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.

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

   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

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.

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).

   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.

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

Add-on(Entity) = SF × Effective Notional
 

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 ρ_k ^CR × Add-on (Entity_k) ]² + ∑_k (1- (ρ_k ^CR)²) × (Add-on (Entity_k))²]^1/2

   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.

   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-on_agg)]}

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

      =0.96521

   Final Calculation of PFE

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

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