## _wp1303

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---

### I. Motivation and overview — key findings and context
- Scale and volatility
  - At the end of 2011, OTC-D markets "stood at almost six times global banking assets and between nine-to-10 times global economic activity."
  - The market value of outstanding OTC-D contracts is "substantially more volatile" than bank assets and economic output.
- Clearing and market structure
  - A majority of OTC-interest rate contracts are cleared.
  - The percentage of OTC credit default swaps (CDS) that are cleared has "been growing remarkably fast since the inception of the crisis."
  - Global clearing of OTC-interest rate products occurs almost exclusively through the SwapClear subsidiary of LCH.Clearnet.
  - Global clearing of OTC-CDS is dominated by ICE Clear Credit and ICE Clear Europe.
- Systemic implications
  - Market power of major CCPs creates conditions for them to be "globally systemic financial institutions."
  - Clearing mandates by G20, absent change in market structure, will "exacerbate the global systemic importance" of these CCPs.
- Importance of CCP pre-funded risk buffers
  - CCPs use methodologies for determining risk buffers similar to those used by banks for trading book capital charges.
  - The paper conducts sensitivity analyses using conventional financial risk models and risk tolerance metrics to assess impact of model parameterizations on CCP required risk buffers.
- Key sensitivities and drivers
  - Netting set definition is the most important input for CCP exposure and capital sizing.
    - Widening netting sets via model-implied correlations and bases across risk factor classes "considerably eases capital requirements."
    - A methodology akin to the Basel 2.5 standardized approach—where netting sets defined only up to a risk factor class—results in a "first-order increase" in margin and default fund requirements.
  - CDS-specific features
    - CDS contracts have "discrete increases in loss experience" on default events; changing risk tolerance metrics from limiting losses up to tail events to limiting losses in the tail can "materially increase capital requirements."
  - Stress calibration and procyclicality
    - Calibrating returns, volatility and market liquidity parameters on a stress period basis increases required margin and default fund.
    - VaR-type metrics with point-in-time inputs exhibit a "high degree of procyclicality"; stress-period parameter inputs can mitigate this and attenuate contagion effects.
- Policy implication
  - Benefits may arise from prudential authorities adopting a more prescriptive approach that identifies acceptable risk tolerance metrics and sets perimeters for CCP calibration of key parameter inputs.
  - Concern about regulatory arbitrage if prudential standards for same financial risks differ between banks and CCPs.

### II. Systemic importance of global CCPs — assessment summary
- Evaluation framework: size, interconnectedness, substitutability.
- Market-scale specifics
  - "More than ⅓ of outstanding gross notional in the OTC-interest rates market is cleared."
  - Cleared gross notional outstanding for single-name credit derivatives "doubling each year over the last three years."
  - Credit derivatives exhibit higher per-dollar-notional volatility in market values due to embedded JtD risk.
- Lack of substitutability
  - SwapClear and ICE Clear "novate close-to-100 percent of centrally cleared derivatives trades in their respective markets" and are "too-difficult-to-substitute."
- Interconnectedness
  - Major CCPs (SwapClear, ICE Clear, CME) are directly connected to the largest G-SIBs, increasing their effectiveness as "financial risk and stress transmitters."
  - A common set of G-SIB CMs increases joint global systemic importance even without direct inter-CCP financial links.

### III. CCPs’ risk management frameworks and capital buffers — core elements
- Two types of credit exposure
  - Current market value exposure → Variation Margin (VM)
    - VM is provisioned on a daily basis; VM is net across a CM’s contracts.
  - Potential future exposure (PFE) → Initial Margin (IM)
    - IM covers potential movements in CCP’s exposure to a CM over a fixed time horizon at a given confidence level.
    - IM posting is one-sided (posted by CMs to the CCP); requires daily or more frequent provisioning and adjustment.
- Tail risk and Default Fund (DF)
  - Tail risk not captured by margin models is intended to be absorbed by the pre-funded DF.
  - DF mutualizes losses across the membership; recalculation typically at least monthly.
- Membership and novation
  - CCPs novate contracts directly with their CMs, typically large internationally active banks; client-leg assignment post-novation goes to the CM designated by the client.

### IV. CCP Initial Margin (IM) models — SwapClear and ICE Clear Credit
- SwapClear’s IM model (cleared interest rate derivatives)
  - Empirical distribution generated each day using a look-back sampling window of 1250 (working) days.
  - Returns scaled by a prevailing volatility parameter estimated via a scaling approach applied to historical data.
  - Loss distribution: a gain-loss distribution for each outstanding cleared portfolio is generated.
  - IM calculation: the worst-case loss (akin to using a 100 percent confidence level) over a five-day holding period is calculated and this portfolio loss acts as the basis of the IM charged by SwapClear.
- ICE Clear Credit’s IM model (cleared CDS)
  - Baseline theoretical stress scenario simulation plus add-ons for liquidity, concentration, bases, and JtD risk factors.
  - Netting set concept with proprietary model-implied index-to-SN and cross-maturity bases to reduce outstanding net positions relative to instrument-level netting.
  - ES calibrated at a 99 percent confidence level under a five-day close-out assumption forms the core of IM.
  - Add-on charges: liquidity charge, concentration charge, basis risk charge, JtD charge, recovery sensitivity.
  - IM due from a CM = ES + add-on charges.

### V. Default Fund (DF) models — SwapClear and ICE Clear Credit
- SwapClear DF construction
  - Uses a wider set of (historical and theoretical) stress scenarios than the IM 1250 day look-back.
  - Generates a gain-loss distribution under a five-day close-out and computes the worst-case loss per CM.
  - Unmargined worst-case loss = worst-case loss − IM.
  - SwapClear DF = sum of the largest and second largest unmargined worst-case losses (under the same scenario) + a 10 percent buffer.
  - Pro-rata mutualization: DFi = (IM_i,quarter_avg / Σ_j IM_j,quarter_avg) * DF.
  - Reported figures:
    - At end-2011, SwapClear had total IM = US$ 17.2 billion and DF = US$ 206 million.
    - DF increased to US$ 4 billion by October 2012 following changes including creation of a segregated DF with a size floor of £ 1 billion and increases in CMs’ minimum contributions from £ 2 million to £ 10 million.
- ICE Clear Credit DF construction
  - Baseline theoretical ES at 99.75 percent confidence under a five-day close-out plus add-ons for stress to bases and JtD risk factors.
  - Bases stress up to twice the magnitude used in IM; three obligors assumed to JtD (instead of one under IM).
  - Unmargined worst-case loss = DF-relevant value − IM (if positive).
  - DF = sum of the two largest unmargined worst-case losses + the JtD charge.
  - Pro-rata mutualization: DFi = (UMWCL_i / Σ_j UMWCL_j) * DF.

### VI. Simulation design and key assumptions
- Consolidation and scope
  - Original dataset: 68 CMs including G-SIB subsidiaries; consolidated to 44 CMs by combining group-affiliate CMs.
  - Total gross notional volume of OTC interest rate derivatives cleared by SwapClear as of December 31, 2011 = US$ 283.4 trillion.
  - Cleared OTC-interest rate derivatives composition at end-2011: IRS 82 percent, OIS 14 percent, Basis Swaps 3 percent, FRAs 1 percent (broad swaps = 99 percent).
  - SwapClear analysis assumed IRS = 86 percent and OIS = 14 percent of SwapClear gross notional.
- Currency and maturity
  - Over 98 percent of cleared swaps are in six currencies.
  - Original TtMs assumed from set {2, 5, 10, 20, 30, 50} years and allocated symmetrically across remaining TtM buckets.
  - OIS assumed one-year remaining TtM for valuation.
- Allocation to CMs and constraints
  - For 34 reporting CMs: share outstanding at SwapClear estimated by dividing reported IRS & OIS notional by 99 percent, then allocating 85 percent of that adjusted notional to SwapClear.
  - For CMs reporting only OTC interest rate derivatives, assume 78 percent are IRS and OIS, then apply the two-step allocation.
  - For non‑reporting CMs, allocate equal shares of remaining total SwapClear gross notional.
  - Constraints produce 117 constraints (44 CMs × 73 IRS/OIS contracts); iterative proportional fitting used to simulate contract-level positions.
- Hedging scenarios
  - Overlapping ratio OR_ij = sum_min(L_ij, S_ij) / (sum(L_ij) + sum(S_ij)) per CM used to characterize direct hedging.
  - Three sets of simulated positions:
    - Positions 1 (high direct hedging): overlapping ratios in [0.99, 0.996].
    - Positions 2 (intermediate direct hedging): overlapping ratios in [0.84, 0.93].
    - Positions 3 (low direct hedging): overlapping ratios in [0.51, 0.74].
  - Aggregate portfolio balance requirement: some simulations enforce each CM’s total long and short positions equal.

### VII. Valuation and market simulation methodology
- Valuation primitives
  - IRS and OIS valued as PV(receive-fixed leg) − PV(pay-float leg); OIS floating leg uses geometric average of overnight rates.
  - CDS valued as PV(premium leg) − PV(protection leg); PVBP and default density bootstrapped from traded CDS.
- Market data modeled
  - Short-term LIBOR (< 6 months), interest rate futures (6 months–4 years), IRS rates (1–50 years), relevant overnight rates (Federal Funds, EONIA, SONIA, SARON), and CDS premia for SN and MN 5-year instruments.
- Scenario generation approaches
  - Historical stress scenarios (SwapClear-like): 1250 day look-back, rolling five-day or 10-day standardized returns scaled by prevailing volatility estimated via EWMA.
  - Theoretical stress scenarios: fit series with asymmetric GARCH, standardized residuals fitted non-parametrically, joint residuals fitted with a copula to generate synthetic stressed scenarios.

### VIII. Results — Cleared IRS and OIS (key quantitative findings)
- SwapClear reported figures and simulated sensitivity to hedging (Table 5)
  - SwapClear actual buffers (as of end-2011): Initial Margin = US$ 17.2, Default Fund = US$ 4.0 (note: DF increase to US$ 4 billion by October 2012 mentioned elsewhere).
  - Positions 1 (high hedging): IM = US$ 17.5, DF = US$ 9.2; overlapping ratio range [0.99, 0.996]; asset-liability ratio range [0.99, 1.00].
  - Positions 2 (intermediate hedging): IM = US$ 168.8, DF = US$ 89.4; overlapping ratio range [0.84, 0.93]; asset-liability ratio range [0.87, 1.10].
  - Positions 3 (low hedging): IM = US$ 619.5, DF = US$ 499.0; overlapping ratio range [0.51, 0.74]; asset-liability ratio range [0.64, 1.48].
  - Interpretation: Capital requirements are highly sensitive to the degree of direct hedging by CMs.
  - Validation: Positions 2 best approximates actual CM fair-value asset-to-liability ratios ([0.92, 1.09]) observed in end-2011 data.
- Sensitivity to market-condition calibration (Table 6)
  - Market condition scenarios
    - Normal: standardized returns = last five working days of 2011; end-2011 volatility; five-day close-out.
    - Volatile: volatility calibrated to September 16, 2008 (Lehman default).
    - Illiquid: close-out period = 10 days.
  - Impact on Positions 1
    - Normal: IM = US$ 17.5, DF = US$ 9.2.
    - Volatile: IM = US$ 21.5, DF = US$ 55.6.
    - Illiquid: IM = US$ 19.4, DF = US$ 47.1.
  - Finding: Stress-period volatility calibration or longer close-out periods increases IM modestly and DF substantially.
- Procyclicality of IM (Figure 7)
  - Using EWMA rolling volatilities, IM (Positions 1) would have jumped from US$ 8.6 billion to US$ 33.7 billion in 2008Q3 (a four-fold increase) around the Lehman event.
- Robustness to Lehman-week stress (Table 7)
  - Simulated comparison September 10 to September 17, 2008 under Positions 1 and standardized returns:
    - Under normal market conditions, total unmargined loss = US$ 7,989 million; Default Fund = US$ 2,732 million.
    - Under stressed volatility, unmargined losses drop by 82 percent; under doubled close-out period, unmargined losses vanish.
  - Conclusion: IM sized using stressed/downturn volatility or longer close-out assumptions significantly reduces pressure on DF; DF sufficient to cover total unmargined loss in tested cases.

### IX. Results — Cleared CDS (key quantitative findings)
- Tail risk and risk-measure sensitivity (example G-SIB CM, five-day close-out, normal markets)
  - 90 percent VaR (10 percent quantile) = loss of US$ 280 million.
  - 99 percent VaR (one percent quantile) = loss of US$ 630 million.
  - Maximum loss = US$ 2.3 billion.
  - A 99.75 percent VaR IM of US$ 960 million would be less than half the capital needed to cover the maximum loss.
- ES versus VaR impact (normal market conditions)
  - VaR (99%) Margin = US$ 8.2; DF (99.75%) = US$ 7.1; total (excluding VM) = US$ 15.3.
  - ES (99%) Margin = US$ 18.8; DF (99.75%) = US$ 16.2; total = US$ 35.0.
  - Conclusion: ES more than doubles IM and DF relative to VaR for CDS under normal conditions.
- Sensitivity to market-condition calibration (Table 9)
  - For ICE Clear end-2011 using VaR and ES:
    - Stressed volatility and longer close-out increase total capital markedly.
    - Using VaR: stressed volatility and longer close-out increase total capital by 140 percent and 200 percent respectively relative to normal.
    - Using ES: stressed volatility and longer close-out increase total capital by 90 percent and 47 percent respectively relative to normal.
- Robustness to Lehman-week stress (Table 10)
  - Setting IM using stressed volatility or longer close-out times resulted in the CCP meeting CM defaults without resorting to the DF in the tested cases.
- Procyclicality (Figure 9)
  - IM based on rolling daily returns and volatilities would have jumped almost four times between Q2 and Q3 of 2008 reflecting spike in volatility around Lehman; procyclicality can exacerbate liquidity pressures.

### X. Modeling credit spreads and residuals (Appendix II)
- Empirical residual behavior
  - Residuals of standardized returns of 30 cleared CDS contracts do not follow a normal distribution nor can a t–distribution adequately describe them because of fat-tails.
  - Some CDS time series exhibit zero variance for long periods (examples: Valero Energy, Verizon), producing extreme standardized residuals when variance is zero for extended periods.
- Modeling approach and distributional issues
  - GARCH with time-varying conditional variance is reasonable to capture prolonged zero-variance periods and fat tails.
  - Mixed Paretotail (Pareto tails + kernel smoothed interior) is used in the literature but presents difficulties when combined with copula simulation:
    - Random numbers generated from a copula have uniform margins.
    - About 99 percent of margins generated from the mixed Paretotail distribution are concentrated in [0.5, 0.7].
    - Applying uniform copula margins to the mixed Paretotail fitted distribution can overweight upper and lower 10 percent quantiles relative to real data.
  - Non-parametric margins preferred for copula simulation:
    - Non-parametric residual margins align simulated margins more closely with real-data margins, especially in tails.
    - Non-parametric margins still do not match real-data concentration in [0.3, 0.7], but values there are close to zero and do not cause large discrepancies.
- Modeling implication
  - Use of GARCH + non-parametric marginal estimation with copula dependence mitigates artificial overweighting of tails and better matches observed residual margins in simulated scenarios.

### XI. Policy implications and recommendations
- Conservatism and comparability
  - CCP risk management and prudential standards should be as conservative and comprehensive as for similar risks borne by CMs (banks’ trading book capital).
  - Avoid regulatory arbitrage by aligning CCP requirements with CM prudential treatment.
- Netting set and compartmentalization
  - Netting set definition across risk factor classes materially affects IM and DF sizing.
  - Narrow netting sets restricting offsets to within individual risk factor classes (Basel 2.5-style) would raise CCP capital unless direct offsets dominate.
  - Consider compartmentalizing portfolio models to limit offsetting between major risk factor classes (analogous to BCBS trading book reforms).
- Calibration to stress periods
  - Mandate stress-period calibration of returns, volatility, and instrument liquidity in CCP risk models to reduce procyclicality and increase resilience.
  - A hypothetical portfolio run by all CCPs could benchmark degree of offsetting and parameter sensitivity.
- Risk metric choice for CDS
  - JtD risk in CDS implies substantial tail risk; ES rather than VaR raises IM and DF significantly and could incentivize lower-tail-risk portfolio design by CMs.
- Standardization and disclosure
  - Greater prescription and standardization of CCP risk-model calibration and buffer calculation could reduce systemic risk.
  - Enhanced disclosure by CCPs of their risk models would enable assessment and convergence toward robust benchmarks.
- Overall message
  - Given CCPs’ systemic importance and sensitivity of their capital buffers to hedging, calibration, close-out assumptions, and risk-measure choice, prudential regulators should adopt conservative, standardized, and transparent approaches to CCP risk-model calibration and buffer sizing to limit systemic vulnerability and procyclicality.

### XII. Appendices — clearing-member lists and statistics
- Consolidated list of Clearing Members (CMs) at SwapClear (Table A1) — 44 consolidated CMs listed (examples include Abbey National Treasury Services PLC; ABN Amro; Bank of America-Merrill Lynch; Barclays; BNP Paribas; Citigroup; Goldman Sachs; HSBC; JP Morgan; Morgan Stanley; UBS; Wells Fargo; etc.).
  - Source: LCH.Clearnet.
- List of Clearing Members at ICE Clear (Table A2) — members listed (Bank of America-Merrill Lynch; Barclays; BNP Paribas; Citigroup; Credit Suisse; Deutsche Bank; Goldman Sachs; HSBC; JP Morgan; Morgan Stanley; Nomura; Société Generale; Royal Bank of Scotland; UBS; Unicredit Bank AG).
  - Sources: ICE Clear Credit and ICE Clear Europe.
- Key statistic
  - Number of cleared CDS contracts analyzed (Appendix II): 30 cleared CDS contracts.

*Italic: Content derived from _wp1303 - References (source PDF).*

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

### _wp1303 - References

### Content listings: tables, figures, boxes, appendixes
- Tables
  - 1. Currency profile of cleared swaps and maturity profile of cleared IRS
  - 2. Mapping Original TtM into Maturity Buckets
  - 3. CM Outstanding Notional at Contract Level
  - 4. CM Outstanding Positions at Contract Level
  - 5. Impact of Changes in Direct Hedging on CCP Capital Requirements
  - 6. Impact of Changing Market Conditions on CCP Risk Buffers
  - 7. Adequacy of Buffers under Different Capital Models During Lehman Week
  - 8. Size of CCP Risk Buffer under VaR and ES
  - 9. Impact of Changing Market Conditions on CCP Risk Buffers
  - 10. Adequacy of Risk Buffers to Lehman-type Event
- Figures
  - 1. Size of the OTC-Derivatives Markets
  - 2. Size of Selected G-SIBs’ OTC-Derivatives Exposures
  - 3. The G-SIB-CCP Network
  - 4. CCPs in the Global Financial Network
  - 5. Representative CM Gross Notional OTC-Interest Rate Derivatives Positions
  - 6. Comparing Simulated Asset-liability Ratios with Real Data
  - 7. SwapClear IM Using Rolling Volatilities
  - 8. Five-day Close-out Gain-loss Distribution for a G-SIB CM
  - 9. ICE Clear Initial Margin Using Rolling Daily Returns and Volatilities
  - 10. Comparing Daily Returns on CDS on Two SN Obligors
  - 11. Comparing Standardized Residuals on CDS on Two SN Obligors
  - 12. Fitting Residuals Using a Mixed Paretotail and Kernel Smoothed Interior
  - 13. Residual Margins from Simulated (Copula) and Real (Paretotail) Data
  - 14. Residual Margins from Simulated and Real (Non-parametric) Data
- Boxes
  - 1. CCPs’ IM Models
  - 2. CCPs’ DF Models
- Appendixes
  - I. List of CMs at SwapClear, ICE Clear Credit and ICE Clear Europe
  - II. Modeling Credit Spreads
- Appendix Tables
  - A1. Consolidated List of CMs at SwapClear
  - A2. List of CMs at ICE Clear

### Glossary (selected acronyms and terms)
- A-IRB Advanced Internal Ratings Based
- CCP Central Counterparty
- CDS Credit Default Swap
- CM Clearing Member
- CME Chicago Mercantile Exchange
- DF Default Fund
- DTCC Depository Trust and Clearing Corporation
- EONIA Euro Overnight Index Average
- ES Expected Shortfall
- EWMA Exponentially Weighted Moving Average
- FRA Forward Rate Agreement
- FVA Fair Value of Assets
- FVL Fair Value of Liabilities
- G14 Group of 14 Dealer Banks
- G-20 Group of 20 Countries
- GARCH Generalized Auto Regressive Conditional Heteroskedasticity
- GN Gross Notional
- G-SIB Global Systemically Important Bank
- ICE Inter Continental Exchange
- IM Initial Margin
- IRS Single-currency Interest Rate Swap
- ISDA International Swaps and Derivatives Association
- JtD Jump-to-Default
- LIBOR London Interbank Offered Rate
- MN Multi-name
- OIS Single-currency Overnight Interest Rate Swap
- OR Overlapping Ratio
- OTC-D Over-the-Counter Derivative
- PFE Potential Future Exposure
- SARON Swiss Average Rate Overnight
- SIB Systemically Important Bank
- SN Single-name
- SONIA Sterling Overnight Index Average
- TtM Time-to-Maturity
- VaR Value-at-Risk
- VM Variation Margin

### I. Motivation and overview — key findings and context
- Scale and volatility of global OTC-D markets
  - At the end of 2011, OTC-D markets "stood at almost six times global banking assets and between nine-to-10 times global economic activity."
  - The market value of outstanding OTC-D contracts is "substantially more volatile" than bank assets and economic output.
- Clearing and market structure
  - A majority of OTC-interest rate contracts are cleared.
  - The percentage of OTC credit default swaps (CDS) that are cleared has "been growing remarkably fast since the inception of the crisis."
  - Global clearing of OTC-interest rate products occurs almost exclusively through the SwapClear subsidiary of LCH.Clearnet.
  - Global clearing of OTC-CDS is dominated by ICE Clear Credit and ICE Clear Europe.
- Systemic implications
  - Market power of major CCPs creates conditions for them to be "globally systemic financial institutions."
  - Clearing mandates by G20, absent change in market structure, will "exacerbate the global systemic importance" of these CCPs.
- Importance of CCP pre-funded risk buffers (capital requirements)
  - CCPs use methodologies for determining risk buffers similar to those used by banks for trading book capital charges.
  - The paper conducts sensitivity analyses using conventional financial risk models and risk tolerance metrics to assess impact of model parameterizations on CCP required risk buffers.
- Sensitivities and key drivers
  - The most important input is the definition of the netting set used to determine a CCP’s outstanding exposures.
    - Widening netting sets via model-implied correlations and bases across risk factor classes "considerably eases capital requirements."
    - A methodology akin to the Basel 2.5 standardized approach—where netting sets defined only up to a risk factor class—results in a "first-order increase" in margin and default fund requirements.
  - CDS-specific features
    - CDS contracts have "discrete increases in loss experience" on default events; changing risk tolerance metrics from limiting losses up to tail events to limiting losses in the tail can "materially increase capital requirements."
  - Stress calibration and procyclicality
    - Calibrating returns, volatility and market liquidity parameters on a stress period basis increases required margin and default fund.
    - VaR-type metrics with point-in-time inputs exhibit a "high degree of procyclicality"; stress-period parameter inputs can mitigate this and attenuate contagion effects.
- Policy implication
  - Benefits may arise from prudential authorities adopting a more prescriptive approach that identifies acceptable risk tolerance metrics and sets perimeters for CCP calibration of key parameter inputs.
  - Concern about regulatory arbitrage if prudential standards for same financial risks differ between banks and CCPs.

### II. Systemic importance of global CCPs — summary
- Assessment framework
  - CCPs evaluated against size, interconnectedness and degree of substitutability.
- Market scale specifics
  - "More than ⅓ of outstanding gross notional in the OTC-interest rates market is cleared."
  - Cleared gross notional outstanding for single-name credit derivatives "doubling each year over the last three years."
  - Credit derivatives exhibit higher per-dollar-notional volatility in market values due to embedded JtD risk.
- Lack of substitutability
  - SwapClear and ICE Clear "novate close-to-100 percent of centrally cleared derivatives trades in their respective markets" and are "too-difficult-to-substitute."
- Interconnectedness
  - Major CCPs (SwapClear, ICE Clear, CME) are directly connected to the largest G-SIBs, increasing their effectiveness as "financial risk and stress transmitters."
  - A common set of G-SIB CMs increases joint global systemic importance even without direct inter-CCP financial links.

### III. CCPs’ risk management frameworks and capital buffers — core elements
- Two types of credit exposure from cleared OTC-D contracts
  - Current market value exposure → Variation Margin (VM)
    - VM is provisioned on a daily basis; VM is net across a CM’s contracts.
  - Potential future exposure (PFE) → Initial Margin (IM)
    - IM covers potential movements in CCP’s exposure to a CM over a fixed time horizon at a given confidence level.
    - IM posting is one-sided (posted by CMs to the CCP); requires daily or more frequent provisioning and adjustment.
- Importance of robust pre-funded buffers
  - Contingency arrangements (liquidity backstops, capital calls) are vulnerable to wrong-way risk.
  - Pre-funded buffers are critical because other arrangements may fall in value simultaneously with the risks they are designed to cover.
- Membership and novation practice
  - CCPs novate contracts directly with their CMs, typically large internationally active banks.
  - Client-leg assignment post-novation goes to the CM designated by the client as clearing broker.
- Regulatory and supervisory context
  - Internationally agreed principles outline essential elements of CCP risk management; however, standards for advanced models and techniques are less prescriptive for CCPs than for banks using advanced internal models.

*Italic: Content derived from _wp1303 - References (source PDF)._*

### introduction to these concepts can be found in Gregory (2012).

### CCPs’ IM Models

### SwapClear’s margin model for cleared interest rate derivatives
- Baseline model: uses historical stress scenarios for calibrating IM.
- Empirical distribution: generated each day using a look-back sampling window of 1250 (working) days.
- Scaling: returns are scaled by a prevailing volatility parameter estimated on the basis of a scaling approach applied to historical data.
- Loss distribution: a gain-loss distribution for each outstanding cleared portfolio is generated.
- IM calculation: the worst-case loss (akin to using a 100 percent confidence level) over a five-day holding period is calculated and this portfolio loss acts as the basis of the IM charged by SwapClear.
- Note: detailed documentation was unavailable to the authors owing to its proprietary nature.

### ICE Clear Credit’s margin model for cleared CDS
- Model structure: combines a baseline theoretical stress scenario simulation methodology with add-ons for liquidity, concentration, bases, and JtD risk factors.
- Netting approach: applies a netting set concept to outstanding cleared trades; proprietary model-implied index-to-SN and cross-maturity bases relationships are derived to generate a volume of outstanding net positions of each CM that is smaller than the volume implied by only netting direct offsets at the instrument level.
- Scenario application: a wide set of theoretical scenarios is applied to each CM’s portfolio to generate the expected shortfall (ES) calibrated at a 99 percent confidence level under a five-day close-out assumption.
- Stress coverage: the ES calculation captures stressed credit spreads and stressed interest rate term structure.
- Add-on charges and separate stresses:
  - Liquidity charge: separate models stress the bid-offer width on each type of cleared contract.
  - Concentration charge: provisions against adverse market reaction if significant positions need to be pushed through the market.
  - Basis risk charge: stresses index-to-SN and cross-maturity bases that may change under extreme conditions.
  - JtD charge: models the simultaneous default of one obligor on which the CM has an outstanding CDS trade with ICE Clear.
  - Recovery sensitivity: conditional on JtD, sensitivity to different recovery rate assumptions is modeled.
- IM calculation: the IM due from a CM is the sum of the ES and these add-on charges.
- Note: detailed documentation was unavailable to the authors owing to its proprietary nature.

### Tail risk and the Default Fund (DF)
- Tail risk: CCPs are subject to tail risk not captured by margin models.
- Default fund purpose: CCPs build a second layer of risk buffer called the default fund (DF) to pre-fund tail risk related losses.
- Mutualization: unlike IM—where each CM pays 100 percent of their own contribution to potential losses to the CCP—the allocation of the DF burden is mutualized across the membership.
- Recalculation frequency: industry practice typically requires recalculation and adjustment of the CMs’ DF contributions at least at a monthly frequency.

*Source: _wp1303 - introduction to these concepts can be found in Gregory (2012).*

### Box 2. CCPs’ DF Models

### Box 2. CCPs’ DF Models

### SwapClear’s DF model
- DF construction:
  - Uses a wider set of (historical and theoretical) stress scenarios than the empirical 1250 day look-back used for IM calibration.
  - Generates a gain-loss distribution for each CM’s outstanding portfolio under a five-day close-out assumption and calculates the worst-case loss.
  - The difference between this worst-case loss and IM is the CM’s unmargined worst-case loss.
  - SwapClear DF = sum of the largest and second largest unmargined worst-case losses (under the same scenario) + a 10 percent buffer.
  - SwapClear mutualizes the DF charge across all its CMs in pro-rata fashion:
    - DFi = (IM_i,quarter_avg / Σ_j IM_j,quarter_avg) * DF (notation as in source).
- Reported figures and changes:
  - At end-2011, SwapClear had total IM = US$ 17.2 billion and DF = US$ 206 million.
  - DF increased to US$ 4 billion by October 2012 following changes including creation of a segregated DF with a size floor of £ 1 billion and increases in CMs’ minimum contributions from £ 2 million to £ 10 million.

### ICE Clear Credit’s DF model
- DF construction:
  - Combines a baseline theoretical ES calculation set at a 99.75 percent confidence level under a five-day close-out with add-ons for stress to bases and JtD risk factors.
  - Stress to bases relationships up to twice the magnitude used in its IM model; three obligors assumed to JtD instead of one under IM.
  - The difference between this value and the CM’s IM (if positive) is the CM’s unmargined worst-case loss.
  - DF = sum of the two largest unmargined worst-case losses + the JtD charge.
  - Each CM’s share calculated pro-rata:
    - DFi = (UMWCL_i / Σ_j UMWCL_j) * DF (notation as in source).

### IM and DF modeling approach (methodology overview)
- For centrally cleared interest rate swaps (IRS, OIS, basis swaps):
  - IM estimated with historical volatility-scaled distribution of returns based on a 1250 day look-back under a five-day close-out; worst-case loss per CM pins IM.
  - DF starts with a wider set of theoretical stress scenarios and is set equal to a Cover 2 charge (sum of two largest unmargined losses).
- For centrally cleared CDS:
  - IM set via a theoretical VaR model (five-day close-out) at a 99 percent confidence level.
  - DF set to Cover 2 using a theoretical VaR model with confidence level 99.75 percent.
- Netting and hedging:
  - Conservative definition of CCP netting set is used—no netting across risk factor classes (as in Basel 2.5 standardized approach).
  - Correlation or basis implied hedging is modeled directly via the joint distribution of changes in market value.
- Sensitivity analyses include:
  - For swaps: varying instrument-by-instrument hedging, stress-period-based risk parameters, longer close-out periods.
  - For CDS: changing risk measure from VaR to ES, using stress-period-based inputs.

### Simulation of CMs’ positions (summary of simulation constraints and assumptions)
- Aggregate and consolidation:
  - Original dataset: 68 CMs including G-SIB subsidiaries; consolidated to 44 CMs by combining group-affiliate CMs.
  - Total gross notional volume of OTC interest rate derivatives cleared by SwapClear as of December 31, 2011 = US$ 283.4 trillion.
  - Cleared OTC-interest rate derivatives composition at end-2011: IRS 82 percent, OIS 14 percent, Basis Swaps 3 percent, FRAs 1 percent (broad swaps = 99 percent).
  - For SwapClear analysis: assume IRS = 86 percent and OIS = 14 percent of SwapClear gross notional.
- Currency and maturity constraints:
  - Over 98 percent of cleared swaps are in six currencies; IRS remaining TtM distributed across maturity buckets (Table 1 in source).
  - Original TtMs assumed from set {2, 5, 10, 20, 30, 50} years and allocated symmetrically across remaining TtM buckets.
  - OIS assumed one-year remaining TtM for valuation.
- Allocation to CMs:
  - For 34 CMs reporting notional, the share outstanding at SwapClear estimated by: divide reported IRS & OIS notional by 99 percent, then allocate 85 percent of that adjusted notional to SwapClear.
  - For CMs reporting only OTC interest rate derivatives (not split), assume 78 percent are IRS and OIS; then apply the two-step allocation.
  - For non‑reporting CMs, allocate equal shares of remaining total SwapClear gross notional.
- Constraints produce 117 constraints (44 CMs × 73 IRS/OIS contracts) for the IRS/OIS simulation problem; iterative proportional fitting used to simulate granular contract-level positions.
- Hedging metrics and scenarios:
  - Overlapping ratio OR_ij = sum_min(L_ij, S_ij) / (sum(L_ij) + sum(S_ij)) per CM (equation (3) in source) used to characterize direct hedging.
  - Three sets of simulated positions chosen to span plausible overlapping ratios:
    - Positions 1: high direct hedging, overlapping ratios in [0.99, 0.996].
    - Positions 2: intermediate direct hedging, overlapping ratios in [0.84, 0.93].
    - Positions 3: lower direct hedging, overlapping ratios in [0.51, 0.74].
  - Aggregate portfolio balance requirement: each CM’s total long and short positions equal (equation (4) in source) used in some simulations.

### Valuation and market simulation
- Valuation formulas summarized (as in source): IRS and OIS valued as PV(receive-fixed leg) − PV(pay-float leg); OIS floating leg uses geometric average of overnight rates; CDS valued as PV(premium leg) − PV(protection leg), PVBP and default density bootstrapped from traded CDS.
- Market data simulated include:
  - Short-term LIBOR (< 6 months), interest rate futures (6 months–4 years), IRS rates (1–50 years), relevant overnight rates (Federal Funds, EONIA, SONIA, SARON), and CDS premia for SN and MN 5-year instruments.
- Two modeling approaches:
  - Historical stress scenarios (SwapClear-like): 1250 day look-back, rolling five-day or 10-day standardized returns scaled by prevailing volatility estimated via EWMA.
  - Theoretical stress scenarios: fit series with asymmetric GARCH, standardized residuals fitted non-parametrically, joint residuals fitted with a copula to generate synthetic stressed scenarios.

### Results — Cleared IRS and OIS (key findings)
- Sensitivity to direct hedging (Table 5 results):
  - SwapClear actual buffers (as of end-2011): Initial Margin = US$ 17.2, Default Fund = US$ 4.0 (note: DF increase to US$ 4 billion by October 2012 mentioned elsewhere).
  - Positions 1 (high hedging): IM = US$ 17.5, DF = US$ 9.2; overlapping ratio range [0.99, 0.996]; asset-liability ratio range implied [0.99, 1.00].
  - Positions 2 (intermediate hedging): IM = US$ 168.8, DF = US$ 89.4; overlapping ratio range [0.84, 0.93]; asset-liability ratio range [0.87, 1.10].
  - Positions 3 (low hedging): IM = US$ 619.5, DF = US$ 499.0; overlapping ratio range [0.51, 0.74]; asset-liability ratio range [0.64, 1.48].
  - Interpretation: Capital requirements are highly sensitive to the degree of direct hedging by CMs; lower direct hedging dramatically increases IM and DF.
  - Validation: Positions 2 best approximates actual CM fair-value asset-to-liability ratios ([0.92, 1.09]) observed in end-2011 data.
- Sensitivity to market-condition calibration (Table 6 results):
  - Market condition scenarios defined:
    - Normal market conditions: standardized returns = last five working days of 2011; end-2011 volatility; five-day close-out.
    - Volatile market conditions: volatility calibrated to September 16, 2008 (Lehman default).
    - Illiquid market conditions: close-out period = 10 days.
  - Impact on Positions 1:
    - Normal: IM = US$ 17.5, DF = US$ 9.2.
    - Volatile: IM = US$ 21.5, DF = US$ 55.6.
    - Illiquid: IM = US$ 19.4, DF = US$ 47.1.
  - Findings: calibrating to stressed volatility or longer close-out periods increases IM and raises DF substantially (DF increases of over 300–400 percent in some cases).
- Procyclicality of IM (Figure 7 result):
  - Using EWMA rolling volatilities, IM (Positions 1) would have jumped from US$ 8.6 billion to US$ 33.7 billion in 2008Q3 (a four-fold increase) around the Lehman event.
- Robustness to Lehman-week stress (Table 7):
  - Under simulated Positions 1 and standardized returns as of September 10, 2008, comparing market moves between September 10 and September 17, 2008:
    - Under normal market conditions, some CMs show unmargined losses; total unmargined loss = US$ 7,989 million; Default Fund = US$ 2,732 million in that comparison (table format preserved as in source).
    - Under volatile or illiquid calibrations (stressed volatility or longer close-out), unmargined losses drop by 82 percent (stressed volatility) and vanish when doubling close-out period.
    - Conclusion: IM sized using stressed/downturn volatility or longer close-out assumptions significantly lowers pressure on DF; DF sufficient to cover total unmargined loss in all tested cases.

### Results — Cleared CDS (key findings)
- Tail risk and choice of risk measure:
  - Example G-SIB CM gain-loss distribution (five-day close-out, normal markets):
    - 90 percent VaR (10 percent quantile) = loss of US$ 280 million.
    - 99 percent VaR (one percent quantile) = loss of US$ 630 million.
    - Maximum loss = US$ 2.3 billion.
    - A 99.75 percent VaR IM of US$ 960 million would be less than half the capital needed to cover the maximum loss.
  - Use of ES versus VaR materially increases capital requirements:
    - Under normal market conditions:
      - VaR (99%) Margin = US$ 8.2; DF (99.75%) = US$ 7.1; total (excluding VM) = US$ 15.3.
      - ES (99%) Margin = US$ 18.8; DF (99.75%) = US$ 16.2; total = US$ 35.0.
    - Conclusion: ES more than doubles IM and DF relative to VaR in normal conditions for CDS.
- Sensitivity to market-condition calibration (Table 9 results):
  - For ICE Clear end-2011 using VaR and ES:
    - Normal: IM (VaR 99%) = US$ 23.2; DF = US$ 8.0 ; IM (ES 99%) = US$ 23.5; DF = US$ 14.4 (source table shows multiple figures; see source for full breakdown).
    - Stressed calibrations (volatile or illiquid) increase total capital requirements substantially:
      - Using VaR: stressed volatility and longer close-out increase total capital by 140 percent and 200 percent respectively relative to normal.
      - Using ES: stressed volatility and longer close-out increase total capital by 90 percent and 47 percent respectively relative to normal.
- Robustness to Lehman-week stress (Table 10):
  - Setting IM using stressed volatility or longer close-out times resulted in the CCP meeting CM defaults without resorting to the DF in the tested cases.
- Procyclicality of IM for CDS (Figure 9 result):
  - IM based on rolling daily returns and volatilities would have jumped almost four times between Q2 and Q3 of 2008 reflecting spike in volatility around Lehman; IM procyclicality can exacerbate liquidity pressures.

### Policy implications and recommendations (major themes and prescriptions)
- Conservatism and comparability:
  - CCPs’ risk management and prudential standards should be as conservative and comprehensive as those for similar risks borne by CMs (banks’ trading book capital).
  - Avoid regulatory arbitrage by setting CCP requirements comparable to CM prudential treatment.
- Netting sets and compartmentalization:
  - Defining netting sets across multiple risk factor classes materially affects IM and DF sizing.
  - Narrowing netting sets to permit offsetting only within individual risk factor classes (as in Basel 2.5 standardized approach) would raise CCP capital unless direct offsets dominate.
  - Consider compartmentalizing portfolio models to limit offsetting between major risk factor classes (analogous to BCBS trading book reforms).
- Calibration to stress periods:
  - IM and DF increase significantly when moving from point-in-time to stress-period calibration of volatility and close-out assumptions.
  - Mandate stress-period calibration of returns, volatility, and instrument liquidity in CCP risk models to reduce procyclicality and increase resilience.
  - Consider a hypothetical portfolio run by all CCPs to benchmark degree of offsetting and variability from data/parameter choices.
- Choice of risk metric for CDS:
  - For CDS, the presence of JtD risk implies substantial tail risk; using ES rather than VaR raises IM and DF significantly.
  - Using ES could incentivize CMs to redesign portfolios toward lower tail risk.
- Standardization and disclosure:
  - Current international standards are non-prescriptive; greater standardization and prescriptive methodologies for calculating CCP risk buffers could reduce systemic risk.
  - Greater disclosure by CCPs of their risk models would enable assessment and convergence toward robust benchmarks.
- Overall policy message:
  - Given the systemic importance of CCPs in cleared OTC-D markets and the sensitivity of CCP capital buffers to hedging, calibration, close-out assumptions, and risk metric choice, prudential regulators should adopt conservative, standardized, and transparent approaches to CCP risk-model calibration and buffer sizing to limit systemic vulnerability and procyclicality.

*Italic: Source — Box 2. CCPs’ DF Models (extracted content provided).*

### APPENDIX I. LIST OF CMS AT SWAPCLEAR, ICE CLEAR CREDIT AND ICE CLEAR EUROPE

### APPENDIX I. LIST OF CMS AT SWAPCLEAR, ICE CLEAR CREDIT AND ICE CLEAR EUROPE

### Consolidated list of Clearing Members (CMs) at SwapClear (Table A1)
- Abbey National Treasury Services PLC
- ABN Amro
- Banca IMI SpA
- Banco Bilbao Vizcaya Argentaria, SA
- Bank of America-Merrill Lynch
- Bank of Montreal
- Bank of New York Mellon
- Bank of Nova Scotia
- Barclays
- BNP Paribas
- Bayerische Landesbank
- Belfius Bank
- Canadian Imperial Bank of Commerce
- Citigroup
- Commerzbank
- Credit Agricole
- Credit Suisse
- Danske Bank
- Dekabank Deutsche Girozentrale
- Dexia Bank
- DZ Bank
- Goldman Sachs
- HSBC
- ING Bank NV
- JP Morgan
- Landesbank Baden-Württemberg
- Lloyds TSB
- Mitsubishi UFJ
- Morgan Stanley
- Natixis
- Nomura
- Nordea Bank Finland PLC
- Rabobank
- Royal Bank of Canada
- Royal Bank of Scotland
- Santander
- Société Generale
- Standard Chartered
- Mizuho
- Toronto Dominion
- UBS
- Unicredit
- Wells Fargo

- Source: LCH.Clearnet

### List of Clearing Members at ICE Clear (Table A2)
- Bank of America-Merrill Lynch
- Barclays
- BNP Paribas
- Citigroup
- Credit Suisse
- Deutsche Bank
- Goldman Sachs
- HSBC
- JP Morgan
- Morgan Stanley
- Nomura
- Société Generale
- Royal Bank of Scotland
- UBS
- Unicredit Bank AG

- Sources: ICE Clear Credit and ICE Clear Europe

### Key statistics
- Number of cleared CDS contracts analyzed (Appendix II): 30 cleared CDS contracts.

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### APPENDIX II. MODELING CREDIT SPREADS

### Empirical behavior of residuals and returns
- The residuals of the standardized returns of 30 cleared CDS contracts do not follow a normal distribution nor can their behavior be adequately described by a t–distribution owing to fat-tails.
- Some CDS time series exhibit zero variance for long periods of time; examples cited include CDS on Valero Energy and Verizon.
- Standardized residuals can exhibit extreme values when variance is zero for extended periods (example: Verizon CDS).

### Modeling approach and distributional issues
- It is reasonable to fit such series with a GARCH model with time varying conditional variance.
- A mixture of the Pareto distribution (in the tails) and a kernel smoothed interior is used in the literature to capture extreme residuals (mixed Paretotail).
- Difficulties with mixed Paretotail approach when fitting a copula:
  - Random numbers generated from a copula have uniform margins.
  - About 99 percent of the margins generated from the mixed Paretotail distribution are concentrated in the region [0.5. 0.7].
  - Applying uniformly distributed copula margins to the fitted Paretotail distribution leads to a larger proportion of simulated residuals in the upper and lower 10 percent quantiles, putting larger weight on tails than observed in real data concentrated in [0.5, 0.7].
- Consequently, the authors use a non-parametric distribution for residual margins to better match uniformly distributed margins simulated by the copula:
  - Under the non-parametric distribution, margins of the residuals are closer to the uniformly distributed margins simulated by the copula, especially in the tails where weights from simulated and real data are close.
  - The non-parametric margins still do not follow the uniform distribution in the range [0.3, 0.7], where the real data is concentrated in the [0.5, 0.55] range and the simulated data are uniformly distributed; however, values in the [0.3, 0.7] range are close to zero and do not result in large discrepancies between simulated and real data.

### Modeling implications and rationale
- Use of GARCH for time-varying conditional variance addresses prolonged zero-variance periods and fat tails in residuals.
- Mixed Paretotail fits can conflict with copula-based simulation because of mismatch between empirical concentration ([0.5. 0.7]) and uniform margins from copula draws, leading to over-emphasis on extreme quantiles.
- Non-parametric margin estimation aligns simulated margins more closely with real-data margins, reducing artificial overweighting of tails when combining marginal fits with copula dependence structure.

- Figures referenced (authors' calculations): Figure 10 (Daily returns on CDS for two SN obligors), Figure 11 (Standardized residuals), Figure 12 (Fitting residuals with mixed Paretotail and kernel smoothed interior), Figure 13 (Residual margins: simulated copula vs real Paretotail), Figure 14 (Residual margins: simulated vs real non-parametric).

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*Source: APPENDIX I and APPENDIX II, _wp1303 - APPENDIX I. LIST OF CMS AT SWAPCLEAR, ICE CLEAR CREDIT AND ICE CLEAR EUROPE_*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp1303.pdf_