Book traversal links for 2. Potential Future Exposure Calculation
2. Potential Future Exposure Calculation
C 52/2017 STA Effective from 1/4/2021All 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 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 |
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 Dj,k | Hedging Set level Effective Notional Dj,k (IR) |
HS 1 (USD) | 3 | 78,693,868 | 59,269,963 (Partial offset) |
2 | -36,253,849 | ||
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-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