## _wp1388

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---

### I. THE NEED FOR MARKET-BASED TOP-DOWN STRESS TESTS
- Context and motivation
  - The global financial crisis experienced in 2008-9 prompted a major shift toward assessing systemic risk and simultaneous defaults in the financial sector.
  - Top-down macro stress tests gained importance (IMF, 2012) but standard top-down tests can be data intensive.
- Purpose of the paper
  - Proposes a simple methodology for conducting structural market-based top-down macro stress tests using market estimates of a bank’s probability of default to calculate the behavior of its capital-to-asset ratio under different macro-stress scenarios.
- Comparison of frameworks
  - Standard top-down stress tests: specify one or more severe macroeconomic scenarios that affect all banks; often assume one-way transmission from the real economy to banks though some frameworks (e.g., RAMSI) allow two-way feedback.
  - Market-based top-down stress tests: use market information on default risk (e.g., probabilities of default) to assess solvency impacts; justified because banks are vulnerable to runs driven by market perceptions.
- Examples and practice
  - U.S. 2009 SCAP assessed nineteen U.S. financial organizations under two macro scenarios; release of results compressed CDS spreads (Figure 1).
  - CCAR: supervisory top-down stress tests used to evaluate and approve bank capital plans.
- Limitations and cautions
  - Market prices may overestimate or underestimate risk because default risk premium is time-varying; illiquid secondary markets can reduce reliability.

### II. DATA CHALLENGES ASSOCIATED WITH TOP-DOWN STRESS TESTS
- Data availability
  - Economic data: publicly available, usually with a lag.
  - Market data (interest rates, bond spreads, CDS): accessible via providers such as Bloomberg or Thomson Reuters Datastream.
  - Financial institutions’ granular data: mainly available in restricted supervisory reports and credit registers (Canatta and Kruger, 2009).
- Implications for different users
  - National central banks/supervisors: can collect granular data from supervised institutions.
  - IMF-World Bank FSAP: benefit from cooperation with national authorities to obtain detailed data.
  - Private sector analysts: often limited to public regulatory filings and annual reports; may need to make assumptions about portfolio composition.
- Methods to obtain probabilities of default
  - Fundamentals-based methods: Altman Z-score, credit scoring, Moody’s RiskCalc using financial ratios.
  - Market-based methods: reverse-engineer asset pricing models from bond yields, CDS spreads, equity prices; produce risk-neutral probabilities that can be transformed into real-world probabilities.
- Note on broader exercise
  - Assembling data is only the first step; scenario design and econometric specification linking economic/financial variables to balance-sheet behavior and probabilities of default are necessary (see cited literature).

### III. METHODOLOGY
- Structural modeling foundation
  - Uses Merton (1974) option-price analogy: equity as a call option on assets.
  - Key relationship (as presented): probability of default p over horizon T associated with capital structure:
    - (1)  T TDV p   )2/()/ln(
      - where V/D is the inverse of the debt to asset ratio, μ and σ are the growth rate and volatility of the asset value.
  - Capital-to-asset ratio derives from debt-to-asset ratio:
    - (2) VDVK/1/ .
  - Monotonicity:
    - (3) 0 ),/( K/V   GVKGp .
- Linking probabilities to scenarios
  - Specify model F linking probability of default to macro variables X and market risk factors M:
    - (4) ).,( ttt MXFp
  - Mapping from scenarios to capital ratios:
    - (5)  ),( / 1 tt MXFGVK   .
- Extensions and calibrations
  - Methodology built on Merton but extendable to stochastic interest rates, jumps, and default barriers.
  - Calibration can use market prices and parameters (e.g., as provided by Moody’s Analytics).

### IV. A NUMERICAL ILLUSTRATION
- Data and sample
  - Individual bank data for thirteen banks in an advanced emerging market economy.
  - Quarterly time-series of probabilities of default over a one-year horizon (Moody’s one-year EDFs) during the period 2006 Q3 to 2012 Q3.
  - EDF: physical (real-world) probability of default combining equity prices, equity volatility, balance sheet data, and Moody’s historical default data (Bohn and Crosbie, 2003).
- EDF descriptive statistics (sample period 2006Q3 – 2012 Q3, in percent)
  - Source: Moody’s Analytics.
  - Minimum / Median / Mean / Maximum / Standard deviation
    - Bank 1 0.05 / 0.79 / 1.56 / 7.25 / 1.97
    - Bank 2 0.03 / 0.47 / 0.65 / 2.64 / 0.71
    - Bank 3 0.06 / 0.25 / 0.40 / 3.03 / 0.59
    - Bank 4 0.05 / 3.74 / 7.46 / 26.04 / 7.67
    - Bank 5 0.05 / 1.15 / 1.60 / 5.59 / 1.64
    - Bank 6 0.07 / 0.30 / 0.73 / 4.64 / 1.16
    - Bank 7 0.09 / 0.62 / 1.09 / 5.87 / 1.26
    - Bank 8 0.03 / 0.20 / 0.28 / 1.28 / 0.29
    - Bank 9 0.02 / 0.28 / 0.31 / 1.08 / 0.26
    - Bank 10 0.06 / 0.20 / 0.51 / 3.09 / 0.82
    - Bank 11 0.03 / 0.33 / 0.79 / 5.27 / 1.18
    - Bank 12 0.03 / 0.28 / 0.40 / 1.44 / 0.39
    - Bank 13 0.18 / 2.84 / 6.41 / 26.11 / 7.92
- EDF dynamics and fitting
  - Most banks experienced sharp EDF increases during 2008 crisis; some solvency problems appeared in second half of 2012 for four banks.
  - Simple non-linear models estimated linking EDF behavior to year-on-year real GDP changes using quarterly data 2006 Q3 to 2012 Q3 (for some banks 2010 Q3–2012 Q3).
  - Three model families fitted:
    - One-term exponential: y = a exp(b x)
    - Rational polynomial: y = (a x + b) / (x + c)
    - Second-degree polynomial: y = a x^2 + b x + c
  - Selected estimated coefficients (95 percent confidence levels shown in brackets) — Source: Moody’s Analytics and author’s calculations.
    - Exponential curves
      - Bank 1: a 10.40 (6.45 ,14.36)  b -0.56 (-0.76 ,-0.36)
      - Bank 2: a 3.19 (1.92 ,4.45)  b -0.45 (-0.62 ,-0.27)
      - Bank 4: a 25.49 (10.39 ,40.59)  b -0.34 (-0.56 ,-0.12)
      - Bank 5: a 5.67 (2.88 ,8.46)  b -0.33 (-0.51 ,-0.15)
      - Bank 8: a 1.60 (1.09 ,2.11)  b -0.52 (-0.67 ,-0.36)
      - Bank 9: a 1.24 (0.97 ,1.51)  b -0.38 (-0.46 ,-0.29)
      - Bank 10: a 9.02 (0.64 ,17.41)  b -0.58 (-0.93 ,-0.23)
      - Bank 12: a 1.84 (1.28 ,2.40)  b -0.42 (-0.55 ,-0.29)
      - Bank 13: a 351.90 (15.15 ,88.65)  b -0.35 (-0.57 ,-0.13)
    - Rational polynomial curve (Bank 6 / Bank 7 shown together in table)
      - a -53.56 (-759.41 ,652.29)  -19.56(-112.67 ,73.55)
      - b 249.71 (-3019.78 ,3519.21)  93.75(-341.96 ,529.47)
      - c 29.82 (-385.67 ,445.31)  8.65(-40.16 ,57.4665)
    - Polynomial curve (Banks 3 and 11)
      - a 0.08 (0.02 ,0.13)  0.15(0.06 ,0.24)
      - b -0.82 (-1.26 ,-0.38)  -1.66(-2.47 ,-0.85)
      - c 2.26 (1.42 ,3.10)  4.62(3.06 ,6.17)
  - Goodness-of-fit: fit described as “quite good” despite single explanatory macro variable; noted counterintuitive increases in default probabilities for growth rates > 7 percent for two banks (not realized in scenarios).
- Scenario design and calibration
  - Structural model parameters set equal to those calculated by Moody’s Analytics by end-2012.
  - Four five-year scenarios considered: Baseline; V-shaped recession; Double-dip (two-year recession); L-shaped recession.
  - Macro scenarios — GDP growth year-on-year (selected quarterly values as presented)
    - Baseline / V-shaped recession / Double dip recession / L-shaped recession
      - 2012 Q3 1.78 / 1.80 / 1.80 / 1.80
      - 2012 Q4 0.94 / 0.94 / 0.96 / 0.95
      - 2013 Q1 1.14 / -0.14 / 0.36 / 0.14
      - 2013 Q2 1.49 / -1.78 / -0.52 / -1.01
      - 2013 Q3 1.87 / -3.24 / -1.28 / -1.99
      - 2013 Q4 2.33 / -3.89 / -1.63 / -2.46
      - 2014 Q1 2.25 / -2.74 / -1.47 / -2.14
      - 2014 Q2 2.32 / -0.36 / -0.52 / -1.01
      - 2014 Q3 2.36 / 2.00 / 0.33 / -0.05
      - 2014 Q4 2.40 / 3.66 / 1.02 / 0.55
      - 2015 Q1 2.72 / 4.35 / 2.03 / 1.43
      - 2015 Q2 2.89 / 4.38 / 2.60 / 1.83
      - 2015 Q3 2.92 / 3.99 / 2.97 / 2.03
      - 2015 Q4 2.98 / 3.60 / 3.26 / 2.28
      - 2016 Q1 3.20 / 3.54 / 3.42 / 2.33
      - 2016 Q2 3.40 / 3.58 / 3.58 / 2.39
      - 2016 Q3 3.43 / 3.62 / 3.61 / 2.32
      - 2016 Q4 3.39 / 3.66 / 3.55 / 2.16
      - 2017 Q1 3.42 / 3.76 / 3.59 / 2.15
      - 2017 Q2 3.45 / 3.84 / 3.64 / 2.21
      - 2017 Q3 3.48 / 3.91 / 3.68 / 2.26
      - 2017 Q4 3.47 / 3.91 / 3.64 / 2.26
- Results: impact on capital-to-asset ratios
  - Using equation (5) and estimated non-linear EDF models, changes in banks’ capital-to-asset ratios relative to 2012 Q3 were computed.
  - General pattern: capital-to-asset ratio fell during first two years of recession scenarios and often recovered when growth resumed.
  - Magnitude: declines ranged from 20 percent to 60 percent for some banks, making it possible that some banks could default (capital-to-asset becomes non-positive) or breach minimum regulatory capital ratios under additional assumptions (e.g., asset values remain constant).
  - Figure 6 presented per-bank changes under Baseline, V-shape, Double Dip, and L-shape scenarios; in some banks results indicated “Default” under severe scenarios.

### V. CONCLUSIONS
- Role and trade-offs
  - Top-down stress tests are important tools for monitoring systemic risks; standard top-down tests require granular banking data that may be unavailable to many analysts.
  - Market-based top-down stress tests offer an alternative using historical probabilities of default and market data to model responses to macro and market risk factors.
- Contribution of the structural market-based approach
  - Mapping from changes in probability of default to changes in capital structure is achieved via a structural model of default risk, enabling assessment of regulatory capital-ratio breaches.
- Caveats and complementarities
  - Market prices can be influenced by default-risk premia, liquidity risk premia, and potential market manipulation.
  - Market prices can react faster to new information and may reflect run dynamics driven by expectations; hence market-based structural top-down stress tests can complement standard tests, especially when detailed portfolio data are unavailable.

*Source: _wp1388 - References (IMF working paper; extracted content provided).*

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

### References

### I. THE NEED FOR MARKET-BASED TOP-DOWN STRESS TESTS
- Context and motivation
  - The global financial crisis experienced in 2008-9 prompted a major shift toward assessing systemic risk and simultaneous defaults in the financial sector.
  - Top-down macro stress tests gained importance (IMF, 2012) but standard top-down tests can be data intensive.
- Purpose of the paper
  - Proposes a simple methodology for conducting structural market-based top-down macro stress tests using market estimates of a bank’s probability of default to calculate the behavior of its capital-to-asset ratio under different macro-stress scenarios.
- Comparison of frameworks
  - Standard top-down stress tests: specify one or more severe macroeconomic scenarios that affect all banks; often assume one-way transmission from the real economy to banks though some frameworks (e.g., RAMSI) allow two-way feedback.
  - Market-based top-down stress tests: use market information on default risk (e.g., probabilities of default) to assess solvency impacts; justified because banks are vulnerable to runs driven by market perceptions.
- Examples and practice
  - U.S. 2009 SCAP assessed nineteen U.S. financial organizations under two macro scenarios; release of results compressed CDS spreads (Figure 1).
  - CCAR: supervisory top-down stress tests used to evaluate and approve bank capital plans.
- Limitations and cautions
  - Market prices may overestimate or underestimate risk because default risk premium is time-varying; illiquid secondary markets can reduce reliability.

### II. DATA CHALLENGES ASSOCIATED WITH TOP-DOWN STRESS TESTS
- Data availability
  - Economic data: publicly available, usually with a lag.
  - Market data (interest rates, bond spreads, CDS): accessible via providers such as Bloomberg or Thomson Reuters Datastream.
  - Financial institutions’ granular data: mainly available in restricted supervisory reports and credit registers (Canatta and Kruger, 2009).
- Implications for different users
  - National central banks/supervisors: can collect granular data from supervised institutions.
  - IMF-World Bank FSAP: benefit from cooperation with national authorities to obtain detailed data.
  - Private sector analysts: often limited to public regulatory filings and annual reports; may need to make assumptions about portfolio composition.
- Methods to obtain probabilities of default
  - Fundamentals-based methods: Altman Z-score, credit scoring, Moody’s RiskCalc using financial ratios.
  - Market-based methods: reverse-engineer asset pricing models from bond yields, CDS spreads, equity prices; produce risk-neutral probabilities that can be transformed into real-world probabilities.
- Note on broader exercise
  - Assembling data is only the first step; scenario design and econometric specification linking economic/financial variables to balance-sheet behavior and probabilities of default are necessary (see cited literature).

### III. METHODOLOGY
- Structural modeling foundation
  - Uses Merton (1974) option-price analogy: equity as a call option on assets.
  - Key relationship (as presented): probability of default p over horizon T associated with capital structure:
    - (1)  T TDV p   )2/()/ln(
      - where V/D is the inverse of the debt to asset ratio, μ and σ are the growth rate and volatility of the asset value.
  - Capital-to-asset ratio derives from debt-to-asset ratio:
    - (2) VDVK/1/ .
  - Monotonicity:
    - (3) 0 ),/( K/V   GVKGp .
- Linking probabilities to scenarios
  - Specify model F linking probability of default to macro variables X and market risk factors M:
    - (4) ).,( ttt MXFp
  - Mapping from scenarios to capital ratios:
    - (5)  ),( / 1 tt MXFGVK   .
- Extensions and calibrations
  - Methodology built on Merton but extendable to stochastic interest rates, jumps, and default barriers.
  - Calibration can use market prices and parameters (e.g., as provided by Moody’s Analytics).

### IV. A NUMERICAL ILLUSTRATION
- Data and sample
  - Individual bank data for thirteen banks in an advanced emerging market economy.
  - Quarterly time-series of probabilities of default over a one-year horizon (Moody’s one-year EDFs) during the period 2006 Q3 to 2012 Q3.
  - EDF: physical (real-world) probability of default combining equity prices, equity volatility, balance sheet data, and Moody’s historical default data (Bohn and Crosbie, 2003).
- EDF descriptive statistics (sample period 2006Q3 – 2012 Q3, in percent)
  - Source: Moody’s Analytics.
  - Minimum / Median / Mean / Maximum / Standard deviation
    - Bank 1 0.05 / 0.79 / 1.56 / 7.25 / 1.97
    - Bank 2 0.03 / 0.47 / 0.65 / 2.64 / 0.71
    - Bank 3 0.06 / 0.25 / 0.40 / 3.03 / 0.59
    - Bank 4 0.05 / 3.74 / 7.46 / 26.04 / 7.67
    - Bank 5 0.05 / 1.15 / 1.60 / 5.59 / 1.64
    - Bank 6 0.07 / 0.30 / 0.73 / 4.64 / 1.16
    - Bank 7 0.09 / 0.62 / 1.09 / 5.87 / 1.26
    - Bank 8 0.03 / 0.20 / 0.28 / 1.28 / 0.29
    - Bank 9 0.02 / 0.28 / 0.31 / 1.08 / 0.26
    - Bank 10 0.06 / 0.20 / 0.51 / 3.09 / 0.82
    - Bank 11 0.03 / 0.33 / 0.79 / 5.27 / 1.18
    - Bank 12 0.03 / 0.28 / 0.40 / 1.44 / 0.39
    - Bank 13 0.18 / 2.84 / 6.41 / 26.11 / 7.92
- EDF dynamics and fitting
  - Most banks experienced sharp EDF increases during 2008 crisis; some solvency problems appeared in second half of 2012 for four banks.
  - Simple non-linear models estimated linking EDF behavior to year-on-year real GDP changes using quarterly data 2006 Q3 to 2012 Q3 (for some banks 2010 Q3–2012 Q3).
  - Three model families fitted:
    - One-term exponential: y = a exp(b x)
    - Rational polynomial: y = (a x + b) / (x + c)
    - Second-degree polynomial: y = a x^2 + b x + c
  - Selected estimated coefficients (95 percent confidence levels shown in brackets) — Source: Moody’s Analytics and author’s calculations.
    - Exponential curves
      - Bank 1: a 10.40 (6.45 ,14.36)  b -0.56 (-0.76 ,-0.36)
      - Bank 2: a 3.19 (1.92 ,4.45)  b -0.45 (-0.62 ,-0.27)
      - Bank 4: a 25.49 (10.39 ,40.59)  b -0.34 (-0.56 ,-0.12)
      - Bank 5: a 5.67 (2.88 ,8.46)  b -0.33 (-0.51 ,-0.15)
      - Bank 8: a 1.60 (1.09 ,2.11)  b -0.52 (-0.67 ,-0.36)
      - Bank 9: a 1.24 (0.97 ,1.51)  b -0.38 (-0.46 ,-0.29)
      - Bank 10: a 9.02 (0.64 ,17.41)  b -0.58 (-0.93 ,-0.23)
      - Bank 12: a 1.84 (1.28 ,2.40)  b -0.42 (-0.55 ,-0.29)
      - Bank 13: a 351.90 (15.15 ,88.65)  b -0.35 (-0.57 ,-0.13)
    - Rational polynomial curve (Bank 6 / Bank 7 shown together in table)
      - a -53.56 (-759.41 ,652.29)  -19.56(-112.67 ,73.55)
      - b 249.71 (-3019.78 ,3519.21)  93.75(-341.96 ,529.47)
      - c 29.82 (-385.67 ,445.31)  8.65(-40.16 ,57.4665)
    - Polynomial curve (Banks 3 and 11)
      - a 0.08 (0.02 ,0.13)  0.15(0.06 ,0.24)
      - b -0.82 (-1.26 ,-0.38)  -1.66(-2.47 ,-0.85)
      - c 2.26 (1.42 ,3.10)  4.62(3.06 ,6.17)
  - Goodness-of-fit: fit described as “quite good” despite single explanatory macro variable; noted counterintuitive increases in default probabilities for growth rates > 7 percent for two banks (not realized in scenarios).
- Scenario design and calibration
  - Structural model parameters set equal to those calculated by Moody’s Analytics by end-2012.
  - Four five-year scenarios considered: Baseline; V-shaped recession; Double-dip (two-year recession); L-shaped recession.
  - Macro scenarios — GDP growth year-on-year (selected quarterly values as presented)
    - Baseline / V-shaped recession / Double dip recession / L-shaped recession
      - 2012 Q3 1.78 / 1.80 / 1.80 / 1.80
      - 2012 Q4 0.94 / 0.94 / 0.96 / 0.95
      - 2013 Q1 1.14 / -0.14 / 0.36 / 0.14
      - 2013 Q2 1.49 / -1.78 / -0.52 / -1.01
      - 2013 Q3 1.87 / -3.24 / -1.28 / -1.99
      - 2013 Q4 2.33 / -3.89 / -1.63 / -2.46
      - 2014 Q1 2.25 / -2.74 / -1.47 / -2.14
      - 2014 Q2 2.32 / -0.36 / -0.52 / -1.01
      - 2014 Q3 2.36 / 2.00 / 0.33 / -0.05
      - 2014 Q4 2.40 / 3.66 / 1.02 / 0.55
      - 2015 Q1 2.72 / 4.35 / 2.03 / 1.43
      - 2015 Q2 2.89 / 4.38 / 2.60 / 1.83
      - 2015 Q3 2.92 / 3.99 / 2.97 / 2.03
      - 2015 Q4 2.98 / 3.60 / 3.26 / 2.28
      - 2016 Q1 3.20 / 3.54 / 3.42 / 2.33
      - 2016 Q2 3.40 / 3.58 / 3.58 / 2.39
      - 2016 Q3 3.43 / 3.62 / 3.61 / 2.32
      - 2016 Q4 3.39 / 3.66 / 3.55 / 2.16
      - 2017 Q1 3.42 / 3.76 / 3.59 / 2.15
      - 2017 Q2 3.45 / 3.84 / 3.64 / 2.21
      - 2017 Q3 3.48 / 3.91 / 3.68 / 2.26
      - 2017 Q4 3.47 / 3.91 / 3.64 / 2.26
- Results: impact on capital-to-asset ratios
  - Using equation (5) and estimated non-linear EDF models, changes in banks’ capital-to-asset ratios relative to 2012 Q3 were computed.
  - General pattern: capital-to-asset ratio fell during first two years of recession scenarios and often recovered when growth resumed.
  - Magnitude: declines ranged from 20 percent to 60 percent for some banks, making it possible that some banks could default (capital-to-asset becomes non-positive) or breach minimum regulatory capital ratios under additional assumptions (e.g., asset values remain constant).
  - Figure 6 presented per-bank changes under Baseline, V-shape, Double Dip, and L-shape scenarios; in some banks results indicated “Default” under severe scenarios.

### V. CONCLUSIONS
- Role and trade-offs
  - Top-down stress tests are important tools for monitoring systemic risks; standard top-down tests require granular banking data that may be unavailable to many analysts.
  - Market-based top-down stress tests offer an alternative using historical probabilities of default and market data to model responses to macro and market risk factors.
- Contribution of the structural market-based approach
  - Mapping from changes in probability of default to changes in capital structure is achieved via a structural model of default risk, enabling assessment of regulatory capital-ratio breaches.
- Caveats and complementarities
  - Market prices can be influenced by default-risk premia, liquidity risk premia, and potential market manipulation.
  - Market prices can react faster to new information and may reflect run dynamics driven by expectations; hence market-based structural top-down stress tests can complement standard tests, especially when detailed portfolio data are unavailable.

*Source: _wp1388 - References (IMF working paper; extracted content provided).*

### References

### References

### Stress testing, systemic stability, and supervisory reports
- Alessandri, Piergiorgio, Prasanna Gai, Sujit Kapadia, Nada Mora, and Claus Puhr, 2009, “Towards a Framework for Quantifying Systemic Stability,” International Journal of Central Banking, Vol. 5, No. 3, pp. 47–81.
- Board of Governors of the Federal Reserve Ssytem, 2009, “The Supervisory Capital Assessment Program: Design and Implementation” (Washington, D.C.)
- Burrows, Oliver, David Learmonth, and Jack McKeown, 2012, “RAMSI: A Top Down Stress Testing Model,” Financial Stability Paper No. 17 (London: Bank of England).
- Canatta, Francesco, and Ulrich Kruger, 2009, “Data Needs for Stress-Testing,” in Mario Quagliarello, editor, Stress Testing the Banking System: Methodologies and Applications (Cambridge, England: Cambridge University Press).
- Foglia, Antonella, 2009, “Stress Testing Credit Risk: A Survey of Authorities’ Approaches,” Vol. 5, No. 3, pp. 9–45.
- Glasserman, Paul, Chulmin Kang, and Wanmo Kang, 2012, “Stress Scenario Selection by Empirical Likelihood,” mimeo, Columbia University and Korea Advanced Institute of Science and Technology.
- Greenlaw, David, Anil K. Kashyap, Kermit Schoenholtz, and Hyun Song Shin, 2012, “Stressed Out: Macroprudential Principles for Stress Testing,” Chicago Booth Paper No. 12-08 (The University of Chicago, Booth School of Business).
- Hamerle, Alfred, Rainer Jobst, Michael Knapp, and Matthias Lerner, 2008, “Stress-Testing Credit Value-at-Risk: A Multiyear Approach,” in Daniel Rosch and Harald Scheule, editors, Stress Testing for Financial Institutions: Applications, Regulations and Techniques (London: Risk Books).
- International Monetary Fund, 2012, “Macrofinancial Stress Testing – Principles and Practices,” August 22 (Washington, D.C.).
- International Monetary Fund and the World Bank, 2005, Financial Sector Assessment: A Handbook (Washington, D.C.).
- Quagliarello, Mario, editor, 2009, Stress Testing the Banking System:Methodologies and Applications (Cambridge, England: Cambridge University Press).
- Rosch, Daniel, and Harald Scheule, editors, 2008, Stress Testing for Financial Institutions: Applications, Regulations and Techniques (London: Risk Books).
- Ferry, Danielle H., Tony Hughes, and Min Ding, 2012a, “Stressed EDFTM Credit Measures,” Modeling Methodology, May (Moody’s Analytics).
- Ferry, Danielle H., Tony Hughes, and Ming Ding, 2012b, “Stressed EDF Credit Measures for Western Europe,” Modeling Methodology (Moody’s Analytics).
- Chan-Lau, Jorge A., 2013, Systemic Risk Assessment and Oversight (London: Risk Books).
- Chan-Lau, Jorge A., and Amadou N.R. Sy, 2007, “Distance-to-Default in Banking: A Bridge Too Far?” Journal of Banking Regulation, Vol. 9, No 1, pp. 14–24.
- Burrows, Oliver, David Learmonth, and Jack McKeown, 2012, “RAMSI: A Top Down Stress Testing Model,” Financial Stability Paper No. 17 (London: Bank of England).

### Credit risk modeling, valuation, and portfolio risk
- Altman, Edward, and Edith Hotchkiss, 2006, Corporate Financial Distress and Bankruptcy, 3rd edition (Hoboken, New Jersey: John Wiley and Sons).
- Bielecki, Tomasz R., and Marek Rutkowski, 2002, Credit Risk: Modeling, Valuation and Hedging (Berlin: Springer Verlag).
- Bohn, Jeffrey R., and Peter Crosbie, 2003, “Modeling Default Risk: Modeling Methodology,” Moody’s KMV.
- Bohn, Jeffrey R., and Roger M. Stein, 2009, Active Credit Portfolio Management in Practice (Hoboken, New Jersey: John Wiley and Sons).
- Duffie, Darrell J., and Kenneth S. Singleton, 2003, Credit Risk: Pricing, Measurement, and Management (Princeton, New Jersey: Princeton University Press).
- Lando, David, 2004, Credit Risk Modeling: Theory and Applications (Princeton, NJ: Princeton University Press).
- Wilson, Thomas C., 1997a, “Portfolio Credit Risk I,” Risk, Vol. 10, No. 9, pp. 111–117.
- Wilson, Thomas C., 1997b, “Portfolio Credit Risk II,” Risk, Vol. 10, No. 10, pp. 56–61.
- Zandi, Mark, 2011, “The Moody’s Analytics US Macroeconomic Model,” (Moody’s Analytics).

### Foundational option pricing and structural credit models
- Black, Fischer, and Myron S. Scholes, 1973, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, Vol. 81, No. 3, pp. 637–54.
- Merton, Robert C., 1974, “On the Pricing of Corporate Debt: the Risk Structure of Interest Rates,” Journal of Finance, Vol. 29, No. 2, pp. 449–70.

*Source: _wp1388 - References*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp1388.pdf_