## _wp11263

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### Introduction and paper objectives
- Proposes and demonstrates a methodology for modeling correlated systemic solvency and liquidity risks for a banking system.
- Jointly models solvency risk and systemic liquidity risk, emphasizing their interaction.
- Principal contributions:
  - Model financial and economic environment volatility, bank loan sector and region concentration levels, bank loan credit quality, and bank capital levels for 10 banks simultaneously.
  - Estimate the probability of banking system systemic solvency and liquidity risks.
  - Evaluate pre-emptive measures to moderate systemic risks and their impacts.
- Situates approach relative to literature and empirical evidence on the 2008–2009 global crises and supervisory stress-testing approaches that trigger systemic liquidity shocks from solvency concerns.

### Definition of systemic liquidity risk and policy implications
- Definition:
  - Systemic liquidity shock = "an aggregate shortage of liquidity, i.e. a situation in which many institutions face liquidity shortages simultaneously, as opposed to one institution suffering a liquidity shortage."
  - Systemic liquidity risk = "the probability that this situation takes place."
- Liquidity shortage manifestations:
  - funding liquidity risk: inability to roll over funding;
  - market liquidity risk: inability to trade assets at normal bid/ask spreads; or both.
- Diagnostic and policy implications:
  - Similar-looking systemic liquidity shocks may have different origins (aggregate preference shock, infrastructure malfunctioning, solvency concerns) requiring different policy responses.
  - For the U.S. banks application the paper:
    - develops a capital surcharge aimed at minimizing the probability that any given bank would experience a destabilizing run;
    - for crisis management proposes recapitalizing or closing insolvent banks and disclosing enough information to eliminate uncertainties about bank solvency.
  - Liquidity injections effective if they allow banks to deleverage by exchanging liquidity for troubled assets, unlikely to be effective if reluctance stems from funding of suddenly poor quality assets.
  - Balance between liquidity supply and demand requires deleveraging, restoring asset quality and confidence, and disclosure to avoid contagion for solvent institutions.

### Modeling scope, channels, and four-stage procedure
- Motivation:
  - Correlated financial and economic shocks impact sectors and regions unevenly; correlated defaults and declines in recovery rates occur across entities.
  - Most methodologies inadequately model interaction of the four main drivers of bank solvency risk; this paper models them in detail.
- Three modeled channels for a systemic liquidity event:
  - reduction in unsecured funding due to heightened perception of counterparty and default risk;
  - fire sales of assets by stressed banks, lowering asset prices and affecting valuations, margin requirements, funding costs, profitability, and solvency;
  - liquidity hoarding induced by increased uncertainty over counterparty risk and lower asset valuations, leading to systemic liquidity shortfalls.
- Four-stage modeling procedure:
  1. modeling the financial and economic environment;
  2. modeling correlated borrower credit risk;
  3. modeling systemic banking system solvency risk;
  4. modeling correlated systemic liquidity risk.
- Method: thousands of Monte-Carlo simulations simulate correlated changes in asset prices and macro variables between T0 and T1 to revalue bank balance sheets and derive distributions of economic capital-to-asset ratios, number of solvency defaults at T1, and probabilities of future defaults at T2.

### Data, sample construction, and key calibration items
- Stylized U.S. banking system constructed from Call Report and other publicly available data: 10 aggregate banks in four categories:
  - two large banks aggregating U.S. banks with assets above $500 billion (excluding Morgan Stanley and Goldman Sachs);
  - three large banks aggregating U.S. banks with assets between $100–500 billion;
  - three medium-size banks aggregating banks with assets between $10-100 billion;
  - two small banks aggregating banks with assets below 10 billion.
- Quantitative results presented for demonstration purposes only; risk assessments undertaken with ValueCalc Banking System Risk Modeling Software.
- Simulation time-step: T1 = one-year.
- Financial and Economic Environment Model calibrated for two regimes:
  - monthly data 1987 to 2006; and
  - data 2007 to 2010.

### Key calibration differences across regimes (explicit numeric examples)
- Equity returns and volatilities:
  - average sector equity returns fell from "approximately 13 percent" to "approximately 2 percent" per year.
  - average sector equity return volatility increased from "approximately 18 percent" per year to "24 percent" per year.
- Real estate:
  - average regional real estate price changes fell from "approximately 6 percent" to "-9 percent".
  - average regional real estate index volatility increased from "approximately 2 percent" to "5 percent".
- Regression linking real estate to failure rates:
  - Percent_Bank_Failure_Rate = -.021 – 0.387 Percent_Change_Real_Esate_Prices
  - T-Stat: -2.74  -10.1
  - Adjusted R-Square = 0.667
- U.S. bank failures January 1, 2007 to February 25, 2011: 342 failed banks, with distribution:
  - 280 failed banks had assets of less than $1 billion;
  - 54 had assets between $1 and $10 billion;
  - 6 had assets in the $10 to $25 billion range;
  - Named failures with assets: IndyMac ($32 billion), Washington Mutual ($307 billion), Lehman Brothers ($639 billion), Wachovia ($780 billion), Freddie Mac ($850 billion of assets, plus approximately $4 trillion of guarantees), Fannie Mae ($912 billion of assets, plus approximately $6 trillion in guarantees).
- Stylized system composition:
  - mega banks represent approximately 62 percent of total assets for the model banking system.

### Credit risk and mortgage modeling (explicit numeric rules)
- Business and mortgage loan credit risk based on contingent claims models; recovery rates on business loans modeled as increasing (decreasing) with stock market returns.
- Mortgage modeling specifics:
  - Default probabilities by LTV:
    - LTV between 1.2 and 1.4 → default rate = 20 percent;
    - LTV between 1.4 and 1.6 → default rate = 40 percent;
    - LTV between 1.6 and 1.8 → default rate = 60 percent;
    - LTV over 1.8 → default rate = 80 percent.
  - Recovery rates on mortgage loans = value-to-loan ratio less a 30 percent liquidation cost.
- Portfolio concentration: 200 business loans across up to 20 sectors and 200 mortgage loans across up to 20 regions; plus correlated market risk for approximately 100 other bank assets and liabilities.
- Solvency failure rule: bank fails when equity capital to assets falls below 2 percent.
- Interbank recovery rate on defaulted obligations assumed to be 40 percent; interbank exposures allocated proportionally when bilateral identities unknown.

### Modeling systemic liquidity runs and bank behavior
- Liquidity-run driver: bank-specific T2 probability of failure plus system-wide component equal to ten percent of the system-wide weighted average default probability (i.e., adjusted PD = bank PD + ten percent of system weighted average PD).
- Two calibration cases for total liability withdrawal rates:
  - Case 1: withdrawal rates match those experienced by bank holding companies (BHC) with elevated default probabilities during 2007–2010.
  - Case 2: at highest default probabilities withdrawal rates match those experienced by investment banks (low insured deposits); for lower default probabilities reductions in specific liability accounts modeled to match stylized BHC liability structures.
- Bank behavior strategies under runs:
  - Strategy 1: stop lending in interbank and repo markets, liquidate interest-bearing deposits, sell government securities, and sell other securities; if inadequate liquidity, ultimately default.
  - Strategy 2: sell liquid securities and reduce loan portfolios in proportions similar to observed behavior of U.S. BHCs with elevated failure probabilities.
- Fire-sale and haircut calibration:
  - Bid-ask spreads 2000–09 used as proxy for fire-sale prices; at crisis peak (September 2008) bid-ask spreads in the 5–10 percent range across different asset qualities, suggesting a discount factor of 3–5 percent to represent loss when forced to liquidate assets.
- Model captures feedback loops: higher PDs → reluctance to fund → fire sales → lower asset valuations → higher haircuts and funding costs → worsened solvency and liquidity.

### Key simulation results (selected numeric outcomes)
- 1987–2006 calibration (one year time step, no inter-bank defaults):
  - Small risk of bank failures concentrated in thinly capitalized and regionally concentrated smaller banks.
  - No likelihood of systemic solvency or systemic liquidity risks.
- 2007–2010 calibration (one year time step, no inter-bank defaults):
  - Substantially elevated solvency risks; distribution of equity capital ratios shifted negatively with fatter tails.
  - Eight of the ten banks, including the two mega banks, have a risk of failure in the 0.5 percent range.
  - There is a 1 percent joint probability of four banks failing simultaneously (without inter-bank defaults modeled).
- Including inter-bank defaults (2007–2010 calibration):
  - 1 percent joint probability of six banks failing simultaneously.
  - Failures by mega banks have the highest correlations with subsequent bank failures due to large inter-bank credit losses.
- Liquidity-run scenarios (2007–2010 calibration, repeated network methodology):
  - For a -25 percent maximum reduction in total liabilities: 1 percent joint probability of seven banks failing simultaneously.
  - For a -42 percent maximum reduction in total liabilities: 1 percent joint probability of eight banks failing simultaneously.
- Distributional statistics:
  - In 2007–10:Q1 under case 1 (BHC withdrawal rate): about 2 percent probability that 40 percent of banks will simultaneously be unable to make due payments.
  - In 2007–10:Q1 under case 2 (investment bank withdrawal rate): probability that one-third of banks suffer a liquidity shortage increases to 12.7 percent.
  - A 1 percent probability of an approximately 18 percent reduction in total banks lending.
  - In case 2, a potential liquidity run could lead to reduction in total loans of up to 43 percent with probability less than 1 percent.
- Simulated total solvency plus liquidity-induced bank failures (Table 17):
  - Max Liquidity Run = 25% Total Assets: Average 1.33; Std. Dev. 1.03; Max 10.00; Min 0.00.
  - Max Liquidity Run = 42% Total Assets: Average 1.43; Std. Dev. 1.19; Max 10.00; Min 0.00.
- Liquidity shortages (Negative Net Cash Flow), 2007–2010 (Table 18) — probability distribution (%):
  - 0 banks: 1.51
  - 1: 75.38
  - 2: 17.17
  - 3: 2.36
  - 4: 1.89
  - 5: 0.57
  - 6: 0.09
  - 7: 0.00
  - 8: 0.09
  - 9: 0.85
  - 10: 0.09
- Loan reductions after liquidity shocks (Case 1 averages, Table 19):
  - Bank 1 Average -12.05 (Std. Dev. 10.49; Max 0.00; Min -33.58)
  - Bank 2 Average -25.99 (Std. Dev. 1.63; Max -19.08; Min -37.63)
  - Bank 3 Average -1.03 (Std. Dev. 4.21; Max 0.00; Min -28.17)
  - Total Banking System Average -2.84 (Std. Dev. 2.94; Max -1.08; Min -27.19)
- Simulated capital ratio summaries (selected):
  - 1987–2006, no inter-bank defaults: Average capital ratios (Banks 1–10): 0.112, 0.062, 0.130, 0.110, 0.086, 0.139, 0.134, 0.108, 0.112, 0.097; Number of Failed Banks Average: 0.010.
  - 2007–2010, no inter-bank defaults: Average capital ratios (Banks 1–10): 0.072, 0.012, 0.110, 0.090, 0.061, 0.124, 0.120, 0.087, 0.092, 0.084; Number of Failed Banks Average: 0.655.
  - 2007–2010 with inter-bank default losses: Average capital ratios (Banks 1–10): 0.072, 0.012, 0.110, 0.090, 0.059, 0.122, 0.120, 0.086, 0.091, 0.083; Number of Failed Banks Average: 1.

### Capital buffer estimates and policy-relevant metrics
- Methodology can estimate additional required capital surcharge/buffer to reduce risk of future bank defaults and liquidity runs to a given confidence level.
- Specific target example:
  - Estimate additional capital buffer required at T0 to reduce to less than 1 percent the probability of a bank experiencing a liquidity run at T1 — equivalent in the model to reducing the T1 probability of a bank failing at T2 to below 10 percent at a 99 percent confidence level.
- Recommended additional equity capital to minimize potential systemic solvency and liquidity risks: substantial additional equity capital (e.g., 3 percent to 20 percent of assets).
- Table 20 (selected entries):
  - Initial Capital Ratios (Banks 1–10): 0.104, 0.057, 0.124, 0.104, 0.080, 0.134, 0.124, 0.095, 0.101, 0.088.
  - Approximate additional equity capital required at T=0 to have 1% probability of a 10% probability of failure at T=1: Banks 1–10: 0.111, 0.216, 0.045, 0.056, 0.123, 0.031, -0.011, 0.049, 0.046, 0.026.

### Policy conclusions and recommendations (selected)
- Systemic risks driven by:
  - Large adverse regime shifts in the financial and economic environment (e.g., 2007–2010).
  - Asset and liability structures, loan credit quality, sector and regional loan concentrations, and equity capital levels.
  - Inter-bank exposures and liquidity shortages leading to forced asset sales at fire-sale prices.
- Policy actions to reduce systemic risk levels include:
  - The achievement of reasonably stable economic growth and avoidance of asset price bubbles.
  - Limitations on the quantity of high credit risk loans with high loan to value ratios.
  - Managing loan concentration risk in banks and across the banking system.
  - More accurate assessments of bank capital requirement levels that account for the interaction between infrequent but severe financial and economic volatility, loan portfolio credit quality, and loan portfolio concentrations.
  - Persistent enforcement of bank capital requirements even during extended periods when banks experience low loan portfolio loss rates.
- Additional policy notes:
  - Deposit insurance schemes likely stabilize funding for insured institutions.
  - Central banks have an important role in providing liquidity to solvent banks facing liquidity pressures.
  - Capital and other risk variables may need adjustment for uninsured institutions to reflect higher liquidity risks.

### Appendix calibrations and selected historical figures
- Simulation methodology uses approximately 50 random variables with trends, volatilities and correlations estimated from monthly historical data; risk-free rates modeled with Hull and White extended Vasicek; equity and FX assumed geometric Brownian motion.
- Selected historical calibration figures (1987–2006 vs 2007–2010):
  - U.S. Industrial Production trend 1987-2006: 0.029 (Percent Per Year); volatility 1987-2006: 0.018; trend 2007-2010: -0.014; volatility 2007-2010: 0.034.
  - U.S. Unemployment Rate trend 1987-2006: -0.020; volatility 1987-2006: 0.087; trend 2007-2010: 0.204; volatility 2007-2010: 0.106.
  - U.S. CPI trend 1987-2006: 0.030; volatility 1987-2006: 0.009; trend 2007-2010: 0.021; volatility 2007-2010: 0.018.
  - Average for 12 Equity Sectors trend 1987-2006: 0.131; volatility 1987-2006: 0.182; trend 2007-2010: 0.021; volatility 2007-2010: 0.238.
  - Average for 20 Real Estate Regions trend 1987-2006: 0.057; volatility 1987-2006: 0.024; trend 2007-2010: -0.088; volatility 2007-2010: 0.051.
- Fire-sale calibration evidence:
  - Coval and Stafford (2007): when around at least 15 percent of owners are distressed sellers of the same stock, average abnormal stock return is -10.1 percent for the first quarter.
  - U.K. calibrated example: selling largest holdings generates price falls of 2 percent for equities, 4 percent for corporate debt and 5 percent for mortgage-back securities.
- Bid-ask spreads and haircuts:
  - Crisis peak (September 2008) bid-ask spreads in the 5–10 percent range; implies discount factor of 3–5 percent representing loss under distressed liquidation.

*Source: _wp11263 — IMF Working Paper (excerpt).*

### 1. Selected Liquidity Stress Testing (ST) Frameworks ................................................................. 6

### 1. Selected Liquidity Stress Testing (ST) Frameworks

### Introduction and paper objectives
- Proposes and demonstrates a methodology for modeling correlated systemic solvency and liquidity risks for a banking system.
- Jointly models solvency risk and systemic liquidity risk, emphasizing their interaction.
- Principal contributions:
  - Model financial and economic environment volatility, bank loan sector and region concentration levels, bank loan credit quality, and bank capital levels for 10 banks simultaneously.
  - Estimate the probability of banking system systemic solvency and liquidity risks.
  - Evaluate pre-emptive measures to moderate systemic risks and their impacts.
- Situates approach relative to literature and empirical evidence on the 2008–2009 global crises (references in text include Gorton and Metrick, 2009; Afonso, Cover, and Schoar, 2010).
- Relates to supervisory stress-testing approaches where systemic liquidity shocks are triggered by solvency concerns (Bank of England work cited: Aikman et al., 2009; Wong and Hui, 2009; van den End and Tabbae, 2009).

### Modeling scope and motivation
- Highlights that correlated financial and economic shocks impact sectors and regions unevenly (example: real estate prices/sector equity returns may fall more sharply in some regions/sectors).
- Notes that entities present at a point in time will be simultaneously impacted by adverse environment events producing correlated defaults and correlated declines in recovery rates.
- Argues most risk assessment methodologies inadequately model interaction of the four main drivers of bank solvency risk; the paper models these in significant detail.

### Data, sample construction, and calibration
- Stress tests applied to a stylized set of U.S. banks using Call Report and other publicly available data.
- Constructed detailed balance sheets for 10 aggregate banks in four categories:
  - two large banks that aggregate the asset and liabilities of all U.S. banks with assets above $500 billion (excluding Morgan Stanley and Goldman Sachs);
  - three large banks that aggregate the assets and liabilities of all U.S. banks with assets between $100–500 billion;
  - three medium-size banks that aggregate banks with assets between $10-100 billion; and
  - two small banks that aggregate banks with assets below 10 billion.
- The quantitative results are based on publicly available data and are presented for demonstration purposes only.
- Risk assessments undertaken with the ValueCalc Banking System Risk Modeling Software, copyright FinSoft, Inc.

### Framework links to empirical evidence and prior work
- Emphasizes that the global financial crisis was not a pure liquidity shock but was triggered by concerns about the value of bank assets—subprime mortgages and structured products affected by the fall in house prices (cited empirical studies).
- Notes relationship to supervisory approaches that model systemic liquidity shocks triggered by solvency concerns.

### Structure of the paper (selected contents)
- The paper contains detailed tables, figures, and appendices including:
  - Simulations of capital ratios under different financial environment calibrations (1987–2006 and 2007–2010) and scenarios with/without inter-bank default losses.
  - Distributional analyses: probabilities of default, simulated total solvency plus liquidity induced bank failures, correlations among incremental bank failures due to inter-bank default losses.
  - Measures of liquidity stress: probability of banks having liquidity shortage (negative net cash flow), simulated percentage reduction in bank loans after liquidity shock, additional equity capital required at T0.
  - Appendices with additional information on how the financial environment was simulated and calibration of asset haircuts in fire-sale contexts.

*Source: _wp11263 - 1. Selected Liquidity Stress Testing (ST) Frameworks, IMF Working Paper (excerpt).*

### Section II defines systemic liquidity risk. Section III presents the methodology and modeling

### _wp11263 - Section II defines systemic liquidity risk. Section III presents the methodology and modeling

### Definition of systemic liquidity risk
- A systemic liquidity shock is "an aggregate shortage of liquidity, i.e. a situation in which many institutions face liquidity shortages simultaneously, as opposed to one institution suffering a liquidity shortage."  
- Systemic liquidity risk is "the probability that this situation takes place."
- A liquidity shortage can manifest as:
  - funding liquidity risk: inability to roll over funding; or
  - market liquidity risk: inability to trade assets at normal bid/ask spreads; or both.
- The stress test (ST) approach views systemic liquidity shocks as more likely in the presence of shocks to fundamentals that depress asset values and make markets reluctant to fund lower quality assets or the institutions that hold them, particularly under incomplete and asymmetric information.
- Systemic liquidity shocks are modeled as reactions to shocks to asset values resulting from borrower defaults and other factors; a liquidity shock (or "run") is an extreme episode of market discipline sorting ex-ante "good" (solvent) and "bad" (insolvent) users of funds.
- Historical context and evidence cited:
  - Global crisis characterized as a system-wide "run" in the securitized banking system (a "run on the repo market") triggered by insolvency problems (Gorton and Metrick (2009)).
  - Changes in the LIBOR-OIS spread during 2007–2008 strongly correlated with changes in credit spreads and repo rates for securitized bonds.
  - Afonso, Cover, and Schoar find counterparty risk concerns played a larger role than liquidity hoarding after Lehman’s bankruptcy.

### Policy implications and diagnostic importance
- Importance of relating policy response to the diagnosis of the shock: similar-looking systemic liquidity shocks can have different origins (aggregate preference shock, infrastructure malfunctioning, solvency concerns) that imply different policy responses.
- For the U.S. banks application the paper:
  - develops a capital surcharge aimed at minimizing the probability that any given bank would experience a destabilizing run; and
  - for crisis management proposes recapitalizing or closing insolvent banks and disclosing enough information to eliminate uncertainties about bank solvency.
- Liquidity injections by a central bank can work if they allow banks to deleverage by exchanging liquidity for trouble assets, but are unlikely to be effective if reluctance stems from funding of suddenly poor quality assets.
- Balance between liquidity supply and demand requires deleveraging, restoring asset quality and confidence, and disclosure to avoid contagion for solvent institutions.

### Modeling steps and channels (overview)
- ST approach builds on a detailed solvency stress test and adds a systemic liquidity component to measure correlated systemic solvency and liquidity risk, assess bank vulnerability to liquidity shortfalls, and design capital surcharges.
- The ST approach models three channels for a systemic liquidity event:
  - a reduction in unsecured funding due to heightened perception of counterparty and default risk;
  - fire sales of assets by stressed banks, lowering asset prices and affecting valuations, margin requirements, funding costs, profitability, and solvency;
  - liquidity hoarding induced by increased uncertainty over counterparty risk and lower asset valuations, leading to systemic liquidity shortfalls.
- Four-stage modeling procedure (Figure 1):
  1. modeling the financial and economic environment;
  2. modeling correlated borrower credit risk;
  3. modeling systemic banking system solvency risk;
  4. modeling correlated systemic liquidity risk.
- Thousands of Monte-Carlo simulations simulate correlated changes in asset prices and macro variables between T0 and T1 to revalue bank balance sheets and derive distributions of economic capital-to-asset ratios, number of solvency defaults at T1, and probabilities of future defaults at T2.

### Data requirements (explicit items)
- Time series of financial and economic environment variables with sufficient length to estimate trends, volatilities, and correlations in "normal" and "stress" periods, including:
  - short-term domestic and foreign interest rates and term structures;
  - interest rate spreads for loans of various credit qualities (securities);
  - foreign exchange rates (as relevant);
  - economic indicators (Gross Domestic Product (GDP), consumer price index; unemployment, and so on);
  - commodity prices (oil, gold, and so on);
  - sector equity indices;
  - regional real estate prices.
- Bank-level information on assets, liabilities, and off-balance-sheet transactions, including hedges:
  - categories of loans, credit quality, maturity structure, currencies of denomination;
  - currency and maturity structure of other assets and liabilities;
  - capital, operating expenses and tax rates;
  - clients’ leverage ratios and recovery rates to calibrate credit risk models;
  - interbank exposures including bilateral credit exposures.
- Information to calibrate behavioral relationships:
  - relationship between banks’ default probabilities and reduction in funding due to creditor concerns about solvency;
  - relationship between asset fire sales and asset values (including haircuts), and their effects on liquidity and solvency ratios.
- Note: expert opinion may substitute for some unavailable data.

### Model calibration to the U.S. financial environment and banking system
- Financial and Economic Environment Model calibrated for two regimes:
  - monthly data 1987 to 2006; and
  - data 2007 to 2010.
- Empirical differences between regimes (examples from Table 2):
  - average sector equity returns fell from "approximately 13 percent" to "approximately 2 percent" per year;
  - average sector equity return volatility increased from "approximately 18 percent" per year to "24 percent" per year;
  - average regional real estate price changes fell from "approximately 6 percent" to "-9 percent";
  - average regional real estate index volatility increased from "approximately 2 percent" to "5 percent".
- Regional real estate prices strongly associated with bank failure rates (Table 3 regression):
  - Percent_Bank_Failure_Rate = -.021 – 0.387 Percent_Change_Real_Esate_Prices
  - T-Stat: -2.74  -10.1
  - Adjusted R-Square = 0.667
- U.S. bank failures January 1, 2007 to February 25, 2011: 342 failed banks (Table 4):
  - 280 failed banks had assets of less than $1 billion;
  - 54 had assets between $1 and $10 billion;
  - 6 had assets in the $10 to $25 billion range;
  - named failures with assets: IndyMac ($32 billion), Washington Mutual ($307 billion), Lehman Brothers ($639 billion), Wachovia ($780 billion), Freddie Mac ($850 billion of assets, plus approximately $4 trillion of guarantees), Fannie Mae ($912 billion of assets, plus approximately $6 trillion in guarantees).
- Stylized banking system: 10 stylized U.S. banks constructed from Call Report Data in four categories:
  - two mega banks (assets > $500 billion; mega banks represent approximately 62 percent of total assets for the model banking system);
  - three large banks (assets between $100–500 billion);
  - three medium banks (assets between $10–100 billion);
  - two small banks (assets below $10 billion).
- Regional and sectoral concentration modeled: small banks lend in one or two states and three sectors; medium banks in larger regions and four sectors; large/mega banks nationally in 20 regions and 14 sectors.

### Credit risk, loan portfolio, and solvency modeling
- Credit risk modeling:
  - Business and mortgage loan credit risk based on contingent claims type models (Black and Scholes (1973), Merton (1973)); future company values linked to simulated sector equity returns plus idiosyncratic shocks.
  - Business credit risk model uses U.S. business credit risk model estimated by Barnhill and Maxwell (2002).
  - Recovery rates on business loans modeled as increasing (decreasing) with stock market returns.
- Mortgage modeling:
  - Loans to individuals modeled entirely as mortgage loans due to data limitations.
  - Initial loan-to-value (LTV) ratios estimated from Fannie Mae and Freddie Mac reports and assumed distributions.
  - Default probabilities by LTV:
    - LTV between 1.2 and 1.4 → default rate = 20 percent;
    - LTV between 1.4 and 1.6 → default rate = 40 percent;
    - LTV between 1.6 and 1.8 → default rate = 60 percent;
    - LTV over 1.8 → default rate = 80 percent.
  - Recovery rates on mortgage loans = value-to-loan ratio less a 30 percent liquidation cost.
- Portfolio concentration modeling:
  - Correlated market and credit risk modeled on 200 business loans across up to 20 sectors and 200 mortgage loans across up to 20 regions; plus correlated market risk for approximately 100 other bank assets and liabilities.
- Solvency outcomes and thresholds:
  - Market value of equity (MVE) computed from simulated asset and liability valuations and income flows; capital ratio computed as MVE / total assets.
  - Bank failure rule: bank modeled as failing when ratio of equity capital to assets falls below 2 percent.
  - Future default probabilities at T2 derived assuming distribution of changes in capital ratios between T1 and T2 equals distribution between T0 and T1.
  - Interbank recovery rate on defaulted interbank obligations assumed to be 40 percent.
  - Interbank exposures allocated proportionally to total interbank borrowing and lending when bilateral identities unknown.

### Modeling correlated systemic liquidity risk and liquidity runs
- Liquidity runs modeled as driven by each bank’s T2 probability of failure plus a system-wide component equal to ten percent of the system-wide weighted average default probability (i.e., adjusted probability of failure includes bank-specific PD + 10 percent of system weighted average PD).
- Two calibration cases for total liability withdrawal rates:
  - Case 1: withdrawal rates match those experienced by bank holding companies (BHC) with elevated default probabilities during 2007–2010.
  - Case 2: at highest default probabilities withdrawal rates match those experienced by investment banks (low insured deposits) to calibrate a more stressed scenario; for lower default probabilities reductions in specific liability accounts modeled (demand deposits, time deposits, jumbo time deposits, Fed Funds, repos, etc.) matching stylized BHC liability structures.
  - Table 11 (referenced) summarizes total liability withdrawal rates associated with different default probability ranges for each case.
- Bank behaviour under runs (two strategies):
  - Strategy 1: stop lending in interbank and repo markets, liquidate interest-bearing deposits, sell government securities, and sell other securities; if inadequate liquidity, ultimately default.
  - Strategy 2: sell liquid securities and reduce loan portfolios in proportions similar to observed behavior of U.S. BHCs with elevated failure probabilities.
- Fire-sale losses and haircuts:
  - Fire-sale selling prices incorporate a high liquidity premium well below fundamental price.
  - Bid-ask spread developments 2000–09 used as proxy for fire-sale prices. At crisis peak (September 2008) bid-ask spreads in the 5–10 percent range across different asset qualities, suggesting a discount factor of 3–5 percent to represent loss when forced to liquidate assets.
- Empirical basis for liquidity behavior calibration:
  - Changes in bank liabilities from 2007 to Q1 2010 used to estimate relation between bank PD and rate of withdrawal of total liabilities over T1 to T2.
  - When multiple bank failures occur, elevated future insolvency risk for remaining banks increases estimated T2 PDs which then drive assumed liquidity outflows per Table 11.
- Model captures feedback loops: higher PDs → reluctance to fund → fire sales → lower asset valuations → higher haircuts and funding costs → worsened solvency and liquidity.

### Key numerical thresholds, parameters, and assumptions (explicit)
- Regimes: 1987–2006 (monthly data) and 2007–2010.
- Equity return examples: "approximately 13 percent" → "approximately 2 percent" per year.
- Equity volatility: "approximately 18 percent" → "24 percent" per year.
- Regional real estate changes: "approximately 6 percent" → "-9 percent"; volatility "approximately 2 percent" → "5 percent".
- Regression: Percent_Bank_Failure_Rate = -.021 – 0.387 Percent_Change_Real_Esate_Prices; T-Stat -2.74  -10.1; Adjusted R-Square 0.667.
- Bank failure counts January 1, 2007 to February 25, 2011: 342 failed banks.
- Stylized bank asset-size buckets: < $1 billion; $1–$10 billion; $10–$25 billion; named large failures with asset values as listed (IndyMac $32 billion; Washington Mutual $307 billion; Lehman Brothers $639 billion; Wachovia $780 billion; Freddie Mac $850 billion of assets plus approximately $4 trillion guarantees; Fannie Mae $912 billion of assets plus approximately $6 trillion guarantees).
- Stylized system: 10 banks; mega banks ~62 percent of system assets.
- Solvency failure threshold: equity capital to assets = 2 percent.
- Interbank recovery rate on defaulted obligations: 40 percent.
- Adjusted probability component for liquidity runs: ten percent of the system-wide weighted average default probability included in a bank’s liquidity run driver.
- Mortgage default rates by LTV bands: 1.2–1.4 → 20 percent; 1.4–1.6 → 40 percent; 1.6–1.8 → 60 percent; >1.8 → 80 percent.
- Mortgage recovery assumption: recovery = value-to-loan ratio less a 30 percent liquidation cost.
- Fire-sale discount proxy: bid-ask spreads at crisis peak 5–10 percent; implies a discount factor of 3–5 percent representing loss under distressed liquidation.
- Simulation time-step used in study: T1 = one-year.

*Source: _wp11263 - Section II defines systemic liquidity risk. Section III presents the methodology and modeling*

### Appendix 2 explains how the bid-ask spreads were estimated

### _wp11263 - Appendix 2 explains how the bid-ask spreads were estimated

### Fire-sale price impacts and calibration evidence
- Empirical and modelling references align with Coval and Stafford (2007), Aikman and others (2009), and Duffie and others (2006).
- Coval and Stafford (2007): when around at least 15 percent of the owners are distressed sellers of the same stock, average abnormal stock return is -10.1 percent for the first quarter, and less than 2 percent for months 4–12.
- Aikman et al (2008), following Duffie et al (2006), model asset j price after a fire sale i_jP as the maximum of zero and the pre-fire-sale price jP multiplied by a discount term that is a function of ijS / jM scaled by parameter θ and shocked by jε. Calibrated U.K. example: selling largest holdings generates price falls of 2 percent for equities, 4 percent for corporate debt and 5 percent for mortgage-back securities.

### Modelling framework: solvency, liquidity, and network effects
- Banks fail from a solvency perspective when simulated capital ratios fall below some critical level (e.g., 2 percent).
- Banks experience liquidity problems when their risk of future insolvency, or the banking system’s overall risk of insolvency, rises to an unacceptable level (e.g., 10 percent).
- The model:
  - Applies a network methodology repeatedly to capture inter-bank default losses until no additional banks fail.
  - Models initial solvency outcomes at T1, then estimates failure probabilities for remaining solvent banks at T2, and uses those to trigger correlated liquidity runs.
  - Adjusts default probabilities by adding a factor equal to 10 percent of the banking system’s weighted average probability of default to account for system-wide stress impacts when estimating runs.
- The model captures interaction between funding and market liquidity and second-round feedback between solvency and liquidity risks (e.g., forced sales of less liquid assets with high liquidity premia).

### Key simulation calibrations and comparative results
- Calibration periods: 1987–2006 financial environment versus 2007–2010 financial environment.
- 1987–2006 calibration (one year time step, no inter-bank defaults):
  - Small risk of bank failures concentrated in thinly capitalized and regionally concentrated smaller banks.
  - No likelihood of systemic solvency or systemic liquidity risks.
- 2007–2010 calibration (one year time step):
  - Substantially elevated solvency risks for all banks; distribution of equity capital ratios shifted negatively with fatter tails.
  - Some small regionally concentrated banks have high failure probabilities.
  - Eight of the ten banks, including the two mega banks, have a risk of failure in the 0.5 percent range.
  - There is a 1 percent joint probability of four banks failing simultaneously (without inter-bank defaults modeled).

### Impact of inter-bank defaults and correlated failures
- Including potential inter-bank defaults (2007–2010 calibration):
  - There is a 1 percent joint probability of six banks failing simultaneously (Table 14).
  - Inter-bank default losses can increase correlated failures (example: from four to six at a 1 percent probability).
  - Failures by mega banks have the highest correlations with subsequent bank failures due to large inter-bank credit losses (Table 15).

### Correlated solvency and liquidity risk outcomes
- Correlation metrics:
  - Simulated correlation of 0.55 between the simulated weighted average probabilities of solvent banks failing at T2 and the simulated percentage of banking system assets held by banks failing at T1.
- Liquidity-run scenarios and joint failure probabilities (2007–2010 calibration; network methodology repeated until no additional failures):
  - For a -25 percent maximum reduction in total liabilities: 1 percent joint probability of seven banks failing simultaneously (liquidity failures can increase correlated failures from six to seven).
  - For a -42 percent maximum reduction in total liabilities: 1 percent joint probability of eight banks failing simultaneously (liquidity failures can increase correlated failures from six to eight).
- Distributional and scenario statistics:
  - In the 2007–10:Q1 financial environment under case 1 (BHC withdrawal rate): about 2 percent probability that 40 percent of banks will simultaneously be unable to make due payments.
  - In the 2007–10:Q1 financial environment under case 2 (investment bank withdrawal rate): the probability that one-third of banks suffer a liquidity shortage increases to 12.7 percent.
  - A 1 percent probability of an approximately 18 percent reduction in total banks lending (distributional result).
  - In case 2, a potential liquidity run could lead to a significant reduction in total loans, of up to 43 percent, although with a low probability of less than 1 percent.

### Capital buffer estimates and policy-relevant metrics
- Methodology can estimate additional required capital surcharge/buffer to reduce risk of future bank defaults and liquidity runs to a given confidence level.
- Specific target example:
  - Estimate additional capital buffer required at T0 to reduce to less than 1 percent the probability of a bank experiencing a liquidity run at T1 — equivalent in the model to reducing the T1 probability of a bank failing at T2 to below 10 percent at a 99 percent confidence level.
- Recommended additional equity capital to minimize potential systemic solvency and liquidity risks: substantial additional equity capital (e.g., 3 percent to 20 percent of assets).
- Small banks typically require the most additional capital due to higher failure probabilities from undiversified asset exposures (notably real estate).

### Summary conclusions and policy recommendations
- Systemic risks driven by:
  - Large adverse regime shifts in the financial and economic environment (e.g., 2007–2010).
  - Asset and liability structures, loan credit quality, sector and regional loan concentrations, and equity capital levels.
  - Inter-bank exposures and liquidity shortages leading to forced asset sales at fire-sale prices.
- Policy actions to reduce systemic risk levels include:
  - The achievement of reasonably stable economic growth and avoidance of asset price bubbles.
  - Limitations on the quantity of high credit risk loans with high loan to value ratios.
  - Managing loan concentration risk in banks and across the banking system.
  - More accurate assessments of bank capital requirement levels that account for the interaction between infrequent but severe financial and economic volatility, loan portfolio credit quality, and loan portfolio concentrations.
  - Persistent enforcement of bank capital requirements even during extended periods when banks experience low loan portfolio loss rates.
- Additional policy notes:
  - Deposit insurance schemes likely stabilize funding for insured institutions.
  - Central banks have an important role in providing liquidity to solvent banks facing liquidity pressures.
  - Capital and other risk variables may need adjustment for uninsured institutions to reflect higher liquidity risks.
- Future research priorities:
  - Assess relationship between system-wide stress levels and liquidity risk for individual banks.
  - Model correlated changes in all liability accounts for banks with elevated solvency risk.
  - Analyze how volatility in bank loan collateral values increases solvency and liquidity risk.
  - Study correlations between repossessed collateral volumes and subsequent price declines/default rates.
  - Investigate correlated sovereign risk and better modeling of potential economic regime shifts.

*Source: _wp11263 - Appendix 2 explains how the bid-ask spreads were estimated*

### APPENDIX I. ADDITIONAL INFORMATION ON HOW THE FINANCIAL ENVIRONMENT WAS

### APPENDIX I. ADDITIONAL INFORMATION ON HOW THE FINANCIAL ENVIRONMENT WAS SIMULATED

### Simulation methodology for financial environments
- Simulated future financial environments use a set of approximately 50 random variables with trends, volatilities and correlations estimated from monthly historical data for the country being analyzed.
- No structural models linking asset prices to economic variables (e.g., unemployment or GDP) are implemented.
- Risk-free interest rates are modeled using the Hull and White extended Vasicek model (Hull and White; 1990, 1993, 1994).
- Risky term structures (AA, A, etc.) are modeled as stochastic lognormal spreads over risk-free, with mean values set approximately equal to forward rates implied by initial term structures to insure positivity of spreads and approximate arbitrage-free risky term structures.
- Equity market indices and FX rate (S) are assumed to follow a geometric Brownian motion with constant expected growth rate (m) and volatility (σ) (Hull, 2008).

### Modeling multiple correlated stochastic variables
- Procedure follows Hull (1997) for n-variate normal distributions; requires specification of correlations between each of the n stochastic variables.
- Independent random samples (x1 ... xn) are drawn from standardized normal distributions; correlated error terms (ε1 ... εn) are calculated from these and the correlation matrix.
- Example for bivariate normal:
  - ε1 = x1
  - ε2 = ρ x1 + x2 sqrt(1−ρ^2)
  - Where x1, x2 = independent random samples from standardized normal distributions, ρ = correlation between the two stochastic variables, and ε1, ε2 = samples from a standardized bivariate normal distribution.

### Calibration of asset haircuts and bid-ask spreads (fire sales)
- Liquidity premium impact on bank equity captured by haircuts based on bid-ask spreads.
- Corporate bonds: BoA/Merrill Lynch U.S. Corporate indices downloaded for AAA, AA, A, BBB, BB, B, and CCC. Index members sorted by issue size; largest 50 issues and subsequent 100 largest pre-2006 issues selected (150 bonds) for each index. AAA index has 61 members; all included regardless of size/issue date.
- Assumption: bonds always in their current credit rating; no rating-history adjustments.
- Government bonds: bid and ask prices for all U.S. Treasury notes/bonds with amounts outstanding > 0 downloaded.
- Spread calculation: ask − bid; arithmetic average across available spreads, ignoring zeros and missing values.
- Pricing source: CBBT (Composite Bloomberg Bond Trader) with execution-price rules described (e.g., at least three executable pricing sources; corporate prices within last fifteen minutes; government within five minutes).

### Key historical calibrations (selected figures)
- U.S. Industrial Production trend 1987-2006: 0.029 (Percent Per Year); volatility 1987-2006: 0.018 (Percent Per Year); trend 2007-2010: -0.014 (Percent Per Year); volatility 2007-2010: 0.034 (Percent Per Year).
- U.S. Unemployment Rate trend 1987-2006: -0.020; volatility 1987-2006: 0.087; trend 2007-2010: 0.204; volatility 2007-2010: 0.106.
- U.S. CPI trend 1987-2006: 0.030; volatility 1987-2006: 0.009; trend 2007-2010: 0.021; volatility 2007-2010: 0.018.
- Average for 12 Equity Sectors trend 1987-2006: 0.131; volatility 1987-2006: 0.182; trend 2007-2010: 0.021; volatility 2007-2010: 0.238.
- Average for 20 Real Estate Regions trend 1987-2006: 0.057; volatility 1987-2006: 0.024; trend 2007-2010: -0.088; volatility 2007-2010: 0.051.

### State-level bank failure rates and real estate price changes (2007–2011)
- Highest percentage of banks in state failing between Jan 2007 - Feb 2011: NV 0.244 with percentage change in home price index Jun 2007 - Dec 2010: -0.543.
- Selected states:
  - AZ 0.175 and -0.517
  - GA 0.174 and -0.310
  - FL 0.153 and -0.431
  - CA 0.119 and -0.382
  - NY 0.020 and -0.085
  - WV 0.000 and -0.031
- Sources: FDIC, Freddie Mac.

### Distribution of failed bank asset sizes (Jan 2007 to Feb 2011)
- Under $1 billion: 281
- $1 to $5 Billion: 48
- $5 to $10 Billion: 5
- $10 to $50 Billion: 7
- Over $300 Billion: 1
- Total: 342

### Bank balance sheet templates (percent assets) — selected highlights
- Small banks (California vs Florida-Georgia):
  - Securities: California 21.34, Florida-Georgia 17.20
  - Loans: California 64.37, Florida-Georgia 68.16
  - Equity Capital incl Minority Interest: California 11.33, Florida-Georgia 6.60
- Medium banks (West Coast / Mid-America / East Coast):
  - Securities: 19.00 / 19.59 / 23.43
  - Loans: 64.92 / 67.72 / 48.87
  - Equity Capital incl Minority Interest: 13.01 / 10.78 / 8.60
- Large banks (Large 1 / Large 2 / Large 3):
  - Securities: 26.76 / 17.65 / 36.90
  - Loans: 43.00 / 61.75 / 43.61
  - Equity Capital incl Minority Interest: 13.11 / 12.01 / 10.50
- Mega banks (Mega 1 / Mega 2):
  - Securities: 32.61 / 49.85
  - Loans: 50.11 / 34.78
  - Equity Capital incl Minority Interest: 10.08 / 8.20
- Source: SNL Financial, Staff estimates.

### Credit quality and loan-level assumptions
- Table of Committed and Outstanding Commercial and Industrial Loans (Selected years, In Billions of Dollars per Year):
  - 1989: Total Committed 92.0; Total Outstanding 245.0
  - 1999: Total Committed 759.0; Total Outstanding 562.0
  - 2008: Total Committed 789.0; Total Outstanding 1208.0
  - 2010: Total Committed 519.0; Total Outstanding 1210.0
- Assumed distribution of initial mortgage loan-to-value (LTV) ratios:
  - 0.355: 0.090 (Percentage of Mortgage Loans)
  - 0.710: 0.110
  - 0.800: 0.350
  - 0.900: 0.120
  - 1.000: 0.080
  - 1.055: 0.150
  - 1.300: 0.100

### Withdrawal rate assumptions for decline in total liabilities (percent)
- Default Probability / Case 1 / Case 2 / Withdrawal Rate:
  - 10-20 / 57-10 / (table format in source)
  - 20-35 / 10-14 / 21
  - >35 / 25 / 42
- Sources: SNL Financial; and author estimates.

### Simulated capital ratio results (selected summaries)
- Using 1987–2006 financial environment, no inter-bank default losses (Table 12):
  - Average capital ratios (Banks 1–10): 0.112, 0.062, 0.130, 0.110, 0.086, 0.139, 0.134, 0.108, 0.112, 0.097
  - Number of Failed Banks Average: 0.010
  - Std. Dev. (Banks 1–10): 0.013, 0.014, 0.012, 0.011, 0.008, 0.006, 0.006, 0.007, 0.009, 0.008
  - Max capital ratios shown (e.g., Bank 1 Max 0.141)
- Using 2007–2010 financial environment, no inter-bank default losses (Table 13):
  - Average capital ratios (Banks 1–10): 0.072, 0.012, 0.110, 0.090, 0.061, 0.124, 0.120, 0.087, 0.092, 0.084
  - Number of Failed Banks Average: 0.655
  - Std. Dev. (Banks 1–10): 0.031, 0.036, 0.026, 0.024, 0.018, 0.014, 0.015, 0.018, 0.022, 0.017
  - Min values include negatives (e.g., Bank 1 Min -0.105; Bank 2 Min -0.173)
- Using 2007–2010 calibration with first and second round inter-bank default losses (Table 14):
  - Average capital ratios (Banks 1–10): 0.072, 0.012, 0.110, 0.090, 0.059, 0.122, 0.120, 0.086, 0.091, 0.083
  - Number of Failed Banks Average: 1
  - Min values extend further negative (e.g., Bank 1 Min -0.145; Bank 2 Min -0.236)

### Correlations and contagion from inter-bank default losses
- Correlations among incremental bank failures due to inter-bank default losses and initial bank failures (selected entries, Table 15):
  - Incremental Number of Banks Failing Step 1 with Step 2: 0.72
  - Incremental Number of Banks Failing Step 1 correlated with Bank 1 Failure: 0.45
  - Incremental Number of Banks Failing Step 2 correlated with Bank 9 or 10 Failure: 0.73
  - Bank 9 or 10 Failure correlations across table: e.g., with Bank 9 Failure 0.95; with Incremental Number of Banks Failing Step 1 0.79
  - Several entries reported as n.a. where not applicable.

### Distributional analysis of bank default probabilities (Table 16)
- Weighted average for banking system Average probability: 0.091
- Individual bank averages:
  - Bank 1 Average 0.287; Std. Dev. 0.270; Min 0.024
  - Bank 2 Average 0.866; Std. Dev. 0.177; Min 0.213
  - Bank 3 Average 0.042; Std. Dev. 0.113; Min 0.006
  - Bank 6 Average 0.020; Std. Dev. 0.100; Min 0.009
  - Bank 7 Average 0.003; Std. Dev. 0.034; Min 0.000
- Percentile detail provided across many percentiles (0.99 down to 0.001) in source.

### Simulated total solvency plus liquidity-induced bank failures (Table 17)
- Two scenarios for Max Liquidity Run:
  - Max Liquidity Run = 25% Total Assets: Average 1.33; Std. Dev. 1.03; Max 10.00; Min 0.00
  - Max Liquidity Run = 42% Total Assets: Average 1.43; Std. Dev. 1.19; Max 10.00; Min 0.00
- Percentiles reported (selected):
  - For Max Liquidity Run = 25%: 0.99 percentile 0.00; 0.95 percentile 1.00; 0.50 percentile 1.00; lower tail 0.001 percentile 9.00
  - For Max Liquidity Run = 42%: 0.99 percentile 0.00; 0.95 percentile 1.00; 0.50 percentile 1.00; 0.001 percentile 10.00

### Liquidity shortages and net cash flows
- Probability of banks having liquidity shortage (Negative Net Cash Flow), 2007–2010 (Table 18):
  - Number of Banks / Probability:
    - 0 banks: 1.51
    - 1: 75.38
    - 2: 17.17
    - 3: 2.36
    - 4: 1.89
    - 5: 0.57
    - 6: 0.09
    - 7: 0.00
    - 8: 0.09
    - 9: 0.85
    - 10: 0.09
- Figures show Net Cash Flows (after asset fire sales), 2007–2010 for each bank/region with probabilities (visual distributions in source).

### Loan reductions after liquidity shocks (selected results)
- Simulated percentage reduction in bank loans after liquidity shock (Case 1 for BHC’s) — averages and extremes (Table 19):
  - Average reductions by bank:
    - Bank 1 Average -12.05 (Std. Dev. 10.49; Max 0.00; Min -33.58)
    - Bank 2 Average -25.99 (Std. Dev. 1.63; Max -19.08; Min -37.63)
    - Bank 3 Average -1.03 (Std. Dev. 4.21; Max 0.00; Min -28.17)
    - Bank 5 Average -8.43 (Std. Dev. 10.54; Max 0.00; Min -41.04)
    - Bank 6 Average -0.50 (Std. Dev. 4.86; Max 0.00; Min -50.57)
  - Total Banking System Average: -2.84 (Std. Dev. 2.94; Max -1.08; Min -27.19)
  - Tail percentiles and extreme minima provided (e.g., 0.001 percentile for Bank 6 -48.82; systemic total -25.07).

### Additional equity capital required for resiliency (Table 20)
- Initial Capital Ratios (Banks 1–10):
  - 0.104, 0.057, 0.124, 0.104, 0.080, 0.134, 0.124, 0.095, 0.101, 0.088
- Approximate additional equity capital required at T=0 to have 1% probability of a 10% probability of failure at T=1:
  - Banks 1–10: 0.111, 0.216, 0.045, 0.056, 0.123, 0.031, -0.011, 0.049, 0.046, 0.026

*Source: ValueCalc Estimates; Bloomberg; SNL Financial; FDIC; Freddie Mac; IMF staff estimates.*

### References

### References

### Complete list

- Acharya, Viral V., Joao A. C. Santos, and Tanju Yorulmazer, 2010, “Systemic Risk and Deposit Insurance Premiums,” Economic Policy Review (New York: Federal Reserve Bank of New York, August).
- Afonso, Gara, Anna Kovner, and Antoinette Shoar, 2010, “Stressed, Not Frozen: The Federal Funds Market in the Financial Crisis,” Federal Reserve Bank of New York Staff Reports No. 437 (March).
- Aikmen, David, Alessandro Piergiorgio, Bruno Eklund, Prasanna Gai, Sujit Kapadia, Elizabeth Martin, Nada Mora, Gabriel Sterne, and Matthew Willison, 2009, “Funding Liquidity Risk in a Quantitative Model of Systemic Stability,” Bank of England Working Paper No. 372 (June).
- Allen, Franklin and Douglas Gale, 2000. "Financial Contagion”, Journal of Political Economy, Vol. 108, No.1 (February), pp.1–33.
- Barnhill, Theodore, and W. Maxwell, 2002, “Modeling Correlated Interest Rate, Exchange Rate, and Credit Risk in Fixed Income Portfolios,” Journal of Banking and Finance, Vol. 26, No. 2–3, pp. 347–74.
- Barnhill, Theodore, and M. Souto, 2009 “Systemic Bank Risk in Brazil: A Comprehensive Simulation of Correlated Market, Credit, Sovereign and Inter-Bank Risks”, Journal of Financial Markets, Institutions & Instruments, Volume 18, Issue 4, (November) pp. 243–283.
- Barnhill, Theodore, P. Papapanagiotou, and Liliana Schumacher, 2002, “Measuring Integrated Market and Credit Risk in Bank Portfolios: An Application to a Set of Hypothetical Banks Operating in South Africa,” Financial Markets, Institutions and Instruments, Vol. 11, No. 5 (December).
- Barnhill, Theodore, and Liliana Schumacher, forthcoming, “Modeling Correlated Systemic Liquidity and Solvency Risks in a Volatile Environment with Incomplete Information,” IMF Working Paper (Washington: International Monetary Fund).
- Basel Committee on Banking Supervision, 2009, “Revisions to the Basel II Market Risk Framework” (Basel: Bank for International Settlements, July).
- ______, 2010a, “Basel III: International Framework for Liquidity Risk Measurement, Standards and Monitoring” (Basel: Bank for International Settlements, December).
- ______, 2010b, “Results of the Comprehensive Quantitative Impact Study” (Basel: Bank for International Settlements, December).
- Bhutta, Neil, Jane Dokko, and Hui Shan, “Consumer Ruthlessness and Strategic Default During the 2007–2009 Housing Bust”, Federal Reserve Board of Governors, July 2010.
- Black, Fischer, and Myron Scholes, 1973, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, Vol. 81, No. 3, pp. 637–54.
- Brunnermeier, Markus, Andrew Crocket, Charles Goodhart, Martin Hellwig, Avi Persaud, and Hyun Song Shin, 2009, “The Fundamental Principles of Financial Regulation” Geneva Reports on the World Economy 11.
- Brunnermeier, Markus, and Lasse Pedersen, 2009, “Market Liquidity and Funding Liquidity,” Review of Financial Studies, Vol. 22, No. 6, pp. 2201–38.
- Cantor, Richard Martin and Varma, Praveen, 2004, “Determinants of Recovery Rates on Defaulted Bonds and Loans for North American Corporate Issuers: 1983–2003.” Journal of Fixed Income (December).
- Coval, Joshua, and Erik Stafford, 2007, “Asset Fire Sales (and Purchases) in Equity Markets,” Journal of Financial Economics, Vol. 86, pp. 479–512.
- Diamond, Douglas, and Philip Dybvig, 1983, “Bank Runs, Deposit Insurance, and Liquidity.” Journal of Political Economy, Vol. 91, No.3, pp. 401-19 (June).
- Duffie, Darrell, Nicolae Gârleanu, and Lasse Pedersen, 2006, “Valuation in Over-the-Counter Markets,” NBER Working Paper No. 12020 (February).
- Farhi, Emmanuel, Mikhail Golosov, and Aleh Tsyvinski, 2009, “A Theory of Liquidity and Regulation of Financial Intermediation,” Review of Economic Studies, Vol. 76, No. 3, pp. 973–92.
- Financial Times, 2008, “Wholesale Jitters Take Toll on HBOS
,” September 16.
- Gorton, Gary, 1988, “Banking Panics and Business Cycles”. Oxford Economic Papers, New Series, Vol. 40, No. 4 (December), pp. 751-781.
- ______and Andrew Metrick, 2009, “Securitized Banking and the Run on the Repo,” NBER Working Paper No. 15223 (August).
- International Monetary Fund (IMF), 2008, Global Financial Stability Report, World Economic and Financial Surveys (Washington: International Monetary Fund, October).
- ______, 2010, Global Financial Stability Report, World Economic and Financial Surveys (Washington: International Monetary Fund, October).
- ______, and Financial Stability Board (IMF/FSB), 2009, “The Financial Crisis and Information Gaps,” Report to the G-20 Finance Ministers and Central Bank Governors (October).
- ______, and Financial Stability Board (IMF/IMF), 2010, “The Financial Crisis and Information Gaps,” Progress Report, action Plans and Time Tables (May).
- J.P. Morgan, CreditMetrics, 1997.
- Merton, Robert, 1973, “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science, Vol. 4 (Spring), pp. 141–83.
- Shin, Hyun Song, 2009, “Reflections on Modern Bank Runs: A Case Study of Northern Rock,” Journal of Economic Perspectives, Vol. 23, No. 1, pp.101–19.
- Shleifer, Andrei, and Robert Vishny, 2010, “Fire Sales in Finance and Macroeconomics,” NBER Working Paper – 16642.
- Taylor, John B., 2008, “The Financial Crisis and The Policy Respones: An Empirical Analysis of What Went Wrong.” Bank of Canada. A Festschrift in Honour of David Doge. Keynote Speech. (November).
- van den End, Jan Willem, 2008, “Liquidity Stress-Tester: A Macro model for Stress-testing Banks’ Liquidity Risk,” Dutch National Bank Working Paper No. 175 (May).
- Varma, Praveen, and Richard Cantor, 2005, "Determinants of Recovery Rates on Defaulted Bonds and Loans for North American Corporate Issuers: 1983-2003,"Journal of Fixed Income, Vol. 14, No. 4 (March), pp. 29–44.
- Wong, Eric, and Cho-Hoi Hui, 2009, “A Liquidity Risk Stress-Testing Framework with Interaction between Market and Credit Risks,” Hong Kong Monetary Authority Working Paper 06/2009.

*IMF Working Paper _wp11263 — References*

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