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 {30 - 20 + 50; 0} = 60
 

Since V-C is positive (equal to V of 60,000), the value of the multiplier is 1, as explained in the Standards.

All the transactions in the netting set belong to the interest rate asset class. So the Add-on for interest rate class must be calculated as well as the multiplier since

PFE = multiplier × Add-on_agg
 

For the calculation of the interest rate add-on, the three trades must be assigned to a hedging set (based on the currency) and to a maturity category (based on the end date of the transaction). In this example, the netting set is comprised of two hedging sets, since the trades refer to interest rates denominated in two different currencies (USD and EUR). Within hedging set “USD”, Trade 1 falls into the third maturity category (>5 years) and Trade 2 falls into the second maturity category (1-5 years). Trade 3 falls into the third maturity category (>5 years) of hedging set “EUR”.

S and E represent the start date and end date, respectively, of the time period referenced by the interest rate transactions.

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

   Calculate Effective Notional Amount

The adjusted notional of each trade is calculated by multiplying the notional amount by the calculated supervisory duration SD as defined in the Standards.

d = Trade Notional × SD = Trade Notional × (exp(-0.05×S) – exp(-0.05 × E)) / 0.05

   Calculate Maturity Category Effective Notional

A supervisory delta is assigned to each trade in accordance with the Standards. In particular:

1. •Trade 1 is long in the primary risk factor (the reference floating rate) and is not an option so the supervisory delta is equal to 1.
2. •Trade 2 is short in the primary risk factor and is not an option; thus, the supervisory delta is equal to -1.
3. •Trade 3 is an option to enter into an interest rate swap that is short in the primary risk factor and therefore is treated as a purchased put option. As such, the supervisory delta is determined by applying the relevant formula using 50% as the supervisory option volatility and 1 (year) as the option exercise date. Assume that the underlying price (the appropriate forward swap rate) is 6% and the strike price (the swaption’s fixed rate) is 5%.

The trade-level supervisory delta is therefore:

Trade	Delta	nstrument Type
Trade 1	1	inear, long (forward and swap)
Trade 2	-1	inear, short (forward and swap)
Trade 3	$$$$	purchased put option

The Maturity Factor MF is 1 for all the trades since they are un-margined and have remaining maturities in excess of one year.

Based on the maturity categories, the Effective Notional D for the USE and EUR hedging sets at the level of the maturity categories are as shown in the table below:

In particular:

Hedging set USD, time bucket 3: D = 1 * 78,693,868 * 1 = 78,693,868

Hedging set USD, time bucket 2: D = -1 * 36,253,849 * 1 = -36,253,849

Hedging set EUR, time bucket 3: D = -0.27 * 37,427,961 * 1 = -10,105,550

   Apply Supervisory Factor

The add-on must be calculated for each hedging set.

For the USD hedging set there is partial offset between the two USD trades:

Effective notional^(IR) _{USD =} [D2² + D3² + 1.4 x D2 x D3]^1/2

   = [(-36,253,849)² + 78,693,868² + 1.4 × (-36,253,849) × 78,693,868]^1/2

   = 59,269,963

For the Hedging set EUR there is only one trade (and one maturity category):

  Effective notional^(IR)_EUR = 10,105,550

In summary:

Aggregation of the calculated add-ons across different hedging sets:

The asset class is interest rates; thus the applicable Supervisory factor is 0.50%. As a result:

 Add-on = SF × Effective Notional = 0.005 × 69,375,513 = 346,878

   Supervisory Correlation Parameters

Correlation is not applicable to the interest rate asset class, and there is no other asset class in the netting set in this example.

   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

   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 [60,000 / (2 × 0.95 × 346,878]}

     =1

   Final Calculation of PFE

In this case the multiplier is equal to one, so the PFE is the same as the aggregate Add-On:

PFE = multiplier × Add-on_agg = 1 × 346,878 = 346,878
 

The exposure EAD to be risk weighted for counterparty credit risk capital requirements purposes is therefore

EAD = 1.4 * (RC + PFE) = 1.4 x (60,000 + 346,878) = 569,629