References (PDF chapter/section).*

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_Source: https://www.imf.org/-/media/files/publications/dp/2020/english/stimfea.pdf_