Managing counterparty risk · RiskAtoms Academy

By the end you will be able to

1Set and monitor PFE limits for counterparties and run a pre-deal check on a new trade.
2Explain what a CVA desk does and how it charges trading desks for counterparty risk.
3Hedge CVA's sensitivity to the counterparty's spread with CDS and its market sensitivity with swaps, and name the limits of those hedges.
4Compute a first SA-CCR exposure on one netting set: replacement cost, PFE add-on, multiplier and alpha 1.4.

Why it matters

Halvergate's treasurer calls: the company has sold another $40m of US goods and wants to sell the dollars forward for two years. A simple, at-market trade, worth nothing today. Before the salesperson can say yes, the credit system runs a check. The answer: the trade would take Halvergate's potential future exposure to 103% of its limit, and it would add £19k of CVA that someone has to pay for. This lesson is about the people and numbers behind that answer.

Core explanation

Limits, a desk and a capital rule

Illustrative dataRiskAtoms Bank plc's derivatives book

The module's OTC book: eight trades (swaps, FX forwards, a bought index put) with four invented counterparties, each one netting set: Halvergate Manufacturing (BBB, no CSA), Corriemoor Bank (A), Saltney Capital (a hedge fund) and Ebbsworth Pension Trustees (AA). Exposures come from 2,000 seeded Monte Carlo paths of a flat GBP rate, GBPUSD and an equity index, half a month apart, out to ten years. Every firm and figure is made up for teaching, in pounds, on one valuation day; none is market data.

Extras for this lesson: the bank's PFE limits for the four counterparties, four candidate trades for the pre-deal check (all at market), and a five-year CDS for hedging. PFE is the 95% quantile from the book's simulation, after collateral where there is a CSA.

The module has built the tools: exposure measures (L3.4.02: Exposure measures), netting (L3.4.04: Netting), collateral and margin (L3.4.05: Collateral and the CSA to L3.4.07: Initial margin and the uncleared margin rules), clearing (L3.4.08: Central counterparties), and the price of what is left, CVA (L3.4.10: CVA basics). Managing counterparty risk day to day means using them in three ways: limits that cap how much the bank can lose to one name, a CVA desk that prices and hedges it, and capital that the regulator requires against it.

PFE limits and the pre-deal check

Credit officers set a PFE limit for each counterparty, larger for stronger names and for those with collateral. Exposure is checked against it every day, and every new trade is checked before it is agreed (the pre-deal check). The check uses the whole PFE profile: here, its peak.

Counterparty	Peak 95% PFE	at	Limit	Used
Halvergate Manufacturing plcno CSA	£13.82m	0.96y	£17m	81%
Corriemoor Bank AGafter collateral	£28.29m	3.00y	£40m	71%
Saltney Capital LPafter collateral	£9.14m	1.96y	£15m	61%
Ebbsworth Pension Trustees Ltdafter collateral	£14.96m	0.96y	£20m	75%

Two details matter. Halvergate's peak, £13.82m, comes just before its one-year FX forward settles; after that the swap alone drives the profile. Corriemoor's collateralised peak of £28.29m is a one-step spike on the day its three-year FX forward settles: the model assumes the bank pays its side while collateral it had posted against the forward is not yet returned. Risk managers watch such settlement spikes, and some limit systems smooth them; here the limit simply leaves room for it.

The CVA desk

ExploreA trade's life, seen by the CVA desk

Click a box to see what happens there.

Quote

The trading desk prices the swap risk-free. The CVA desk adds the trade's incremental CVA: the change in the netting set's CVA, not the trade's CVA on its own, because netting can make it smaller or even negative.

Hedging CVA

Halvergate's CVA of £211k has two kinds of sensitivity. To its credit spread: a CS01 of £1,069 a basis point. Buying CDS protection with the same sensitivity offsets it: with a five-year CDS risky PV01 of 4.21, that is about £2.54m of protection. To rates: Halvergate pays the bank fixed, so when rates rise the swap is worth less to the bank, exposure falls and so does CVA, by £1,996 a basis point. A receive-fixed five-year swap of about £4.48m offsets it. Both hedges must be rebalanced as exposures and spreads move.

Sort itHedgeable, or a reason for a reserve?

Corriemoor's spread: it has liquid single-name CDS.
Halvergate's spread: no CDS trades on it.
CVA's sensitivity to the GBP swap rate.
Saltney defaulting just after a market crash (wrong-way risk).
The cross effect: spreads widen just as rates fall.

Capital: a first look at SA-CCR

Regulators measure counterparty exposure for capital with a formula anyone can check. Under SA-CCR, the exposure at default of a netting set is

\text{EAD} = \alpha\,\big(\text{RC} + \text{multiplier} \times \text{AddOn}^{\text{aggregate}}\big), \qquad \alpha = 1.4

The replacement cost is today's loss on default after collateral. The PFE add-on stands in for the simulation of L3.4.02: Exposure measures: notionals scaled by supervisory factors for how much each asset class can move. The multiplier gives credit for a netting set that is out of the money or over-collateralised. The same alpha of 1.4 multiplies effective EPE under the internal model method, so the two can be compared. The worked example computes it for Halvergate; M4.4: Counterparty, operational and large exposures covers the rest.

The formal version

SA-CCR for interest rate and FX trades (Basel CRE52). For trade $i$ with notional $N_i$ , start $S_i$ , end $E_i$ and maturity $M_i$ (in years):

\begin{aligned} \text{RC} &= \max(V - C,\ 0) \quad\text{(unmargined)} \\ \text{RC} &= \max(V - C,\ \text{TH} + \text{MTA} - \text{NICA},\ 0) \quad\text{(margined)} \\ \text{SD}_i &= \frac{e^{-0.05 S_i} - e^{-0.05 E_i}}{0.05}, \qquad d_i^{\text{IR}} = N_i\,\text{SD}_i \\ d_i^{\text{FX}} &= \text{the foreign currency leg, in the home currency} \\ \text{MF}_i &= \sqrt{\min(M_i, 1)} \quad\text{(unmargined)}, \qquad 1.5\sqrt{\text{MPoR}_i / 250} \quad\text{(margined)} \\ D_k &= \sum_{i \in \text{bucket } k} \delta_i\,d_i\,\text{MF}_i, \qquad k: \ <1\text{y},\ 1\text{–}5\text{y},\ >5\text{y} \\ \text{AddOn}^{\text{IR}} &= 0.5\% \times \sqrt{D_1^2 + D_2^2 + D_3^2 + 1.4\,D_1D_2 + 1.4\,D_2D_3 + 0.6\,D_1D_3} \\ \text{AddOn}^{\text{FX}} &= 4\% \times \Big|\sum_{i \in \text{pair}} \delta_i\,d_i\,\text{MF}_i\Big|, \qquad \text{AddOn}^{\text{aggregate}} = \text{AddOn}^{\text{IR}} + \text{AddOn}^{\text{FX}} \\ \text{multiplier} &= \min\Big\{1,\ 0.05 + 0.95\,\exp\Big(\frac{V - C}{2 \times 0.95 \times \text{AddOn}^{\text{aggregate}}}\Big)\Big\} \end{aligned}

The delta $\delta_i$ is +1 if the trade gains when its risk factor rises and −1 if it loses (a receive-fixed swap loses when rates rise: −1). Asset classes are added with no diversification. With $V - C = -\text{£}20\text{m}$ against Halvergate's add-on the multiplier is 0.163; at −£100m it reaches its floor, 0.050.

The CDS hedge matches sensitivities. A bought CDS with notional $N$ gains about $N \times \text{RPV01} \times \Delta s$ when the spread widens by $\Delta s$ , so

N = \frac{\text{CS01}}{\text{RPV01} \times 0.0001} = \frac{1{,}069}{4.206 \times 0.0001} = \text{£}2.54\text{m}

Try it

Choose a counterparty and a new trade. The chart shows the 95% PFE profile today and with the trade, against the limit; the readouts give the decision and the CVA the desk must charge.

Try itRun a pre-deal check

Counterparty

New trade (the bank's side, at market)

PFE todayPFE with the new tradeLimit

Limit£17.0m

Decisionbreach: refer

Peak PFE today£13.82m (81%)

Peak PFE with the trade£17.43m (103%)

CVA today£210,680

Incremental CVA to charge+£19.5k

A trade that offsets the existing ones lowers both PFE and CVA: the CVA desk pays the trading desk for it. Under a CSA, new trades barely move the profile, because only the move over the margin period of risk is at risk.

Worked example

Halvergate: a pre-deal check and its SA-CCR exposure

From the treasurer's call to the capital number

Step 1 of 5

1
Pre-deal check
Halvergate hedges another £50m floating-rate loan: it pays fixed for five years, so the bank receives fixed. Peak PFE rises from £13.82m to £16.39m (96% of the £17m limit): approved. Incremental CVA £47.9k, charged to the trading desk. The $40m forward of the hook would take it to £17.43m: a breach.

Netting set	Margined?	RC	Add-on	SA-CCR EAD	α × effective EPE
Halvergate Manufacturing plc	no	£0.00m	£4.95m	£6.93m	£3.00m
Corriemoor Bank AG	yes (MPoR 10 days)	£0.50m	£3.56m	£5.69m	£1.93m
Ebbsworth Pension Trustees Ltd	yes (MPoR 10 days)	£11.00m	£3.54m	£16.53m	£5.16m

Corriemoor's CSA (threshold 0, MTA £0.5m) cuts its SA-CCR exposure sharply. Ebbsworth's £10m threshold puts £11m into the replacement cost, and its margined EAD is capped at the unmargined one. Saltney is left out: its option needs a supervisory delta, covered in M4.4: Counterparty, operational and large exposures.

What the credit officer notes

Halvergate: limit £17m, peak PFE £13.82m (81%). New £50m five-year swap approved; the $40m two-year forward referred: as offered it breaches the limit, so a CSA or a smaller or shorter trade would have to be tested again. CVA desk to buy about £2.5m of five-year protection on a proxy name. SA-CCR EAD £6.93m.

Regulatory lens

SA-CCR was published by the Basel Committee in March 2014 to replace the older current exposure and standardised methods, with a Basel implementation date of 1 January 2017; it is now chapter CRE52 of the Basel Framework. Banks with approval may use the internal model method instead (CRE53), with EAD = α × effective EPE. SA-CCR's exposure measure, whichever method a bank uses for capital, also feeds the large exposures limit: since 1 January 2019, a bank's exposure to one counterparty or connected group may not exceed 25% of its Tier 1 capital, or 15% between two global systemically important banks. CVA risk has its own capital charge, in which eligible CDS hedges count (MAR50, M4.3: Market risk capital (FRTB) and CVA). SA-CCR, the IMM and large exposures in full are in M4.4: Counterparty, operational and large exposures; exposure simulation and the XVA desk in M6.6: Counterparty risk and XVA.

Spark Atoms

Spark AtomNever quite zero

SA-CCR's multiplier has a floor of 5%. However much excess collateral a bank holds, or however far a netting set is out of the money, it still carries 5% of its add-on: at V − C = −£100m, Halvergate's multiplier is 0.050. The counterparty could still default after the market has moved the other way.

Spark AtomA hedge that adds risk

Buying CDS protection to hedge CVA creates a new counterparty: the protection seller. If it is cleared, the exposure is to a CCP (L3.4.09: The risks CCPs bring); if not, it needs its own limit, CSA and CVA. And a seller closely tied to the counterparty brings back the wrong-way risk of L3.4.11: Wrong-way risk.

Key takeaways

Each counterparty has a PFE limit; every new trade is checked against it before it is agreed, on the whole netting set.
The CVA desk charges trading desks the incremental CVA of each trade, carries the counterparty risk and hedges it.
CVA hedges: CDS for the spread (Halvergate £2.54m against a CS01 of £1,069), swaps and other market hedges for the exposure; wrong-way and cross effects remain.
SA-CCR: EAD = 1.4 × (RC + multiplier × add-on); Halvergate's at-market set has EAD £6.93m, all from the add-on.
SA-CCR is cautious next to α × effective EPE; collateral and netting reduce both.

Reaction

Check what stuck

Glossary

PFE limit: PFE limit: the most the bank will accept as the peak of a counterparty's potential future exposure (at, say, 95%), set by its credit appetite for that name.
Pre-deal check: Pre-deal check: before a trade is agreed, the new trade is added to the netting set and the resulting PFE compared with the limit.
CVA desk: CVA desk (XVA desk): a central desk that charges trading desks the CVA of each new trade, holds the counterparty risk, and hedges it.
CS01: CS01: the change in CVA for a one basis point rise in the counterparty's credit spread.
SA-CCR: SA-CCR: the Basel standardised approach for counterparty credit risk, which sets exposure at default as 1.4 × (replacement cost + multiplier × PFE add-on).
Replacement cost: Replacement cost: what the bank would lose today if the counterparty defaulted, after collateral; never below zero.
PFE add-on: PFE add-on: SA-CCR's formula for potential future exposure, from adjusted notionals, supervisory factors, deltas and maturity factors, by asset class.
Multiplier: Multiplier: SA-CCR's recognition of excess collateral or negative value, which can cut the add-on to as little as 5% of it.
Supervisory duration: Supervisory duration: SA-CCR's scaling of an interest rate or credit trade's notional by its length, (e^(−0.05S) − e^(−0.05E)) / 0.05.
Maturity factor: Maturity factor: √(min(M, 1 year)/1 year) for unmargined trades, 1.5 × √(MPoR/1 year) for margined ones.
Large exposures limit: Large exposures limit: under Basel, a bank's exposure to one counterparty or connected group may not exceed 25% of its Tier 1 capital (15% between global systemically important banks).

Deep Dives & Origins

Deep Dives

J. Gregory, The xVA Challenge: Counterparty Credit Risk, Funding, Collateral, and Capital, 3rd edition, Wiley, 2015 (the chapters on credit limits, CVA management and hedging). Intermediate.
Basel Committee on Banking Supervision, The standardised approach for measuring counterparty credit risk exposures, March 2014 (with worked examples). Advanced.

Origins

Basel Committee on Banking Supervision, Basel Framework, CRE52 Standardised approach to counterparty credit risk, and CRE53 Internal models method.
Basel Committee on Banking Supervision, “Final standard for measuring and controlling large exposures published by the Basel Committee”, press release, 15 April 2014.
Basel Committee on Banking Supervision, Basel Framework, MAR50 Credit valuation adjustment framework (paragraph 50.18 on eligible hedges).

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