C. Illustration 3
Consider a netting set with three commodity forward contracts. 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 commodity derivatives.
Trade # Nature Underlying Position Direction Residual maturity Notional (thousands) Market value (thousands) 1 Forward (WTI)
Crude OilProtection Buyer Long 9 months 10,000 -50 2 Forward (Brent)
Crude OilProtection Seller Short 2 years 20,000 -30 3 Forward Silver Protection Buyer Long 5 years 10,000 100 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, provided that value is positive. Thus, using the market values indicated in the table (expressed in thousands):
RC = max {V - C; 0} = max {100 - 30 - 50; 0} = 20
The replacement cost is positive and there is no exchange of collateral (so the bank has not received excess collateral), which means the multiplier will be equal to 1.
2. Potential Future Exposure Calculation
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:
di(COM) = current price per unit × number of units in the trade
Trade Current price per unit (unit is barrel for oil; ounces for silver) Number of units in the trade Adjusted Notional Trade 1 100 100 barrels 10,000 Trade 2 100 200 barrels 20,000 Trade 3 20 500 ounces 10,000 The appropriate supervisory delta must be assigned to each trade:
Trade Delta Instrument Type Trade 1 1 linear, long (forward & swap) Trade 2 -1 linear, short (forward & swap) Trade 3 1 linear, long (forward & swap) 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.
Hedging Set Commodity Type Trade Adjusted Notional Supervisory Delta Maturity Factor Effective Notional Energy Crude Oil Trade 1 10,000 1 10,000 x 1 x 0.865 + 20,000x(-1)x1 =-11,350 (full off-setting within the ‘Crude Oil’ commodity type) Energy Crude Oil Trade 2 20,000 -1 1 Metals Silver Trade 3 10,000 1 1 10,000 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(Typekj) = SFTypek(Com) × Effective NotionalTypek(Com)
Hedging Set Commodity Type Effective Notional Supervisory Factor SF Add-on by HS and Commodity type Energy Crude Oil -11,350 18% -2,043 Metals Silver 10,000 18% 1,800 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) = [( Σk ρj(COM) × Add-on (Typekj) )2 + Σk (1- (ρj(COM) )2) × (Add-on (Type j))2]k1/2
Hedging Set Commodity Type ρ Add-on(Typek) Systematic Component (ρ × Add-on(Typek))2 (1 – ρ2) Idiosyncratic Component (1 – ρ2) x (Add-on(Typek)) 2 Add-onj (Only one commodity type in each HS) Energy Crude Oil 40% -2,043 (-817)2 0.84 0.84 × (-2,043)2 2,043 Metals Silver 40% 1,800 (720)2 0.84 0.84 × (1,800)2 1,800 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 = Σj Add-onj
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-onagg)]}
= 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-onagg = 1 × 3,843 = 3,843
3. EAD Calculation
The exposure EAD to be risk weighted for counterparty credit risk capital requirements purposes is therefore
EAD = 1.4 * (RC + PFE) = 1.4 x (20 + 3,843) = 5,408