The following table illustrates the steps typically followed for the add-on calculation, for each of the four commodity hedging sets with non-zero exposure:

   Effective Notional Amount

Trade-level Adjusted Notional calculation for each commodity derivative trade:

d_i^(COM) = current price per unit × number of units in the trade
 

The appropriate supervisory delta must be assigned to each trade:

Since the remaining maturity of Trade 1 is less than a year, at nine months (approximately 187 business days), and the trade is un-margined, its maturity factor is scaled down by the square root of 187/250 in accordance with the requirements of the Standards. On the other hand, the maturity factor is 1 for Trade 2 and for Trade 3, since the remaining maturity of those two trades is greater than one year and they are un-margined.

The trade-level effective notional is equal to the adjusted notional times the supervisory delta times the maturity factor. The basic difference between the WTI and Brent forward contracts effectively is ignored since they belong to the same commodity type, namely “Crude Oil” within the “Energy” hedging set, thus allowing for full offsetting. (In contrast, if one of the two forward contracts were on a different commodity type within the “Energy” hedging set, such as natural gas, with the other on crude oil, then only partial offsetting would have been allowed between the two trades.) Therefore, Trade 1 and Trade 2 can be aggregated into a single effective notional, taking into account each trade’s supervisory delta and maturity factor.

   Supervisory Factor

For each commodity-type in a hedging set, the effective notional amount must be multiplied by the correct Supervisory Factor (SF). As described in the Standards, the Supervisory Factor for both the Crude Oil commodity type in the Energy hedging set and the Silver commodity type in the Metals hedging set is SF=18%.

Thus, the add-on by hedging set and commodity type is as follows:

Add-on(Type_k^j) = SF_Typek^(Com) × Effective Notional_Typek^(Com)
 

   Supervisory Correlation Parameters

The commodity-type add-ons in a hedging set are decomposed into systematic and idiosyncratic components. The commodity subclass correlations parameters are as stated in the Standards, in this case 40% for commodities.

Thus, the hedging set level add-ons are calculated for each commodity hedging set:

Add-on^(COM) = [( Σ_k ρ_j^(COM) × Add-on (Type_k^j) )² + Σ_k (1- (ρ_j^(COM) )²) × (Add-on (Type ^j))²]_k^1/2

However, in this example, since only one commodity type within the “Energy” hedging set is populated (i.e. all other commodity types within that hedging set have a zero add-on), the resulting add-on for the hedging set is the same as the add-on for the commodity type. This calculation shows that when there is only one commodity type within a commodity hedging set, the hedging-set add-on is equal to the absolute value of the commodity-type add-on. (The same comment applies to the commodity type “Silver” in the “Metals” hedging set.)

   Add-on Aggregation

Aggregation of commodity-type add-ons uses full offsetting in the systematic component and no offsetting benefit in the idiosyncratic component in each hedging set. As noted earlier, in this example there is only one commodity type per hedging set, which means no offsetting benefits. Computing the simple summation of absolute values of add-ons for the hedging sets:

Add-on = Σ_j Add-on_j

Add-On = 2,043 + 1,800 = 3,843

   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 / (2 × 0.95 × 3,843)]}

      = 1, since V-C is positive.

   Final Calculation of PFE

PFE = multiplier × Add-on_agg = 1 × 3,843 = 3,843