2. Potential Future Exposure Calculation
C 52/2017 STA Effective from 1/4/2021The following table illustrates the steps typically followed for the add-on calculation:
| Steps | Activities |
| 1. Calculate Effective Notional | Calculate 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 Factors | Add-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 Correlations | Entity-level add-ons are divided into systematic and idiosyncratic components weighted by the correlation factor |
| 4. Aggregate | Aggregation 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
| Trade | Notional Amount | S | E | Supervisory Duration SD | Adjusted Notional d |
| Trade 1 | 10,000,000 | 0 | 3 | 2.785840471 | 27,858,405 |
| Trade 2 | 10,000,000 | 0 | 6 | 5.183635586 | 51,836,356 |
| Trade 3 | 10,000,000 | 0 | 5 | 4.423984339 | 44,239,843 |
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.
| Trade | Delta | Instrument Type |
| Trade 1 | 1 | linear, long (forward and swap) |
| Trade 2 | -1 | linear, short (forward and swap) |
| Trade 3 | 1 | linear, 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).
| Trade | Adjusted Notional | Supervisory Delta | Maturity Factor | Entity Level Effective Notional |
| Trade 1 | 27,858,405 | 1 | 1 | 27,858,405 |
| Trade 2 | 51,836,356 | -1 | 1 | -51,836,356 |
| Trade 3 | 44,239,843 | 1 | 1 | 44,239,843 |
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 Class | Subclass | ρ | SF |
| Credit, Single Name | AA | 50% | 0.38% |
| Credit, Single Name | BBB | 50% | 0.54% |
| Credit, Index | IG | 80% | 0.38% |
Thus, the entity level add-ons are as follows:
Add-on(Entity) = SF × Effective Notional
| Trade | Effective Notional | Supervisory factor SF | Add-on (Entity) |
| Trade 1 | 27,858,405 | 0.38% | 105,862 |
| Trade 2 | -51,836,356 | 0.54% | -279,916 |
| Trade 3 | 44,239,843 | 0.38% | 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
| Trade | ρ | Add-on(Entityk) | ρ × Add-on(Entityk) | (1 – ρ2) | (1 – ρ2) × (Add-on(Entityk))2 |
| Trade 1 | 50% | 105,862 | 52,931 | 0.75 | 8,405,062,425 |
| Trade 2 | 50% | -279,916 | -139,958 | 0.75 | 58,764,860,350 |
| Trade 3 | 80 % | 168,111 | 134,489 | 0.36 | 10,174,120,000 |
| Systematic Component | 47,462 | Idiosyncratic Component | 77,344,042,776 | ||
| Full offsetting | No 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 Component | 47,462 |
| Idiosyncratic Component | 77,344,042,776 |
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