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2. Potential Future Exposure Calculation

C 52/2017 STA Effective from 1/4/2021

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