2. Potential Future Exposure Calculation

C 52/2017 STA يسري تنفيذه من تاريخ 1/4/2021

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.

Trade #	Hedging set	Time bucket	Notional (thousands)	S	E
1	USD	3	10,000	0	10
2	USD	2	10,000	0	4
3	EUR	3	5,000	1	11

The 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 as trade notional (in domestic currency) × supervisory duration Effective notional for each maturity category = Σ(trade-level adjusted notional × supervisory delta × maturity factor), with full offsetting for each of the three maturity categories, in each hedging set (that is, same currency)
2. Apply Supervisory Factors	Add-on for each maturity category in a hedging set (that is, same currency) = Effective Notional Amount for maturity category × interest rate supervisory factor
3. Apply Supervisory Correlations	Add-on for each hedging set = Σ(Add-ons for maturity categories), aggregating across maturity categories for a hedging set. One hedging set for each currency.
4. Aggregate	Simple summation of the add-ons for the different hedging sets

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

Trade	Notional Amount	Time Bucket	S	E	Supervisory Duration SD	Adjusted Notional d
Trade 1	10,000,000	3	0	10	7.869386806	78,693,868.06
Trade 2	10,000,000	2	0	4	3.625384938	36,253,849.38
Trade 3	5,000,000	3	1	11	7.485592282	37,427,961.41

Calculate Maturity Category Effective Notional

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

•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.
•Trade 2 is short in the primary risk factor and is not an option; thus, the supervisory delta is equal to -1.
•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:

Hedging Set	Time Bucket	Adjusted Notional	Supervisory Delta	Maturity Factor	Maturity category-level Effective Notional D
HS 1 (USD)	3	78,693,868	1	1	78,693,868
HS 1 (USD)	2	36,253,849	-1	1	-36,253,849
HS 2 (EUR)	3	37,427,961	-0.27	1	-10,105,550

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:

Hedging set	Time Bucket	Maturity category-level Effective Notional D_j,k	Hedging Set level Effective Notional D_j,k ^(IR)
HS 1 (USD)	3	78,693,868	59,269,963 (Partial offset)
HS 1 (USD)	2	-36,253,849	59,269,963 (Partial offset)
HS 2 (EUR)	3	-10,105,550	10,105,549.58

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

Effective Notional^(IR) = 59,269,963 + 10,105,550 = 69,375,513

(No offset between 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]}

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