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2. Potential Future Exposure Calculation

C 52/2017 STA Effective from 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-onagg
 

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 setTime bucketNotional (thousands)SE
1USD310,000010
2USD210,00004
3EUR35,000111

 

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

StepsActivities
1. Calculate Effective NotionalCalculate 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 FactorsAdd-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 CorrelationsAdd-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. AggregateSimple 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

TradeNotional AmountTime BucketSESupervisory Duration SDAdjusted Notional d
Trade 110,000,00030107.86938680678,693,868.06
Trade 210,000,0002043.62538493836,253,849.38
Trade 35,000,00031117.48559228237,427,961.41
   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:

TradeDeltanstrument Type
Trade 11inear, long (forward and swap)
Trade 2-1inear, short (forward and swap)
Trade 31purchased 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 SetTime BucketAdjusted NotionalSupervisory DeltaMaturity FactorMaturity category-level Effective Notional D
HS 1 (USD)378,693,8681178,693,868
236,253,849-11-36,253,849
HS 2 (EUR)337,427,961-0.271-10,105,550

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 setTime BucketMaturity category-level Effective Notional Dj,kHedging Set level Effective Notional Dj,k (IR)
HS 1 (USD)378,693,86859,269,963
(Partial offset)
2-36,253,849
HS 2 (EUR)3-10,105,55010,105,549.58

 

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-onagg)]}

   = 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-onagg = 1 × 346,878 = 346,878