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  • B. Illustration 2

    Consider a netting set with three credit derivatives: one long single-name CDS written on Firm A (rated AA), one short single-name CDS written on Firm B (rated BBB), and one long CDS index (investment grade). All notional amounts and market values are denominated in USD. This netting set is not subject to a margin agreement and there is no exchange of collateral (independent amount/initial margin) at inception. The table below summarizes the relevant contractual terms of the three derivatives.

    Trade #NatureReference entity / index nameRating reference entityResidual maturityBase currencyNotional (thousands)PositionMarket value (thousands)
    1Single-name CDSFirm AAA3 yearsUSD10,000Protection buyer20
    2Single-name CDSFirm BBBB6 yearsEUR10,000Protection seller-40
    3CDS indexCD X.IGInvestment grade5 yearsUSD10,000Protection buyer0

     

    According to the Standards, the EAD for un-margined netting sets is given by:

    EAD = 1.4 * (RC + PFE)
     

    • 1. Replacement Cost Calculation

      The replacement cost is calculated at the netting set level as a simple algebraic sum (floored at zero) of the derivatives’ market values at the reference date. Thus, using the market values indicated in the table (expressed in thousands):

      RC = max {V - C; 0} = max {20 - 40 + 0; 0} = 0
       

      Since V-C is negative (i.e. -20,000), the multiplier will be activated (i.e. it will be less than 1). Before calculating its value, the aggregate add-on needs to be determined.

    • 2. Potential Future Exposure Calculation

      The following table illustrates the steps typically followed for the add-on calculation:

      StepsActivities
      1. Calculate Effective NotionalCalculate supervisory duration
      Calculate trade-level adjusted notional = trade notional (in domestic currency) × supervisory duration
      Calculate trade-level effective notional amount = trade-level adjusted notional × supervisory delta × maturity factor
      Calculate effective notional amount for each entity by summing the trade-level effective notional amounts for all trades referencing the same entity (either a single entity or an index) with full offsetting
      2. Apply Supervisory FactorsAdd-on for each entity in a hedging set = Entity-level Effective Notional Amount × Supervisory Factor, which depends on entity’s credit rating (or investment/speculative for index entities)
      3. Apply Supervisory CorrelationsEntity-level add-ons are divided into systematic and idiosyncratic components weighted by the correlation factor
      4. AggregateAggregation of entity-level add-ons with full offsetting in the systematic component and no offsetting in the idiosyncratic component

       

         Effective Notional Amount

      The adjusted notional of each trade is calculated by multiplying the notional amount with the calculated supervisory duration SD specified in the Standards.

      d= Trade Notional × SD = Trade Notional × {exp(-0.05×S) – exp(-0.05 × E)} / 0.05

      TradeNotional AmountSESupervisory Duration SDAdjusted Notional d
      Trade 110,000,000032.78584047127,858,405
      Trade 210,000,000065.18363558651,836,356
      Trade 310,000,000054.42398433944,239,843

       

      The appropriate supervisory delta must be assigned to each trade: in particular, since Trade 1 and Trade 3 are long in the primary risk factor (CDS spread), their delta is 1; in contrast, the supervisory delta for Trade 2 is -1.

      TradeDeltaInstrument Type
      Trade 11linear, long (forward and swap)
      Trade 2-1linear, short (forward and swap)
      Trade 31linear, long (forward and swap)

       

      Thus, the entity-level effective notional is equal to the adjusted notional times the supervisory delta times the maturity factor (where the maturity factor is 1 for all three derivatives).

      1

       

       

      TradeAdjusted NotionalSupervisory DeltaMaturity FactorEntity Level Effective Notional
      Trade 127,858,4051127,858,405
      Trade 251,836,356-11-51,836,356
      Trade 344,239,8431144,239,843

       

         Supervisory Factor

       

      The add-on must now be calculated for each entity. Note that all derivatives refer to different entities (single names/indices). A supervisory factor is assigned to each single-name entity based on the rating of the reference entity, as specified in Table 1 in the relevant Standards. This means assigning a supervisory factor of 0.38% for AA-rated firms (Trade 1) and 0.54% for BBB-rated firms (for Trade 2). For CDS indices (Trade 3), the supervisory factor is assigned according to whether the index is investment or speculative grade; in this example, its value is 0.38% since the index is investment grade.

       

      Asset ClassSubclassρSF
      Credit, Single NameAA50%0.38%
      Credit, Single NameBBB50%0.54%
      Credit, IndexIG80%0.38%

       

       

       

      Thus, the entity level add-ons are as follows:

       

      Add-on(Entity) = SF × Effective Notional
       

       

      TradeEffective NotionalSupervisory factor SFAdd-on (Entity)
      Trade 127,858,4050.38%105,862
      Trade 2-51,836,3560.54%-279,916
      Trade 344,239,8430.38%168,111

       

      Supervisory Correlation Parameters

       

      The add-on calculation separates the entity level add-ons into systematic and idiosyncratic components, which are combined through weighting by the correlation factor. The correlation parameter ρ is equal to 0.5 for the single-name entities (Trade 1-Firm A and Trade 2-Firm B) and 0.8 for the index (Trade 3-CDX.IG) in accordance with the requirements of the Standards.

       

      Add-on(Credit) = [ [ ∑k ρk CR × Add-on (Entityk) ]2 + ∑k (1- (ρk CR)2) × (Add-on (Entityk))2]1/2

       

       

       

      TradeρAdd-on(Entityk)ρ × Add-on(Entityk)(1 – ρ2)(1 – ρ2) × (Add-on(Entityk))2
      Trade 150%105,86252,9310.758,405,062,425
      Trade 250%-279,916-139,9580.7558,764,860,350
      Trade 380 %168,111134,4890.3610,174,120,000
      Systematic Component47,462Idiosyncratic Component77,344,042,776
      Full offsettingNo offsetting

       

         Add-on Aggregation

       

      For this netting set, the interest rate add-on is also the aggregate add-on because there are no trades assigned to other asset classes. Thus, the aggregate add-on = 346,878

       

      Aggregation of entity-level add-ons with full offsetting in the systematic component and no offsetting benefit in the idiosyncratic component.

       

      Systematic Component47,462
      Idiosyncratic Component77,344,042,776

       

       

       

         Thus,

       

      Add-on = [ (47,462)2 + 77,344,042,776 ]1/2 = 282,129

       

         Multiplier

       

         The multiplier is given by

       

      multiplier = min {1; Floor+(1-Floor) × exp [(V-C)/(2×(1-Floor)×Add-onagg)]}

       

         = min {1; 0.05 + 0.95 × exp [-20,000 / (2 × 0.95 × 282,129)]}

       

            =0.96521

       

         Final Calculation of PFE

       

      PFE = multiplier × Add-onagg = 0.96521 × 282,129= 272,313
       

       

    • 3. EAD Calculation

      The exposure that would be risk-weighted for the purpose of counterparty credit risk capital requirements is therefore:

      EAD = 1.4 * (RC + PFE) = 1.4 x (0 + 272,313) = 381,238