## _wp08258 - 4. Estimate Conditional

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### FSMD, PoDs, and copula approach
- The FSMD embeds institutions’ distress dependence, capturing linear (correlation) and non-linear dependencies among FIs and allowing these to change through the economic cycle.
- The distress dependence structure in the FSMD is characterized by the CIMDO-copula (Segoviano, 2008).
- Approach: infer copulas directly from the joint movement of individual PoDs rather than selecting parametric copula functions.
- Individual PoDs are inferred from five year CDS spreads; PoDs are risk neutral and adjusted for risk aversion to quantify losses.
- Fixed recovery rate used in PoD estimation: 40 percent.

### Distress dependence matrix (DiDe) — concept and empirical snapshot (3/31/2008)
- Concept:
  - Distress dependence summarized in a conditional probability matrix: entries are P(Row FI | Column FI).
  - Matrix diagonal = 1; off-diagonals = conditional PoDs.
- Empirical snapshot (Table 2, 3/31/2008) — selected conditional PoDs (rows conditioned on columns):
  - FI1 row: FI1 = 1.00; FI2 = 0.30; FI3 = 0.77; FI4 = 0.45; FI5 = 0.42; FI6 = 0.41; FI7 = 0.35; FI8 = 0.32; FI9 = 0.43; FI10 = 0.28; FI11 = 0.36.
  - FI2 row: FI1 = 0.58; FI2 = 1.00; FI3 = 0.63; FI4 = 0.52; FI5 = 0.52; FI6 = 0.55; FI7 = 0.48; FI8 = 0.47; FI9 = 0.54; FI10 = 0.44; FI11 = 0.55.
  - (Additional matrix entries presented in Table 2 of the source.)

### Loss scenarios and formulas
- Two alternative loss scenarios based on conditional probabilities of distress:
  - Scenario 1: Loss due to the probability that at least one FI fails to deliver (the union of conditional PoDs given a specific FI failed to deliver). Scenario 1 embeds the highest probability of occurrence.
  - Scenario 2: Loss due to the probability that exactly one FI fails to deliver (the union of conditional PoDs minus their intersections). Scenario 2 embeds a lower probability of occurrence than Scenario 1.
- Loss formulas (as presented in source):
  - Scenario 1: LSc1|A = ExpA × 1 + Σ_{i=B}^{i=D} Expi × P(Scenario 1|A)
  - Scenario 2: LSc2|A = ExpA × 1 + Σ_{i=B}^{i=D} Expi × P(Scenario 2|A)

### Data and sample used for empirical estimation
- Institutions included (data from before Lehman failure in late Summer 2008):
  - JPMorgan Chase, Citibank, Bank of America, Goldman Sachs, Merrill Lynch, Lehman, Morgan Stanley, Credit Suisse, Bear Stearns, Wachovia, Wells Fargo.
- Counterparty liability data refer to first quarter, 2008 filings for these institutions; Bear Stearns data from 10-K November 2007.
- BIS global OTC derivative survey shows a $3.2 trillion netted counterparty positions (assets and liabilities).
  - Assumption: $1.6 trillion can be used for the total counterparty liabilities that are not “netted.”
  - Sample shows $630 billion of counterparty liabilities, roughly 40 percent of the total OTC data.
  - Note: $3.2 trillion netted position could be lower if adjusted for assigned cash collateral.
- Exchange rate used for Credit Suisse: CHF 1 = $1.132 (March 31).

### Estimated losses (sample of $630 billion not “netted” counterparty liabilities) — 3/31/2008
- Losses in billions of dollars as of 3/31/2008 (Table 3), by FI (FI1..FI11):
  - Scenario 1:
    - FI1: 606.66
    - FI2: 532.94
    - FI3: 607.48
    - FI4: 597.05
    - FI5: 599.67
    - FI6: 603.73
    - FI7: 589.88
    - FI8: 577.05
    - FI9: 602.09
    - FI10: 532.49
    - FI11: 572.77
  - Scenario 2:
    - FI1: 34.221
    - FI2: 63.486
    - FI3: 69.385
    - FI4: 51.633
    - FI5: 30.65
    - FI6: 115.537
    - FI7: 2.72
    - FI8: 100.37
    - FI9: 85.21
    - FI10: 72.02
    - FI11: 116.78

### Extrapolated total losses for the OTC system (scaling sample to total OTC not “netted” liabilities) — 3/31/2008
- Extrapolated losses (Table 4) in billions of dollars as of 3/31/2008 (FI1..FI11):
  - Scenario 1:
    - FI1: 1,596.46
    - FI2: 1,402.48
    - FI3: 1,598.64
    - FI4: 1,571.18
    - FI5: 1,578.08
    - FI6: 1,588.77
    - FI7: 1,552.31
    - FI8: 1,518.55
    - FI9: 1,584.44
    - FI10: 1,401.30
    - FI11: 1,507.30
  - Scenario 2:
    - FI1: 90.05
    - FI2: 430.20
    - FI3: 182.58
    - FI4: 135.86
    - FI5: 80.65
    - FI6: 304.04
    - FI7: 191.37
    - FI8: 264.12
    - FI9: 224.25
    - FI10: 189.54
    - FI11: 307.33
- Interpretation highlighted in source:
  - In the case of a single institution failure, total loss could be as high as $300–$400 billion depending on the FI.
  - When cascade effects are included, total loss could rise to over $1,500 billion.

### Fed balance sheet context (as of April 23, 2008)
- U.S. Treasury securities (AAA) available were just above $500 billion after the $29 billion loan to JPMorgan for Bear Stearns.
- Conclusion in source: Fed’s balance sheet at that time was not big enough to absorb counterparty losses under Scenario 1 if more than one FI fails.

### Policy implications and recommendations (selected)
- Encourage further “cross margining” across product silos (e.g., allow cross netting across legal entities for CDS and repo contracts); multilateral trade terminations on same lines.
- With Fed facilities to prime brokers (Term Auction Facility Loans and Primary Dealer Credit Facility), major derivative players might be induced to use central clearing systems.
- Major dealers’ voluntary commitments include:
  - 75 percent of OTC equity and derivative trades on electronic platforms by January 31, 2009.
  - An auction-based settlement mechanism for CDS contracts.
- Regulatory focus note:
  - Most regulatory efforts focus on credit derivatives (~10 percent of all OTC derivatives); greater focus needed on IRS (interest-rate swaps) market, which is more than six times larger than CDS.
- Collateral recommendations:
  - Collateral should be liquid securities, not merely high credit quality.
  - Collateral should be allowed to be rehypothecated; clearing houses would allow netting down collateral at the exchange acting as Central Counterparty.
  - Collateral standards should require an appropriate amount of collateral be maintained at all times, not just ex post “super margining.”
- Standardization and offsetting of trades:
  - Reduce number of dates to quarterly on CDS (EM monthly).
  - Limit premiums eligible for new trades to increments such as 25bps or 50bps.
  - Convert running premium contracts to all up-front and reduce allowable credit events (as discussed in context of CME–Citadel venture).

*Source: _wp08258 - 4. Estimate Conditional (excerpted content).*

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

### References

### I. Introduction — scope and market size
- Notional amounts of all categories of the OTC contracts reached almost $600 trillion at the end of December 2007.
- Interest rate contracts comprise 66 percent of all OTC derivative market, or about $400 trillion.
- Credit derivatives volume more than doubled in the last year to about $60 trillion.
- The paper’s focus: quantify counterparty risk measured as (expected) losses absorbed by the financial system from the default (or fail) of one or more banks or broker dealers, under two scenarios (described in Section II.D).
- Methodological improvements emphasized:
  - Define the exposure of the financial system to specific financial institutions (FIs).
  - Propose a methodology to estimate the probability that, given a particular institution fails to deliver, other institutions would also fail to deliver, accounting for linear (correlations) and non-linear distress dependence (DD) that changes across the economic cycle.

### II. Counterparty risk: definition and components
- Counterparty risk definition:
  - Cumulative loss to the financial system from a counterparty that fails to deliver on its OTC derivative obligation.
- Two necessary variables to estimate potential cumulative loss:
  - (i) the exposure of the financial system (EFS) to particular institution(s) that fail to deliver;
  - (ii) the probability that, given a particular institution fails to deliver, other institutions in the system would also fail to deliver (conditional probabilities incorporating DD).

### III. Exposure of the financial system to counterparty risk (EFS)
- EFS defined as the liabilities of a particular institution to others in the financial system stemming from its OTC derivatives that have not been netted under a master netting agreement or cross margining agreements where margin/cash is assigned and netted across product categories.
- Notional amounts:
  - Defined as the gross nominal value of all OTC derivative deals concluded and not yet settled on the reporting date.
  - Provide a measure of market size but do not provide a measure of risk.
- Gross market values:
  - Capture open contracts that are in a current gain or loss position at current market prices.
  - Are correlated with notional amounts but are not netted.
- Counterparty risk measurement should be conducted only on “un‑netted” and “unassigned” liabilities.
- Data sources and reporting notes:
  - Counterparty liabilities generally available in U.S. banks and broker dealers’ 10Q and 10K filings; Call Reports on OCC/FDIC website are useful.
  - Some large European institutions may not comply with standard 10Q/10K filings; their counterparty liability data may not be available.
  - Example disclosure (Lehman Form 10‑Q, Feb 29, 2008): “Assets and liabilities at February 29, 2008 were netted down for cash collateral of approximately $26.5 billion and $17.6 billion, respectively. [The ‘Liabilities’ for OTC are $36,063, as in Figure 4, are adjusting for netting and cash collateral.]”

### IV. Distress dependence (DD) and conditional probabilities of distress
- Rationale:
  - Financial institutions (FIs) are linked directly (inter‑bank deposits, syndicated loans) and indirectly (lending to common sectors, proprietary trades).
  - DD tends to rise in times of distress; joint probability of distress (JPoD) may increase nonlinearly relative to individual PoDs.
  - Proper measurement of counterparty risk at the system level must incorporate DD and its variation across the economic cycle.
- Methodological approach (summarized; follows Goodhart and Segoviano (2008)):
  - Conceptualize the financial system as a portfolio of FIs.
  - Infer individual FIs’ probabilities of distress (PoDs) from CDS spreads.
  - Use the Consistent Information Multivariate Density Optimizing (CIMDO) methodology (Segoviano, 2006b), a non‑parametric cross‑entropy approach, to derive the financial system multivariate density (FSMD) from PoDs.
  - From the FSMD estimate pairwise conditional PoDs and the system JPoD.
- Outputs:
  - Conditional distress dependence matrix (DiDe): contains PoD of the FI indicated in the row, conditioned on the FI in the column falling on distress (Table 1 referenced).
- Advantages over traditional models:
  - Captures linear (correlation) and non‑linear dependence among FIs.
  - Allows dependence to change throughout the economic cycle rather than assuming constant correlations.

### V. Comparative and market notes from literature and market measures
- Prior studies and scope limitations:
  - Much recent discussion focused on credit derivatives (CDS) which represent only 10 percent of the overall OTC derivatives market.
  - Barclays Quantitative Credit Strategy Research Note (20th February 2008) focused only on credit derivatives and estimated losses from counterparty risk in the credit derivatives market could range from $36–$47 billion, largely from re‑pricing (gap risk) from a counterparty fail.
    - Barclays assumptions: recovery value of 40 percent and a spread jump range between 10 bps to 60 bps.
    - Barclays did not use “netted” counterparty risk and did not discern between counterparty liabilities and counterparty assets.
  - Market indices such as Credit Derivative Research (CDR) measure average CDS spread of largest 15 credit derivative counterparties but do not account for distress dependence among counterparties nor for exposure (counterparty liabilities).
- Paper’s contribution relative to prior work:
  - Accounts for distress dependence (DD) and for exposure via un‑netted/un‑assigned liabilities.
  - Produces joint and conditional probabilities of default for the portfolio of banks and prime‑brokers.

*Source: _wp08258 - References (excerpted content).*

### 4. E stim ate C on dition al

### _wp08258 - 4. E stim ate C on dition al

### Probabilities of Default and the JPoD from the FSMD
- The FSMD embeds institutions’ distress dependence, capturing linear (correlation) and non-linear dependencies among FIs and allowing these to change through the economic cycle.
- The distress dependence structure in the FSMD is characterized by the CIMDO-copula (Segoviano, 2008).
- Approach: infer copulas directly from the joint movement of individual PoDs rather than selecting parametric copula functions.

### Distress Dependence Matrix (concept)
- The distress dependence between institutions is summarized in a conditional probability matrix (Table 1 illustration): entries are P(Row FI | Column FI).
- Example structure (matrix diagonal = 1, off-diagonals = conditional PoDs).

### Loss Scenarios (framework)
- Two alternative loss scenarios are devised based on conditional probabilities of distress:
  - Scenario 1: Loss due to the probability that at least one FI fails to deliver. This is the union of conditional PoDs given a specific FI failed to deliver. Among the two scenarios, Scenario 1 embeds the highest probability of occurrence.
  - Scenario 2: Loss due to the probability that exactly one FI fails to deliver. This is the union of conditional PoDs minus their intersections; Scenario 2 embeds a lower probability of occurrence than Scenario 1.

- Loss formulas (as presented):
  - Scenario 1: LSc1|A = ExpA × 1 + Σ_{i=B}^{i=D} Expi × P(Scenario 1|A)
  - Scenario 2: LSc2|A = ExpA × 1 + Σ_{i=B}^{i=D} Expi × P(Scenario 2|A)

### Empirical Estimation — Counterparty Risk Exposure (data and sample)
- Data used from before the Lehman failure in late Summer 2008; banks/prime brokers included:
  - JPMorgan Chase, Citibank, Bank of America, Goldman Sachs, Merrill Lynch, Lehman, Morgan Stanley, Credit Suisse, Bear Stearns, Wachovia, Wells Fargo.
- Counterparty liability data refer to first quarter, 2008 filings for these institutions; Bear Stearns data from 10-K November 2007.
- BIS global OTC derivative survey shows a $3.2 trillion netted counterparty positions (assets and liabilities).
  - Assumption: $1.6 trillion can be used for the total counterparty liabilities that are not “netted.”
  - Sample shows $630 billion of counterparty liabilities, roughly 40 percent of the total OTC data.
  - Note: $3.2 trillion netted position could be lower if adjusted for assigned cash collateral.

- OTC notional and counterparty liability figures as of end of March 2008 are presented in the source (charts); exchange rate used for Credit Suisse: CHF 1 = $1.132 (March 31).

### Conditional Probabilities of Distress (methodology and parameters)
- Individual PoDs inferred from five year CDS spreads; PoDs are risk neutral and adjusted for risk aversion to quantify losses.
- Fixed recovery rate used in PoD estimation: 40 percent.
  - Rationale: during distress recovery may vary; cheapest-to-deliver bonds best approximate recovery; Bear merger timing supports fixed recovery for the dataset used.
- Risk aversion-adjusted PoDs (Figure 8) feed into CIMDO methodology to derive FSMD and the DiDe (distress dependence matrix).

### Distress Dependence Matrix — Empirical Snapshot (3/31/2008)
- Table 2 (3/31/2008) presents conditional PoDs among anonymized FI1..FI11. Example entries (rows conditioned on columns):
  - FI1 row (conditional on columns FI1..FI11): FI1 = 1.00; FI2 = 0.30; FI3 = 0.77; FI4 = 0.45; FI5 = 0.42; FI6 = 0.41; FI7 = 0.35; FI8 = 0.32; FI9 = 0.43; FI10 = 0.28; FI11 = 0.36.
  - FI2 row: FI1 = 0.58; FI2 = 1.00; FI3 = 0.63; FI4 = 0.52; FI5 = 0.52; FI6 = 0.55; FI7 = 0.48; FI8 = 0.47; FI9 = 0.54; FI10 = 0.44; FI11 = 0.55.
  - (Additional matrix entries are presented in Table 2 of the source; the table indicates PoDs of row FIs conditioned on column FIs for 3/31/2008.)

### Estimated Losses Under Scenarios (sample of $630 billion not “netted” counterparty liabilities)
- Losses in billions of dollars as of 3/31/2008 (Table 3), by FI (FI1..FI11):
  - Scenario 1:
    - FI1: 606.66
    - FI2: 532.94
    - FI3: 607.48
    - FI4: 597.05
    - FI5: 599.67
    - FI6: 603.73
    - FI7: 589.88
    - FI8: 577.05
    - FI9: 602.09
    - FI10: 532.49
    - FI11: 572.77
  - Scenario 2:
    - FI1: 34.221
    - FI2: 63.486
    - FI3: 69.385
    - FI4: 51.633
    - FI5: 30.65
    - FI6: 115.537
    - FI7: 2.72
    - FI8: 100.37
    - FI9: 85.21
    - FI10: 72.02
    - FI11: 116.78

### Extrapolated Total Losses for the OTC System (scaling sample to total OTC not “netted” liabilities)
- Extrapolated losses (Table 4) in billions of dollars as of 3/31/2008 (FI1..FI11):
  - Scenario 1:
    - FI1: 1,596.46
    - FI2: 1,402.48
    - FI3: 1,598.64
    - FI4: 1,571.18
    - FI5: 1,578.08
    - FI6: 1,588.77
    - FI7: 1,552.31
    - FI8: 1,518.55
    - FI9: 1,584.44
    - FI10: 1,401.30
    - FI11: 1,507.30
  - Scenario 2:
    - FI1: 90.05
    - FI2: 430.20
    - FI3: 182.58
    - FI4: 135.86
    - FI5: 80.65
    - FI6: 304.04
    - FI7: 191.37
    - FI8: 264.12
    - FI9: 224.25
    - FI10: 189.54
    - FI11: 307.33

- Interpretation highlighted in source:
  - In the case of a single institution failure, total loss could be as high as $300–$400 billion depending on the FI.
  - When cascade effects are included, total loss could rise to over $1,500 billion.

- Fed balance sheet context (Figure 9, as of April 23, 2008):
  - U.S. Treasury securities (AAA) available were just above $500 billion after the $29 billion loan to JPMorgan for Bear Stearns.
  - Conclusion: Fed’s balance sheet at that time was not big enough to absorb counterparty losses under Scenario 1 if more than one FI fails.

### Policy Implications and Recommendations (selected suggestions from source)
- Encourage further “cross margining” across product silos (e.g., allow cross netting across legal entities for CDS and repo contracts); multilateral trade terminations on same lines.
- With Fed facilities to prime brokers (Term Auction Facility Loans and Primary Dealer Credit Facility), major derivative players might be induced to use central clearing systems.
- Major dealers’ voluntary commitments include:
  - 75 percent of OTC equity and derivative trades on electronic platforms by January 31, 2009.
  - An auction-based settlement mechanism for CDS contracts.
- Note: Most regulatory efforts focus on credit derivatives (~10 percent of all OTC derivatives); greater focus needed on IRS (interest-rate swaps) market, which is more than six times larger than CDS.
- Collateral recommendations:
  - Collateral should be liquid securities, not merely high credit quality.
  - Collateral should be allowed to be rehypothecated; clearing houses would allow netting down collateral at the exchange acting as Central Counterparty.
  - Collateral standards should require an appropriate amount of collateral be maintained at all times, not just ex post “super margining.”
- Increase offsetting of new trades against old ones via standardization:
  - Reduce number of dates to quarterly on CDS (EM monthly).
  - Limit premiums eligible for new trades to increments such as 25bps or 50bps.
  - Convert running premium contracts to all up-front and reduce allowable credit events (as discussed in context of CME–Citadel venture).

*Source: Goodhart and Segoviano 2008.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08258.pdf_