## _wp13218

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---

### I. Introduction and CCA-GVAR framework
- Goal: develop a framework to analyze interactions between banking sector risk, sovereign risk, corporate sector risk, growth, and credit for a large sample of banks and countries.
- Framework components:
  - Contingent Claims Analysis (CCA) to construct forward-looking risk indicators for banks, banking systems, sovereigns, and corporate sectors.
  - Global Vector Autoregressive (GVAR) model to combine CCA indicators with real GDP growth and credit growth, allowing full endogenous interactions.
- Model coverage and aggregation:
  - Comprises 15 EU countries and the United States; set up for 16 countries, 16 banking sectors, comprising 53 individual banks (41 EU banks plus 12 U.S. banks).
  - Five-variable model includes banking system CCA risk indicators, sovereign risk indicators, corporate sector risk indicators, economic growth and credit to the private sector.
- Data and estimation sample:
  - Monthly sample covering the period from January 2002 to December 2012 (132 observations).
- Uses:
  - Conduct scenario simulations (multiple shocks to selected sovereigns and banking systems), including positive and negative shock scenarios.
  - Scenario responses feed banking/sovereign sub-modules to compute aggregate loss estimates and changes in bank capital.
  - Analytical purpose: examine shocks, spillovers, and tradeoffs among policy alternatives (examples: bank liquidity injections, bank capital increases, purchase of sovereign debt, guarantees of bank senior debt by sovereigns, guarantees of sovereigns by other public bodies).

### II. Rationale, literature linkages, and model choice
- Motivations and channels:
  - Financial sector distress and government contingent liabilities/bailouts are closely linked and affect sovereign credit risk, credit growth, lending/borrowing rates, corporate and household finances, consumption, investment and economic growth.
  - Direct and indirect channels transmit risk within and across countries and sectors.
- Model selection trade-offs:
  - Structural CCA models capture non-linear feedbacks but are difficult to calibrate for multi-country analyses.
  - GVAR models are well suited for macroeconomic interrelationships and can incorporate forward-looking CCA indicators.
  - Integration advantages: CCA indicators are forward-looking market-based measures combining leverage, asset volatility, and risk appetite; sector-level aggregation keeps model tractable.

### III. Contingent Claims Analysis (CCA) methodology — core mechanics and formulas
- Conceptual identities:
  - Asset identity: A = E + D where equity E is modeled as a call option on assets with exercise price equal to default barrier B; risky debt equals default-free debt minus expected loss due to default (implicit put option on assets).
  - Risky Debt = Default-free Debt − Expected Loss Value (ELV) (Equation (1) notation).
- Key formula relations (as presented in source):
  - Yield on risky debt: y = ln/BD yT   (Equation (2) notation).
  - Credit spread expression: s = ln/1 ln(1) rT BD sy    r T ELV r TBe          (Equation (3) notation).
  - Expected loss ratio definition: EL = 1   exp() rT sT ELV Be          (Equation (4) notation) — EL equals the risk neutral default probability (RNDP) times Loss Given Default (LGD).
- Calibration inputs for banks and corporates:
  - Market capitalization values and volatility (historical or from equity options), default barrier estimates from promised debt payments, the risk-free rate, time horizon, and balance sheet debt information.
  - The implicit put option (ELV) is computed from implied asset value and volatility, then used to derive fair-value spreads and expected loss ratios.
- Moody’s KMV / CreditEdge specifics:
  - EDFs, distance-to-distress, and conversions from one-year to five-year cumulative EDFs via Equation (25).
  - Fair Value CDS (FVCDS) computed using sector-average LGD and risk-neutral CEDF (Equation (27)); Expected loss ratio: risk neutral CEDF LGD EL   (Equation (28)).
  - Distinction between risk-neutral and real-world default probabilities linked via market price of risk λ (Equation (23) and (24)).

### IV. Bank/corporate expected loss measures, FVCDS and market distortions
- Expected loss measures:
  - Expected loss ratios have a five year horizon (T=5), monthly frequency, and are expressed in basis points.
  - FVCDS from Moody’s CreditEdge used to obtain bank-by-bank expected loss ratio bEL and corporate expected loss ratio cEL.
- Observed distortions:
  - Implicit and explicit government backing depress observed bank CDS spreads relative to fair value spreads (CCA/FVCDS), especially during crisis periods.
  - Two common distortion patterns:
    - Observed CDS < FVCDS because of implicit/explicit government guarantees.
    - Observed CDS > FVCDS where sovereign spreads are very high, due to sovereign spillovers.
  - Example implications: MKMV implied LGD needed to match observed CDS for some banks in Greece would have to be as high as 160 percent (not sensible); implied LGD > 0.7 considered evidence of sovereign spillover.
- Aggregation:
  - Banking system expected loss ratio ,bs j EL = sum over banks of ωibELib (Equation (5) notation).
  - Corporate sector expected loss ratio ,cs j EL = sum over corporates of ωicELic (Equation (6) notation).
  - Monthly banking and corporate sector aggregate EL ratios for each country are used in the GVAR model; sector EL responses can be disaggregated back to individual firms via initial weights.

### V. GVAR model implementation, data, and sub-modules
- GVAR inputs and dimensionality:
  - Inputs: 16 CCA banking system risk indicators, 16 CCA sovereign credit risk indicators, 16 CCA corporate credit risk indicators, GDP data (16 series), credit data (16 series), and other variables.
  - With five endogenous variables and 16 countries, global model has 80 equations.
  - GDP interpolated from quarterly to monthly by quadratic match sum conversion.
  - ELs are the expected loss ratio at a five year horizon.
- Post-GVAR sub-modules and outputs:
  - Scenario Simulation → GVAR Model → Scenario Responses → Banking Module, Sovereign Module, Corporate Module, Fiscal and Growth Module, EU and Euro Zone aggregates.
  - Banking Module outputs: Expected Losses and spreads, bank-by-bank funding cost impacts, implied market capital impact, government contingent liabilities.
  - Sovereign Module outputs: Expected Losses, credit spreads.
  - Fiscal/Growth outputs: contingent liabilities, borrowing cost changes, Debt to GDP changes.
- Weight matrices:
  - Estimated weight matrices for Real GDP, Credit Growth, Expected Loss Ratio Sovereigns, Expected Loss Ratio Banking Systems, Expected Loss Ratio Corporate Sectors (available from authors upon request).

### VI. Scenario definitions and key T=1 (impact) results
- Scenario definitions:
  - Scenario One—Adverse Shocks to EL Sovereigns in Italy and Spain
  - Scenario Two—Adverse Shocks to EL Banking Systems in Italy and Spain
  - Scenario Three—Positive Shocks to EL Sovereigns in Italy and Spain
  - Scenario Four—Positive shocks to EL banking systems in Italy and Spain
- Implied shock sizes and selected T=1 absolute outcomes (tabulated entries as presented):
  - Adverse shock to Spanish (ES) and Italian (IT) sovereigns: 5 percent marginal; joint 0.7 percent; implied EL relative 18.4% and 19.6%; implied EL absolute 253 and 260 (basis points).
  - Adverse shock to Spanish (ES) and Italian (IT) banking systems: 5 percent marginal; joint 0.8 percent; implied EL relative 15.0% and 24.3%; implied EL absolute 275 and 665 (basis points).
  - Positive shock to Spanish (ES) and Italian (IT) sovereigns: 5 percent marginal; joint 1.6 percent; implied EL relative -23.7% and -21.8%; implied EL absolute -325 and -290 (basis points).
  - Positive shock to Spanish (ES) and Italian (IT) banking systems: 5 percent marginal; joint 0.8 percent; implied EL relative -31.5% and -64.9%; implied EL absolute -576 and -1,774 (basis points).
- Scenario One — Adverse sovereigns (selected T=1 impacts):
  - Italy and Spain ELs increase by about 250–260 basis points on impact (December 2012 reference).
  - Greece sovereign EL ratio increases by approximately 700 basis points at T=1.
  - Banking system EL spillovers: Ireland, Spain, Greece, Italy and Portugal with EL responses between 160–370 basis points.
  - Corporate sector ELs at T=1: Portugal, Spain, Greece, and Ireland with deviations between 46–150 basis points.
  - Real GDP T=1 falls between -0.6 percent (Spain) and -1.4 percent (Greece).
  - Credit T=1 contractions: -0.5 percent (Greece) to -1.4 percent (Italy).
  - Maximum cumulative deviations: Greek sovereign FVCDS would move beyond 10,000 basis points; Ireland and Portugal sovereign FVCDS ≈ 250 basis points; Italy and Spain banking systems cumulative ≈ 140 basis points; Greece cumulative GDP contraction -1.9 percent; Ireland cumulative credit contraction -5.1 percent.
- Scenario Two — Adverse banking systems (selected T=1 impacts):
  - Marginal probabilities 5 percent; joint 0.8 percent.
  - Shock sizes to EL ratios for the two countries: 665 and 275 basis points, respectively.
  - Portugal simulated response at T=1: sovereign +370 basis points; banking system +690 basis points.
  - Corporate ELs: Italy, Portugal, France and Greece with shocks between 90 and 175 basis points.
  - Cumulative deviations: sovereigns 30–110 basis points (Belgium to Portugal); banking systems 160–290 basis points (Belgium to Portugal); corporate up to 90 basis points for Portugal.
  - GDP cumulative contraction up to -0.5 percent for Italy.
  - Credit to private sector cumulative contraction close to -2.5 percent for Spain.
- Scenario Three — Positive sovereigns:
  - Marginal probabilities 5 percent; joint 1.6 percent.
  - ELs for Italy and Spain fall by about 290–352 basis points on impact.
  - Greek sovereign EL ratio falls by about 700 basis points at T=1.
  - Banking systems: Belgium EL decreases by almost 1,000 basis points at T=1.
  - Corporate sector responses range between -35 basis points (Portugal) and -350 basis points (Spain).
  - Cumulative minimum fair-value spread deviations: sovereigns -70 to -310 basis points; banking systems cumulative -500 to -900 basis points (Italy and Belgium); corporate median -65 to -400 basis points (Belgium to Greece).
  - Greece cumulative GDP impact estimated at 5.5 percent.
  - Cumulative credit growth surpasses 8 percent for Ireland.
- Scenario Four — Positive banking systems:
  - Marginal probabilities 5 percent; joint 0.8 percent.
  - ELs for banks in Italy and Spain fall by about 1,700–580 basis points on impact.
  - Italy’s end-sample EL ratio of 2,730 basis points would fall by 65 percent.
  - Sovereigns and banks in Greece, Belgium, and Portugal benefit notably: sovereign EL fall -230 basis points for Portugal and -800 basis points for Greece; banking system ELs decrease ~800 basis points for Belgium and -2,300 for Greece.
  - Corporate sectors benefiting include Italy, Portugal, Spain and Greece with EL responses between -135 and -180 basis points.
  - Real GDP T=1: Spain’s GDP rises by +0.9 percent.
  - Credit growth T=1: credit in Spain grows by 2.7 percent.
  - Cumulative observations: Portugal’s and Belgium’s sovereigns move back into the safe zone (< 400 basis points); their banking system fair value spreads remain elevated: 770 basis points for Belgium and 550 basis points for Portugal.
- Comparative inference:
  - Positive impulses to sovereign risk have more potential to compress jointly banks’ and sovereigns’ risk (fair value credit spreads) when scenarios are comparable probabilistically.
  - Across scenarios, bank credit spread responses are generally more pronounced than sovereign risk measures; corporate sector is generally the least affected.

### VII. Nonlinear relationships and "safe zones" (Box 1 empirical summaries)
- Empirical nonlinearities for a typical bank (CreditEdge sample ~ three years):
  - High CCACR of 0.8 to 0.9 (8 or 9 percent):
    - EDF is very low.
    - EL is low (around 0.05, or 500 bps).
    - Credit spreads are low (around 100 bps).
  - Distress periods when CCACR falls from 0.3 to 0.1:
    - EDF is very high (6 to 7 percent).
    - Spreads reach about 700 to 900 bps.
    - EL is 0.3 to 0.4 (3000 to 4000 bps).
  - Once CCACR below 3 percent:
    - EDF increases over 1 percent.
    - Spreads start exceeding a 250 bps “threshold”.
    - EL is higher than 1000 bps.
- Regression snippets cited (as in source):
  - y = 0.1217x 1.0815 R² = 0.9987 (EL Ratio (in bps) plot)
  - y = 320.9x 0.5 R² = 0.829 (Fair Value Spread (bps) plot)
  - y = 0.0272x -0.265 R² = 0.8541 (Expected Default Frequency (EDF in %) plot)
  - y = 0.9854x -0.494 R² = 0.7648 (Mkt Cap/Assets Ratio (CCACR in %) plot)
- Safe zones and thresholds:
  - Central safe zone — investment grade and above:
    - CCACR 3 percent and above
    - EL of 1000 bps or less
    - Spreads less than 200 bps
    - EDF of less than 0.5 percent
  - Slightly larger safe zone (below investment grade):
    - EDFs less than 1.5 percent
    - Spreads 400 bps or less
    - EL less than 2000 bps
    - CCACR above 2.5 percent
- Ratings and spreads:
  - Investment grade defined as ratings BBB- and higher.
  - Spreads of 400 bps or less correspond to EDFs of about 1.5–2 percent and ratings of B or higher.
  - Sharp increase in spreads and EDFs below rating B indicates significant non-linearity.

### VIII. Policy levers, risk mitigation options and framework extensions
- Risk mitigation instruments (from source list):
  - Increase market capital; increase regulatory capital; increase solvency ratio.
  - Increase assets, change asset composition and lower asset volatility.
  - Guarantees on bank senior debt; asset protection guarantees.
  - Guarantees or insurance or selling CDS protection on sovereign debt.
  - Debt purchases by public entity (SMP/OMT, EFSF/ESM, other).
  - Debt purchases by banks (e.g., LTRO).
  - Debt equity conversion / Bail-in; extending debt maturity or restructuring.
  - EU wide deposit insurance; EU wide bank resolution; mutualize/socialize existing and/or new sovereign debt.
- Framework extensions suggested:
  - Consider alternative thresholds/criteria for the ‘low risk zone’.
  - Adapt framework for conditional/unconditional forecasting of CCA-GVAR model variables.
  - Include additional fiscal variables.
  - Employ a regime-switching GVAR to allow state-dependent simulated shock scenarios.
  - Evaluate changes in FVCDS spreads on market capital and CCA capital ratio for banking systems and individual banks.
  - Simulate counterfactual scenarios assuming unconventional policy active/inactive or program status activated/deactivated.
  - Assess out-of-sample forecast performance and switch sectorial linkages off to examine channel contributions to forecast accuracy.

### IX. Conclusions — key takeaways (as stated in source)
- The CCA-GVAR framework links forward-looking CCA risk indicators in a multi-country GVAR to analyze interplay across banking, sovereign, corporate sectors, real activity and credit growth.
- Empirical setup: 13 EU countries plus Norway, Switzerland, and the United States; sample period January 2002 to December 2012.
- Adverse shock findings:
  - A negative shock to sovereigns in Italy and Spain is more potent than a negative shock to their banking systems in inducing adverse responses across sovereigns, banks, and corporates.
  - Real activity and credit contract markedly under adverse sovereign shocks.
- Positive shock findings:
  - Positive impulses to sovereign risk have more potential to compress jointly banks’ and sovereigns’ risk (fair value credit spreads).
- Cross-scenario ordering:
  - Bank credit spread responses are generally more pronounced than sovereign risk measures; corporate sector is generally the least affected.

*Source content drawn from _wp13218 - References (PDF), sections I–VII and appendices as provided.*

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

### _wp13218 - References

### I. Introduction and overview of CCA-GVAR framework
- Goal: develop a framework to analyze interactions between banking sector risk, sovereign risk, corporate sector risk, growth, and credit for a large sample of banks and countries.
- Framework components:
  - Contingent Claims Analysis (CCA) to construct forward-looking risk indicators for banks, banking systems, sovereigns, and corporate sectors.
  - Global Vector Autoregressive (GVAR) model to combine CCA indicators with real GDP growth and credit growth, allowing full endogenous interactions.
- Model coverage and aggregation:
  - Comprises 15 EU countries and the United States.
  - Set up for 16 countries, 16 banking sectors, comprising 53 individual banks (41 EU banks plus 12 U.S. banks).
  - Five-variable model includes banking system CCA risk indicators, sovereign risk indicators, corporate sector risk indicators, economic growth and credit to the private sector.
- Data and estimation sample:
  - Monthly sample covering the period from January 2002 to December 2012 (132 observations).
- Uses of the framework:
  - Conduct scenario simulations (multiple shocks to selected sovereigns and banking systems), including positive and negative shock scenarios.
  - Scenario responses feed banking/sovereign sub-modules to compute aggregate loss estimates and changes in bank capital.
  - Analytical purpose: examine shocks, spillovers, and tradeoffs among policy alternatives (examples of policies include bank liquidity injections, bank capital increases, purchase of sovereign debt, guarantees of bank senior debt by sovereigns, guarantees of sovereigns by other public bodies).

### II. Rationale, literature linkages, and model choice
- Motivations:
  - Financial sector distress and government contingent liabilities/bailouts are closely linked and affect sovereign credit risk, credit growth, lending/borrowing rates, corporate and household finances, consumption, investment and economic growth.
  - Direct and indirect channels transmit risk within and across countries and sectors.
- Relationship to literature and modeling alternatives:
  - Structural CCA models capture non-linear feedbacks between sovereign and banking sector risk but are difficult to calibrate for multi-country, multidimensional analyses.
  - Asset pricing approaches relate asset price declines to changes in risk premiums and macro variables (e.g., Gabaix 2008).
  - Econometric and VAR approaches link financial risk indicators to macro variables; Global VAR models are well suited for macroeconomic interrelationships and can include financial risk indicators.
  - Network models and factor-augmented VARs can incorporate CCA indicators; trade-offs exist between tractability for macro analysis and detailed micro-network representation.
- Advantages of integrating CCA with GVAR:
  - CCA indicators are forward-looking (market-based), combine leverage, asset volatility, and risk appetite into a single indicator, and can be transformed into credit spreads.
  - Sector-level aggregation keeps model size manageable for multi-country macro analysis.

### III. Contingent Claims Analysis (CCA) methodology and key formulas
- CCA description:
  - A risk-adjusted balance sheet framework where asset value A equals equity market value E plus risky debt D.
  - Assets are stochastic; equity is modeled as a call option on assets with exercise price equal to the default barrier B.
  - Risky debt equals default-free debt minus expected loss due to default (implicit put option on assets).
- Core identity:
  - Risky Debt = Default-free Debt − Expected loss due to default
  - Expressed: rT DBeELV    (Equation (1) notation from source)
- Yield on risky debt:
  - y = ln/BD yT   (Equation (2) notation from source)
- Credit spread expression:
  - s = ln/1 ln(1) rT BD sy    r T ELV r TBe          (Equation (3) notation from source)
- Expected loss ratio definition:
  - EL = 1   exp() rT sT ELV Be          (Equation (4) notation from source)
  - Note: The expected loss ratio equals the risk neutral default probability (RNDP) times Loss Given Default (LGD) (as described in Appendix I).
- Calibration inputs for banks and corporates:
  - Market capitalization values and volatility (historical or from equity options), default barrier estimates from promised debt payments, the risk-free rate, time horizon, and balance sheet debt information.
  - The implicit put option (expected loss value, ELV) is computed from implied asset value and volatility, then used to derive fair-value spreads and expected loss ratios.

### IV. Bank and corporate expected loss measures, fair-value spreads, and observed distortions
- Use of Moody’s CreditEdge:
  - Moody’s CreditEdge database provides a long time series of risk indicators and a Fair Value CDS spread (FVCDS) that serves as a proxy for the model-implied fair value spread.
  - FVCDS is used to obtain bank-by-bank expected loss ratio bEL and corporate expected loss ratio cEL.
- Expected loss ratio details:
  - Expected loss ratios have a five year horizon (T=5), monthly frequency, and are expressed in basis points.
- Observed market distortions and interpretation:
  - Implicit and explicit government backing depress observed bank CDS spreads relative to fair value spreads (CCA/FVCDS), especially during crisis periods.
  - Empirical findings from the literature: during 2008–2009, fair value spreads from CCA were often higher than observed market CDS spreads for banks (examples cited: Gray et al. 2008, Gapen 2009, Moody’s Analytics 2011, Gray and Jobst 2011, Schweikhard and Tsemelidakis 2012).
  - Two common distortion patterns:
    - Observed CDS spreads of banks are lower than fair-value spreads because of implicit/explicit government guarantees.
    - For banks in countries with very high sovereign spreads, observed bank CDS is frequently higher than the bank fair value spread due to sovereign spillovers.
- Interpretation of FVCDS:
  - FVCDS and associated expected loss ratios are described as “purer” forward-looking measures of bank risk because they are less distorted by government guarantees or sovereign spillovers (i.e., situations where FVCDS > CDS or CDS > FVCDS are identifiable).

### V. Model implementation, outputs, and sub-modules
- GVAR model structure:
  - GVAR consists of 16 local country models combined with weighting matrices and cross-country linkages (trade and credit channels).
  - Inputs to the GVAR include CCA banking system risk indicators (16), CCA sovereign credit risk indicators (16), CCA corporate credit risk indicators (16), GDP data (16 series), credit data (16 series), and other variables.
- Post-GVAR sub-modules and outputs:
  - Scenario Simulation → GVAR Model → Scenario Responses, which feed:
    - Banking Module: banking system responses (Expected Losses and spreads), bank-by-bank output results (funding cost impacts, Expected Losses, implied market capital impact, government contingent liabilities).
    - Sovereign Module: sovereign output results (Expected Losses, credit spreads, other).
    - Corporate Module: corporate output results (Expected Losses, credit spreads).
    - Fiscal and Growth Module: contingent liabilities, borrowing cost changes, Debt to GDP changes.
    - EU and Euro Zone aggregates: aggregate banking and sovereign debt expected losses, aggregate bank capital impact.
- Use cases:
  - Quantify spillovers between sovereigns and banks, between countries, and measure macroeconomic impacts (GDP growth and credit growth) under alternative shock scenarios.

*Italic: Source content drawn from _wp13218 - References (PDF), sections I–II as provided.*

### Box 1. Relationships between CCA Capital Ratio, EDF, FVCDS and Expected Loss Ratio

### Box 1. Relationships between CCA Capital Ratio, EDF, FVCDS and Expected Loss Ratio for a Typical Bank

### Nonlinear relationships between CCACR, EDF, FVCDS, and EL
- The typical pattern is compiled from a data sample covering approximately three years from the CreditEdgePlus database (Moody’s).
- Key empirical points:
  - If the CCACR is high, 0.8 to 0.9 (8 or 9 percent):
    - EDF is very low.
    - EL is low (around 0.05, or 500 bps).
    - Credit spreads are low (around 100 bps).
  - In distress periods, when the CCACR falls from 0.3 to 0.1:
    - EDF is very high (6 to 7 percent).
    - Spreads reach about 700 to 900 bps.
    - EL is 0.3 to 0.4 (equal to 3000 to 4000 bps).
  - Once the capital ratio starts moving below 3 percent:
    - EDF increases over 1 percent.
    - Spreads start exceeding a 250 bps “threshold”.
    - EL is higher than 1000 bps.
    - There is increasing risk of negative shocks leading to sharply higher spreads and EDFs.
- The dynamics are non-linear.
- Empirical regression snippets shown in Figure 2 (as in the source):
  - y = 0.1217x 1.0815 R² = 0.9987 (EL Ratio (in bps) plot)
  - y = 320.9x 0.5 R² = 0.829 (Fair Value Spread (bps) plot)
  - y = 0.0272x -0.265 R² = 0.8541 (Expected Default Frequency (EDF in %) plot)
  - y = 0.9854x -0.494 R² = 0.7648 (Mkt Cap/Assets Ratio (CCACR in %) plot)

### Safe zones and thresholds (interpretation of Figure 2)
- Central (safest) zone — investment grade and above:
  - CCACR 3 percent and above
  - EL of 1000 bps or less
  - Spreads less than 200 bps
  - EDF of less than 0.5 percent
- Slightly larger safe zone (just below investment grade):
  - EDFs less than 1.5 percent
  - Spreads are 400 bps or less
  - EL is less than 2000 bps
  - CCACR is above 2.5 percent

### Relationships of ratings, EDFs, and spreads (summary of Figure 3)
- Investment grade defined as ratings BBB- and higher.
- Spreads of 400 bps or less correspond to EDFs of about 1.5–2 percent and ratings of B or higher.
- Sharp increase in spreads and EDFs below rating B indicates significant non-linearity: once rating becomes sub-investment grade, spreads and default probabilities increase sharply as ratings decline further.

### Aggregation of Expected Loss Ratios for Banking Systems and Corporate Sector (Section B)
- For country j, compute weighted averages of expected loss ratios of major banks/corporates using market value of assets as weights.
- Banking system expected loss ratio: ,bs j EL
  - Equation (5) as given in the source:
    ,,
    1
    x
    bs  jib i
    ELEL
    
- Corporate sector expected loss ratio: ,cs j EL
  - Equation (6) as given in the source:
    ,,
    1
    x
    cs  jic i
    ELEL
    
- Monthly banking and corporate sector aggregate EL ratios for each country are used in the GVAR model.
- Sector EL responses can be transformed back into EL for individual banks and corporates using the initial weights; individual EL responses can be related to changes in capital, EDF, spreads (and the Expected Loss Value, the implicit put option described earlier).
- Note: Household ELs (mortgage and other debt) are desirable but data are not available for all countries.

### Sovereign CCA Expected Loss Ratio (Section C)
- Equity values unavailable for sovereigns, so actual market sovereign CDS spreads are used (assume no guarantor; CDS reflects sovereign credit risk).
- The CDS spread for a sovereign (as well as banks and corporate) is a function of the time horizon and the expected loss ratio.
- Formula for the sovereign CDS, expressed in basis points, as given in the source:
  - (7)                                    
    1
    10000*[ln(1)]
    sovsov
    T
    CDSEL
- Solving for the expected loss ratio for the sovereign as a function of time horizon and sovereign CDS value given in the source:
  - (8)                                 
    1   exp(  ()/ 10000)
    sovSov
    CDSTEL
- For sovereigns, the five-year CDS is used since it is the most liquid.
- Transmission channels emphasized:
  - Mark-to-market fall in sovereign bond values held by banks reduces bank assets and can increase bank-funding costs.
  - Severe sovereign distress can erode value of official support (guarantees) → knock-on contagion effects → potential systemic financial and sovereign debt crises.
  - Recapitalization funded by increased sovereign borrowing increases sovereign risk.
- Note references to further details on sovereign CCA framework and risk transmission in Appendix I (as per source).

### Using EL in the GVAR framework and policy levers
- Benefit: shocks to EL can be related to shocks to CCA capital ratio, EDF and spreads; model output responses can be transformed from EL to corresponding changes in capital ratios, EDFs, and spreads.
- The “safe zone” can be thought of as a target zone achievable via combinations of policies:
  - Capital injections
  - Increasing the level and lowering asset volatility
  - Risk transfer policies (described in more detail later in the source)

### Data inputs and model integration (summary from later sections)
- CCA-GVAR model variables: real GDP, credit to the private sector, sovereign EL, national banking system EL, corporate sector EL.
- Data frequency and sample:
  - Monthly frequency
  - January 2002 to December 2012 (132 observations)
  - 16 countries (13 EU countries plus Norway, Switzerland and the U.S.)
- GDP interpolated from quarterly to monthly by quadratic match sum conversion.
- With five endogenous model variables and 16 countries, global model has 80 equations.
- ELs are the expected loss ratio at a five year horizon.
- Example: Figure 4 (Italy) shows sovereign, banking system, and corporate ELs expressed in basis points, alongside real GDP and credit growth (yoy rates); banking sector EL spikes when real activity sharply dropped over 2008–2009.

*Source: Moody’s CreditEdge data and author estimates (content as presented in the supplied PDF).*

### Appendix IV, we transform the relative changes back to absolute EL basis point changes by

### Appendix IV, we transform the relative changes back to absolute EL basis point changes by

### Implied shock sizes and T=1 responses
- Implied shock sizes at T=1 (EL relative) and Implied shock sizes at T=1 (EL absolute in basis points) appear in the source tables.
- Tabulated entries (as extracted from the source):
  - Adverse shock to Spanish (ES) and Italian (IT) sovereigns5%0.7%18.4%19.6%253260
  - Adverse shock to Spanish (ES) and Italian (IT) banking systems5%0.8%15.0%24.3%275665
  - Positive shock to Spanish (ES) and Italian (IT) sovereigns5%1.6%-23.7%-21.8%-325-290
  - Positive shock to Spanish (ES) and Italian (IT) banking systems5%0.8%-31.5%-64.9%-576-1,774
- Note: A ranking of severity based on absolute EL measures is partly reflective of the start point levels of EL taken as reference (December 2012).

### Shock Scenario One—Adverse Shock to Sovereigns in Italy and Spain
- Marginal shock probabilities set to 5 percent; joint probability of 0.7 percent.
- ELs for Italy and Spain increase by about 250–260 basis points on impact (December 2012 reference).
- Greece sovereign EL ratio increases by approximately 700 basis points at T=1.
- Spillovers to banking system ELs: Ireland, Spain, Greece, Italy and Portugal with EL responses ranging between 160–370 basis points.
- Corporate sector ELs at T=1: Portugal, Spain, Greece, and Ireland attain highest ranks with deviations ranging between 46–150 basis points.
- GDP and credit T=1 impacts:
  - GDP falls by between -0.6 percent (Spain) and -1.4 percent (Greece) in the first month.
  - Credit to the private sector for top five affected countries contracts by -0.5 percent (Greece) and -1.4 percent (Italy) in the first month.
- Maximum cumulative deviations (Appendix VI) highlights:
  - Greek sovereign maximum cumulative fair-value CDS would move beyond 10,000 basis points (not plotted).
  - Ireland and Portugal simulated sovereign fair value CDS responses equal about 250 basis points.
  - Italian and Spanish banking systems rank sixth and seventh with cumulative maximum responses around 140 basis points.
  - Corporate sector response for Greece equals 210 basis points.
  - Greece’s GDP cumulatively contracts by -1.9 percent.
  - Ireland’s credit to the private sector contracts by -5.1 percent.

### Shock Scenario Two—Adverse Shock to Banking Systems in Italy and Spain
- Marginal probabilities set to 5 percent; joint probability of 0.8 percent.
- Shock sizes to EL ratios for the two countries: 665 and 275 basis points, respectively.
- T=1 shock profiles:
  - Peripheral countries strongly affected; selected countries (Sweden, Norway, Austria, France, Germany) show EL indicators falling on impact (French sovereign EL falls by about 70 basis points).
  - Portugal simulated response at T=1: sovereign +370 basis points; banking system +690 basis points.
- Corporate sector ELs: Italy, Portugal, France and Greece with shocks ranging between 90 and 175 basis points.
- Cumulative deviations:
  - Sovereign deviations range between 30 basis points (Belgium) and 110 basis points (Portugal).
  - Banking system deviations range between 160 basis points (Belgium) and 290 basis points (Portugal).
  - Corporate sector responses approach 90 basis points for Portugal.
  - GDP cumulative contraction up to -0.5 percent for Italy.
  - Credit to private sector contracts by close to -2.5 percent for Spain.

### Shock Scenario Three—Positive Shock to Sovereigns in Italy and Spain
- Marginal shock probabilities set to 5 percent; joint probability of 1.6 percent.
- ELs for Italy and Spain fall by about 290–352 basis points on impact.
- Greek sovereign EL ratio falls by about 700 basis points at T=1.
- Banking systems: Belgium EL decreases by almost 1,000 basis points at T=1.
- Corporate sector responses range between -35 basis points (Portugal) and -350 basis points (Spain).
- Cumulative minimum (most negative) fair-value spread deviations:
  - Sovereign fair value spreads fall by between -70 basis points (Belgium) and -310 basis points (Portugal).
  - Banking system cumulative deviations range between -500 and -900 basis points for Italy and Belgium, respectively.
  - Corporate sector median responses range between -65 basis points (Belgium) and -400 basis points (Greece).
  - Greece cumulative GDP impact estimated at 5.5 percent.
  - Cumulative credit growth surpasses 8 percent for Ireland.

### Shock Scenario Four—Positive Shock to Banking Systems in Italy and Spain
- Marginal shock probabilities set to 5 percent; joint probability of 0.8 percent.
- ELs for banks in Italy and Spain fall by about 1,700–580 basis points on impact.
- Italy’s end-sample EL ratio of 2,730 basis points would fall by 65 percent.
- Sovereigns and banks in Greece, Belgium, and Portugal benefit notably:
  - Sovereign EL fall by -230 basis points for Portugal and -800 basis points for Greece.
  - Banking system ELs decrease by close to 800 basis points for Belgium and -2,300 for Greece.
- Corporate sectors benefiting include Italy, Portugal, Spain and Greece with EL responses ranging between -135 and -180 basis points.
- Real GDP T=1 responses: Spain’s GDP rises by +0.9 percent upon arrival of the shock.
- Credit growth responses: credit in Spain grows by 2.7 percent.
- Cumulative observations:
  - Portugal’s and Belgium’s sovereigns move back into the safe zone (< 400 basis points).
  - Their banking system fair value spreads remain at elevated levels: 770 basis points for Belgium and 550 basis points for Portugal.
- Comparative inference: Positive impulses to sovereign risk have more potential to compress jointly banks’ and sovereigns’ risk (fair value credit spreads) when scenarios are comparable probabilistically.

### Risk Mitigation Policies, Extensions and Applications
- Drivers of CCA risk indicators: asset value and volatility, default barrier, and leverage.
- Ways to mitigate risk (lower EL and reduce spreads) include:
  - Increase market capital; increase regulatory capital; increase solvency ratio.
  - Increase assets, change asset composition and lower asset volatility.
  - Guarantees on bank senior debt; asset protection guarantees.
  - Guarantees or insurance or selling CDS protection on sovereign debt.
  - Debt purchases by public entity (SMP/OMT, EFSF/ESM, other).
  - Debt purchases by banks (e.g., LTRO).
  - Debt equity conversion / Bail-in; extending debt maturity or restructuring.
  - EU wide deposit insurance; EU wide bank resolution; mutualize/socialize existing and/or new sovereign debt.
- Specific quantitative references in the source:
  - Box 1 and Figure 2 referenced for magnitudes of changes in EL (figures/tables in source).
- Framework extensions suggested:
  - Consider alternative thresholds/criteria for the ‘low risk zone’.
  - Adapt framework for conditional/unconditional forecasting of CCA-GVAR model variables.
  - Include additional fiscal variables.
  - Employ a regime-switching GVAR to allow state-dependent simulated shock scenarios.
  - Evaluate changes in FVCDS spreads on market capital and CCA capital ratio for banking systems and individual banks.
  - Simulate counterfactual scenarios assuming unconventional policy active/inactive or program status activated/deactivated.
  - Assess out-of-sample forecast performance and switch sectorial linkages off to examine channel contributions to forecast accuracy.

### Conclusions (key takeaways)
- The CCA-GVAR framework links forward-looking CCA risk indicators in a multi-country GVAR to analyze interplay across banking, sovereign, corporate sectors, real activity and credit growth.
- Empirical setup: 13 EU countries plus Norway, Switzerland, and the United States; sample period January 2002 to December 2012.
- Adverse shock findings:
  - A negative shock to sovereigns in Italy and Spain is more potent than a negative shock to their banking systems in inducing adverse responses across sovereigns, banks, and corporates.
  - Real activity and credit contract markedly under adverse sovereign shocks.
- Positive shock findings:
  - Positive impulses to sovereign risk have more potential to compress jointly banks’ and sovereigns’ risk (fair value credit spreads).
- Across scenarios, bank credit spread responses are generally more pronounced than sovereign risk measures; corporate sector is generally the least affected.

*Source: _wp13218 - Appendix IV, we transform the relative changes back to absolute EL basis point changes by*

### APPENDIX I. CONTINGENT CLAIMS ANALYSIS

### APPENDIX I. CONTINGENT CLAIMS ANALYSIS

### A. Contingent Claims Analysis: Merton Model — overview and mechanics
- Core idea: Default occurs when market value of assets, A, falls below a distress barrier, B (typically defined as all short-term debt plus a fraction of long-term debt).
- In a risk-adjusted (CCA) balance sheet: A = E + D where E is equity market value and D is risky debt.
- Equity is modeled as an implicit call option on assets with exercise price equal to the default barrier, B.
- Risky Debt = Default-free Debt − Expected Loss Value (ELV).
  - Equation (17): rT DBeELV  
- The ELV is the value of a put option on A with exercise price B, time horizon T, risk-free rate r, and asset volatility σA.
- Calibration: use market equity value, E, and equity volatility, σE, plus the distress barrier to solve for asset value A and asset volatility σA via two equations (equations 18 and 19).
  - Equation (18): 12 N( )N( ) rT EA dBed  
  - Equation (19): 1 () EA EA N dσσ
  - Intermediate terms d1 and d2 defined in (20):
    - 1 2 ln 2 A A A r B d T T σ σ    (first d)
    - 2 2 ln 2 A A A r B d T T σ σ    (second d)
- Once A and σA are known, ELV is computed from:
  - Equation (21): 201 (()) rT ELVA N dBeN d  
- Risk-neutral probability of default is 2 ()Nd .
- Credit spread formula:
  - Equation (22): 1 ln(1) T sEL 
- Expected Loss (EL) related formula given:
  - 2 () * rT ELV ELNdLGD Be   

Key points on inputs and interpretation:
- Equity and equity volatility are forward-looking, market-based inputs.
- Asset value is unobservable but implied through the above CCA/Merton calibration.
- The ELV (implicit put) captures the present value of expected loss due to default.

### B. Moody’s Model Overview (KMV / CreditEdge)
- KMV adapted Merton’s approach for commercial use in the 1990s; KMV purchased by Moody’s in 2002.
- Moody’s CreditEdge provides daily data on EDFs, market value of assets, risk indicators for tens of thousands of institutions and corporations worldwide.
- EDF calculation: iterative procedure solving for asset volatility using equity return volatility, equity values, distress barrier from book liabilities, and a time horizon to obtain distance-to-distress and map to expected default probabilities (EDFs).
- Moody’s CreditEdge coverage: daily EDFs for 35,000 corporations and financial institutions in 55 countries.
- Distinction between risk-neutral and real-world default probabilities:
  - Risk-neutral distance-to-default: d2, default prob = 2 ()Nd with asset drift r.
  - Real-world distance-to-default: d2,μ, default prob = 2, ()Ndμ with asset drift μA.
- Relationship via market price of risk λ:
  - Equation (23): 2,2 ()()N dN dt μ λ   
- CAPM-based estimate of λ used by CreditEdge:
  - Equation (24): , A AM A r SR λ ρ σ μ   
  - CreditEdge data: ,AM ρ has fluctuated around 0.5 to 0.7 and SR was 0.6 before the crisis and reached a high of 1.2 at the peak of the 2008–09 crisis.
- Converting EDFs and computing fair-value measures:
  - One-year to cumulative five-year conversion:
    - Equation (25): 5 51 1 (1) yryr CEDF EDF    
  - Cumulative risk-neutral EDF formula:
    - Equation (26): ( ) 1, risk neutral TA M CEDFN NCEDFSR T ρ   
  - Fair Value CDS (FVCDS) computed using sector-average LGD (banking sector average for banks; respective corporate sector LGD for corporates).
    - Equation (27): ( ) 1 ln 1 risk neutral FVCDS CEDF LGD T   
  - Expected loss ratio:
    - Equation (28): risk neutral CEDF LGD EL  

Empirical and interpretive findings from CreditEdge:
- In normal periods, observed CDS and FVCDS are equal or close.
- During 2008–2009 financial crisis, explicit and implicit government guarantees depressed observed CDS such that FVCDS > observed CDS.
- Difference between FVCDS and observed CDS can be interpreted as market-implied government contingent liabilities.
- Examples and LGD implications:
  - For some banks in Greece and Portugal, observed bank CDS spreads have surpassed FVCDS spreads since the sovereign crisis began in Europe in 2010.
  - MKMV implied LGD needed to match observed CDS spreads would have to be as high as 160 percent (example for banks in Greece) — an LGD exceeding 100 percent is not sensible.
  - For many banks the MKMV implied LGD needed to match observed CDS is about 1.3 to 1.6; an LGD of 0.7 may be plausible, so any implied LGD higher than 0.7 is evidence of sovereign spillover.
- Data sample used for bank analysis: 53 banks from CreditEdge database, distributed as:
  - 12 in United States, 5 in United Kingdom, 1 in Austria, 2 in Belgium, 1 in Denmark, 4 in France, 2 in Germany, 4 in Greece, 2 in Ireland, 3 in Italy, 4 in Netherlands, 1 in Norway, 3 in Portugal, 3 in Spain, 4 in Sweden, and 2 in Switzerland.

### C. Sovereign–bank spillovers and feedback loops
- Mechanisms of interaction:
  - Mark-to-market fall in sovereign bond values held by domestic banks reduces bank assets.
  - This raises bank funding costs and can erode perceived official support (guarantees).
  - Erosion of guarantees increases deposit withdrawals or funding cutoff risk, triggering higher bank spreads.
  - Higher bank distress increases government contingent liabilities (guarantee costs), raising sovereign spreads.
- Adverse feedback loop: sovereign stress ↔ banking-sector stress can create a vicious cycle, potentially spiraling into systemic financial crisis and sovereign debt crisis if government capacity to honor guarantees is strained.
- Figure conceptual summary (textual):
  - Spillovers from the sovereign to banks: A. Mark-to-market fall in value of govt bonds held by local banks; B. Increase in bank funding costs; C. Erosion in potential for official support; D. Mark-to-market fall in value of govt. bonds held by foreign banks; E. Similar sovereigns come under pressure; F. Contagion channels (A, B, & C); G. Rise in counter-party credit risk; H. Withdrawal of funding for risky banks; I. Increase in contingent liabilities of govt.
- Empirical observation: When sovereign spreads are high, they “spill over” into bank spreads, often pushing observed CDS above FVCDS; this indicates weakened perceived guarantees and direct sovereign-to-bank contagion.

### D. Weight matrices (GVAR estimation) — note and contents
- The appendix includes estimated weight matrices for:
  - Real GDP
  - Credit Growth
  - Expected Loss Ratio Sovereigns
  - Expected Loss Ratio Banking Systems
  - Expected Loss Ratio Corporate Sectors
- Note: "The weight matrices presented here have been estimated jointly with the GVAR’s other parameters. Weight error bounds are not reported here; they are available from the authors upon request. See text for further details."

*Source: APPENDIX I. CONTINGENT CLAIMS ANALYSIS, _wp13218 - APPENDIX I. CONTINGENT CLAIMS ANALYSIS*

### APPENDIX III. INPUT DATA FOR THE CCA-GVAR MODEL

### APPENDIX III. INPUT DATA FOR THE CCA-GVAR MODEL

### Data sources and variables
- Source: Moody’s CreditEdge, Eurostat, and author estimates.
- Risk indicators and series used (per country):
  - EL_CORP_<country code>
  - EL_SOV_<country code>
  - EL_FIN_<country code>
  - Credit growth (rhs)
  - GDP growth (rhs)
- Country coverage (examples shown): Austria, Belgium, Denmark, France, Germany, Greece, Ireland, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom, United States.
- Sample period axis labels shown: 2002M01 through 2012M09.

### Time-series ranges and axes (examples preserved exactly as shown)
- Percentage axis ticks repeated across country charts include values such as:
  - -30%, -20%, -15%, -10%, -8%, -6%, -5%, -4%, -3.5%, -3.0%, -2.5%, -2.0%, -1.6%, -1.4%, -1.2%, -1.0%, -0.8%, -0.6%, -0.5%, -0.4%, -0.3%, -0.2%, -0.1%, 0.0%, 0.1%, 0.2%, 0.3%, 0.4%, 0.5%, 0.6%, 0.8%, 1.0%, 1.5%, 2.0%, 2.5%, 3.0%, 4.0%, 6.0%, 8.0%, 10.0%, 12.0%, 14.0%, 15.0%, 20.0%, 25.0%, 30.0%, 35.0%, 40.0%
- Absolute value (rhs) axes in level units vary by country chart (examples preserved):
  - 0, 200, 400, 600, 800, 1000, 1200, 1400, 1500, 1600, 1800, 2000, 2500, 3000, 3500, 4000, 4500, 5000, 6000, 7000, 8000, 10000, >10,000

### Notes on Appendix III content
- Appendix III presents country-by-country panels that combine EL sovereign, bank, and corporate expected loss (EL_) series with credit growth and GDP growth series for the period labeled 2002M01–2012M09.
- Charts label the three EL series and the two macro series consistently: EL_CORP_<code>, EL_SOV_<code>, EL_FIN_<code>, Credit growth (rhs), GDP growth (rhs).

*Source: _wp13218 - APPENDIX III. INPUT DATA FOR THE CCA-GVAR MODEL (Moody’s CreditEdge, Eurostat, and author estimates).*

---

### APPENDIX IV. SCENARIO PROFILES ON IMPACT AT T=1

### Scenario definitions (titles preserved exactly)
- Scenario One—Adverse Shocks to EL Sovereigns in Italy and Spain
- Scenario Two—Adverse Shocks to EL Banking Systems in Italy and Spain
- Scenario Three—Positive Shocks to EL Sovereigns in Italy and Spain
- Scenario Four—Positive shocks to EL banking systems in Italy and Spain

### Variables and depiction at T=1 (elements preserved)
- For each scenario the following variables are presented (Absolute (left axis/blue) and Relative (right axis/green)):
  - EL SOVEREIGNS
  - EL BANKS
  - EL CORPORATE
  - Real GDP
  - Credit
- Country code order shown on panels (examples preserved in captions):
  - Scenario One EL SOVEREIGNS: GR IT ES PT IE NL UK CH DE FR US NO SE AT DK BE
  - Scenario One EL BANKS: IE ES GR IT PT UK NL SE DE CH FR US NO DK BE AT
  - Scenario One EL CORPORATE: PT ES GR IE AT NL DK BE IT DE CH SE US UK FR NO
  - Scenario One Real GDP: GR IE ES NO IT NL PT SE FR AT BE US CH DE UK DK
  - Scenario One Credit: IT FR IE ES GR NO BE SE NL PT DK CH UK AT US DE
- Numeric axis labels shown in the scenario profile panels (examples preserved exactly):
  - %-axes: -20%, -15%, -12%, -10%, -7%, -6%, -5%, -4%, -3%, -2.5%, -2.0%, -1.6%, -1.5%, -1.4%, -1.2%, -1.0%, -0.8%, -0.6%, -0.5%, -0.4%, -0.3%, -0.2%, -0.1%, 0.0%, 0.1%, 0.2%, 0.3%, 0.4%, 0.5%, 0.6%, 0.8%, 1.0%, 1.5%, 2.0%, 2.5%, 3.0%, 3.5%, 4.0%, 5.0%, 8.0%, 13.0%, 18.0%, 25.0%, 30.0%
  - Absolute axes examples: -100, 0, 100, 200, 300, 400, 500, 600, 700, 800 (EL SOVEREIGNS panel); -300, -200, -100, 0, 100, 200, 300, 400 (EL BANKS panel); -40, -20, 0, 20, 40, 60, 80, 100, 120, 140, 160 (EL CORPORATE panel)

### Source
- Source: Author estimates.

*Source: APPENDIX IV. SCENARIO PROFILES ON IMPACT AT T=1 (author estimates).*

---

### APPENDIX V. DYNAMIC SCENARIO RESPONSES

### Presentation structure
- Dynamic responses shown across horizons (panel tick labels 1,3,5,7,9,11,13,15,17,19,21,23 corresponding to plotted time points).
- For each scenario the following series are plotted over the horizon:
  - Credit
  - Real GDP
  - EL BANKS (relative)
  - EL CORPORATE (relative)
  - EL SOVEREIGNS (relative)
- Country order shown on panels (consistent list): AT, BE, CH, DE, DK, ES, FR, GR, IE, IT, NL, NO, PT, SE, UK, US.

### Axis and numeric ranges preserved exactly (selected examples by scenario)
- Scenario One:
  - Credit axis: -3.5% to 1.5% with ticks including -3.5%, -3.0%, -2.5%, -2.0%, -1.5%, -1.0%, -0.5%, 0.0%, 0.5%, 1.0%, 1.5%
  - Real GDP axis: -1.6% to 0.6% with ticks including -1.6%, -1.4%, -1.2%, -1.0%, -0.8%, -0.6%, -0.4%, -0.2%, 0.0%, 0.2%, 0.4%, 0.6%
  - EL BANKS (relative) axis: -100% to 40% with ticks -100%, -80%, -60%, -40%, -20%, 0%, 20%, 40%
  - EL CORPORATE (relative) axis: -40% to 60% with ticks -40%, -30%, -20%, -10%, 0%, 10%, 20%, 30%, 40%, 50%, 60%
  - EL SOVEREIGNS (relative) axis: -80% to 100% with ticks -80%, -60%, -40%, -20%, 0%, 20%, 40%, 60%, 80%, 100%
- Scenario Two:
  - Credit axis: -2.5% to 2.0% with ticks -2.5%, -2.0%, -1.5%, -1.0%, -0.5%, 0.0%, 0.5%, 1.0%, 1.5%, 2.0%
  - Real GDP axis: -0.6% to 0.6% with ticks -0.6%, -0.4%, -0.2%, 0.0%, 0.2%, 0.4%, 0.6%
  - EL BANKS (relative) axis: -80% to 40%
  - EL CORPORATE (relative) axis: -40% to 20%
  - EL SOVEREIGNS (relative) axis: -70% to 30%
- Scenario Three:
  - Credit axis: -1.0% to 2.5%
  - Real GDP axis: -0.5% to 2.0%
  - EL BANKS (relative) axis: -50% to 30%
  - EL CORPORATE (relative) axis: -40% to 20%
  - EL SOVEREIGNS (relative) axis: -60% to 20%
- Scenario Four:
  - Credit axis: -3.0% to 3.0%
  - Real GDP axis: -0.8% to 1.0%
  - EL BANKS (relative) axis: -80% to 80%
  - EL CORPORATE (relative) axis: -15% to 40%
  - EL SOVEREIGNS (relative) axis: -40% to 100%

### Source
- Source: Author estimates.

*Source: APPENDIX V. DYNAMIC SCENARIO RESPONSES (author estimates).*

---

### APPENDIX VI. MAXIMUM CUMULATIVE IMPULSE RESPONSES ALONG TWO-YEAR HORIZON

### Scenarios and variables reported (titles preserved)
- Scenario One—Negative Shocks to EL Sovereigns in Italy and Spain
- Scenario Two—Negative Shocks to EL Banking Systems in Italy and Spain
- Scenario Three—Positive Shocks to EL Sovereigns in Italy and Spain
- Scenario Four—Positive Shocks to EL Banking Systems in Italy and Spain

### Metrics presented (per scenario)
- For each scenario, maximum cumulative impulse responses along a two-year horizon are reported for:
  - SOVEREIGNS: Absolute FVCDS (left axis/blue) and Relative EL (right axis/green)
  - BANKS: Absolute FVCDS (left axis/blue) and Relative EL (right axis/green)
  - CORPORATE: Absolute FVCDS (left axis/blue) and Relative EL (right axis/green)
  - Real GDP (percent)
  - Credit (percent)
- Selected numeric axis markers preserved exactly (examples):
  - Sovereigns absolute/relative axes example: 0% to 100% and 0 to 400 (absolute), labels include 0, 50, 100, 150, 200, 250, 300, 350, 400
  - Banks absolute axis example: 0 to 700 with ticks 0, 100, 200, 300, 400, 500, 600, 700; relative axes include percentages up to 30% or negative percentages shown in other scenarios
  - Corporate absolute axes example: 0 to 250 with ticks 0, 50, 100, 150, 200, 250; relative axes example: -6.0% to 1.0% (Real GDP), -6.0% to 10.0% (Credit) depending on scenario
  - Scenario Three banks absolute example: -3,708 and negative percent ranges such as -160% to 0% shown explicitly on panels
  - Scenario Four banks absolute example: -987 and axis ticks showing -800 to 400

### Source
- Source: Author estimates.

*Source: APPENDIX VI. MAXIMUM CUMULATIVE IMPULSE RESPONSES ALONG TWO-YEAR HORIZON (author estimates).*

---

### APPENDIX VII. SIGNIFICANCE OF SCENARIO RESPONSES

### Purpose and note
- The table indicates whether maximum/minimum responses (maximum/minimum depending on the variables’ stress orientation and the type of the scenario) were significant at a 1 percent, 5 percent, or 10 percent level. See text for details.

### Significance summary (matrix-style entries preserved as coded in source)
- EL SOV:
  - Scenario 1: 1 10 5 10 10 10 5
  - Scenario 2: 1 0 5 10
  - Scenario 3: 5 10 10 5
  - Scenario 4: 10 10 10 10 10 10 10 10 10 10
- EL FIN:
  - Scenario 1: 1 5 5 5 5 5 5 5 5 5 5
  - Scenario 2: 2 5 10 10
  - Scenario 3: 1 0 105
  - Scenario 4: 1 0 5
- EL CORP:
  - Scenario 1: 1 10 10 1 0 5 10 10 10 10
  - Scenario 2: 2 10 105 10
  - Scenario 3: 3 10 55
  - Scenario 4: 4 10 10
- GDP:
  - Scenario 1: 1 5 10 5 5 10
  - Scenario 2: 2 5 10 10
  - Scenario 3: 3 10 55
  - Scenario 4: 4 10 10 10 5 10 10 10
- CREDIT:
  - Scenario 1: 1 5 15 15 15 10 10 15
  - Scenario 2: 2 5 10 10
  - Scenario 3: 3 5 10 1
  - Scenario 4: 4 10 5 5

(Note: entries above are transcribed exactly as they appear in the source table block; they indicate significance coding per scenario and series.)

### Source
- Source: Author estimates.

*Source: APPENDIX VII. SIGNIFICANCE OF SCENARIO RESPONSES (author estimates).*

### REFERENCES

### _wp13218 - REFERENCES

### Key references on sovereign, bank, and systemic risk measurement
- Acharya, V., I. Drechsler, P. Schnabl, 2011, “A Pyrrhic Victory? – Bank Bailouts and Sovereign Credit Risk”, NBER Working Paper 17136, NBER Cambridge MA.
- Bohn, J., 2000, “An Empirical Assessment of a Simple Contingent Claims Model for the Valuation of Risky Debt,” Journal of Risk Finance, 1, pp. 55–77.
- Gapen M. T., Gray, D. F., Lim C. H., Xiao Y., 2005, “Measuring and Analyzing Sovereign Risk with Contingent Claims,” IMF Staff Papers Volume 55.
- Gapen M. T., 2009, “Evaluating the implicit guarantee to Fannie Mae and Freddie Mac using contingent claims” in Credit, Capital, Currency, and Derivatives: Instruments of Global FinancialStability or Crisis? (International Finance Review), ed. JJ Choi, MG Papaioannou, 10:329–52. Bingley, UK: Emerald Group.
- Gray, D. F., Merton R. C. and Z. Bodie, 2007, “Contingent Claims Approach to Measuring and Managing Sovereign Credit Risk, Journal of Investment Management, 5(4), pp. 5–28.
- Gray, D., A. Jobst, S. Malone, 2011, “Sovereign Debt, Banking Sector Vunerability, and Dynamic Risk Spillovers in Europe,” EC conference on Debt and Growth, December 2010.
- Jobst, A. and D. Gray, 2013, “Systemic Contingent Claims Analysis –Estimating Market-Implied Systemic Risk”, IMF Working Paper 13/54 (Washington: International Monetary Fund).

### Contingent claims, option-pricing, and foundational theory
- Merton, R.C., 1973, “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science, 4 (Spring), pp. 141-83 (Chapter 8 in Continuous-Time Finance).
- Merton, R.C., 1974, “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance, 29 (May), pp. 449-70. (Chapter 12 in Continuous-Time Finance).
- Merton, R.C., 1977, “An Analytic Derivation of the Cost of Loan Guarantees and Deposit Insurance: An Application of Modern Option Pricing Theory.” Journal of Banking and Finance, 1 (June), pp. 3-11 (Chapter 19 in Continuous-Time Finance).
- Merton, R. C., 1992, Continuous-Time Finance. Oxford, U.K.: Basil Blackwell, (Rev. ed.).
- Merton, R.C., Billio, M., Getmansky, M., Gray, D., Lo, A.W. and L. Pelizzon, 2013, “On a New Approach for Analyzing and Managing Macrofinancial Risks,” Financial Analysts Journal, 69(2).

### Global VAR, international transmission, and macro-financial dynamics
- Chudik, A. and M. Fratzscher, 2011, “Identifying the global transmission of the 2007–2009 financial crisis in a GVAR model”, European Economic Review, 55(3), pp. 325–339.
- Dees, S., F. Di Mauro, M.H. Pesaran, and L.V. Smith, 2007, “Exploring the international linkages of the euro area: A global VAR analysis“, Journal of Applied Econometrics, 22, pp. 1-38.
- Eickmeier, S. and T. Ng, 2011, “How do credit supply shocks propagate internationally? A GVAR approach”, Bundesbank Discussion Paper No. 27/2011.
- Gross, M. 2013, “Estimating GVAR weight matrices”, ECB Working Paper No. 1523.
- Pesaran, M.H., Schuermann, T. and S.M. Weiner, 2004, “Modeling Regional Interdependencies Using a Global Error-Correcting Macroeconometric Model”, Journal of Business & Economic Statistics, 22(2).
- Pesaran, M.H., Schuermann, T., Treutler, B.-J. and S.M. Weiner, 2006, “Macroeconomic Dynamics and Credit Risk: A Global Perspective”, Journal of Money, Credit, and Banking, 38(5), pp. 1211-1261.
- Pesaran, M.H., Schuermann, T. and L.V. Smith, 2009, “Forecasting economic and financial variables with global VARs”, International Journal of Forecasting, 25(4), pp. 642–675.
- Pesaran, M.H., Smith, L.V. and R.P. Smith, 2007, “What if the UK or Sweden had joined the euro in 1999? An empirical evaluation using a Global VAR”, International Journal of Finance & Economics, 12(1), pp. 55–87.

### Empirical validation, credit measures, and CDS-related studies
- Backus, David, Foresi, Silvereio and Liuren Wu, 2004, “Accounting for Biases in Black-Scholes,” Working Paper, New York University, Goldman Sachs Group, and Baruch College.
- Dwyer, D. and I. Korablev, 2007, “Power and Level Validation of Moody’s KMV EDF™ Credit Measures in North America, Europe, and Asia,” Moody’s Analytics White Paper.
- Dwyer, D., Z. Li, S. Qu, H. Russell and J. Zhang, 2010, “CDS-implied EDF™ Credit Measures and Fair-value Spreads,” Moody’s Analytics White Paper.
- Korablev, Irina and S. Qu, 2009, “Validating the Public EDF Model Performance During the Credit Crisis”, Moody’s Analytics White Paper.
- Schweikhard, F.A., and Z. Tsesmelidakis. 2012. “The Impact of Government Interventions on CDS and Equity Markets”, Paper presented at Preliminary Program of the Allied Social Science Associations, Chicago (January).
- Ejsing, J. and W. Lemke, 2009, “The Janus-Headed Salvation: Sovereign and Bank Credit Risk Premia During 2008-09”, ECB Working Paper No. 1127, December.
- Binder, M. and M. Gross, 2013, “Regime Switching Global Vector Autoregressive Models”, ECB Working Paper 1569, August.

### Macrofinancial frameworks, systemic risk, and stress testing
- Gray, D. and S. Malone, 2008, Macrofinancial Risk Analysis, (Wiley Finance Book).
- Gray, D. F., Merton R. C. and Z. Bodie, 2008, “A New Framework for Measuring and Managing Macrofinancial Risk and Financial Stability”, Harvard Business School Working Paper No. 09–015.
- Gray, D., A. Jobst, 2011, “Modeling Systemic Financial Sector and Sovereign Risk,” Sveriges Riksbank Economic Review, September.
- Gray, D. F., Jobst, A. A., and S. Malone, 2010, “Quantifying Systemic Risk and Reconceptualizing the Role of Finance for Economic Growth,” Journal of Investment Management, 8(2), pp. 90-110.
- Gray, D. and S. Malone, 2012, “Sovereign and Financial Sector Risk: Measurement and Interactions”, Annual Review of Financial Economics, 4(9).
- Gray, D. and J. Walsh, 2008, “Factor Model for Stress-testing with a Contingent Claims Model of the Chilean Banking System.” IMF Working Paper 08/89. (Washington: International Monetary Fund).
- Garcia, C., D. Gray, L. Luna, J. Restrepo, 2011, “Incorporating Financial Sector into Monetary Policy Models: Application to Chile”, IMF WP/11/228.
- Crouhy, M., Galai, D. and Mark, R., 2000, Risk Management, McGraw Hill, New York.

### IMF and institutional reports cited
- International Monetary Fund (IMF), 2010, “Global Financial Stability Report: Sovereigns, Funding, and Systemic Liquidity” (October).
- International Monetary Fund (IMF), 2013, “Old Risks, New Challenges,” Chapter 2 on Sovereign CDS Market (April).
- ECB, 2013, Financial Stability Review, Box 8 pages 87 to 90, May.

### Selected theoretical and empirical macro-finance contributions
- Gabaix. X., 2008, “Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance”, NBER Working Paper 13724, NBER Cambridge, MA.
- Draghi, M., F. Giavazzi, R. C. Merton, 2003, “Transparency, Risk Management and International Financial Fragility” NBER Working Paper 9806, June. (Earlier version presented at the Fourth Geneva Conference on the World Economy: Financial Markets: Shock Absorbers or Shock Creators? May 2002.)
- Pesaran, M.H., Schuermann, T. and S.M. Weiner, 2004, “Modeling Regional Interdependencies Using a Global Error-Correcting Macroeconometric Model”, Journal of Business & Economic Statistics, 22(2).
- Davidson, R. and J.G. MacKinnon, 2005, “Bootstrap methods in econometrics”, Chapter 23 in Palgrave Handbook of Econometrics: Volume 1 Theoretical Econometrics, ed. K. Patterson and T.C. Mills, Basingstoke, Palgrave Macmillan.

*References list as provided in _wp13218 - REFERENCES*

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