Lab Test: Counterparty credit risk · RiskAtoms Academy

How it works

Eight problems from the people who watch a bank's derivatives counterparties: the counterparty risk analyst, the exposure team, collateral and margin, the CVA desk and regulatory reporting. Most follow one new client, Harrowden Airways Ltd, from its first trades to its default, its CSA, its CVA and its capital, and need more than one lesson. Answer each part (the unit is shown beside the box; £, %, commas, a minus sign and an x after a multiple are fine), press Check, then step through the worked solution. Numeric answers are marked right within a small tolerance, so round sensibly as you go. Keep a calculator handy.

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.

The problems use the module's methods with new inputs: a new airline client (Harrowden Airways Ltd) and a new hedge fund (Quillmere Capital LP), both invented, and a new default at the module's clearing house. They use hand-sized, closed-form versions of the calculations rather than the full simulation, so every answer can be checked by hand. All figures are made up.

Problem 1A new airline client, and the day it fails

L3.4.01 · L3.4.04

Counterparty risk analyst, credit risk

Harrowden Airways Ltd (invented), a UK airline with no rating, opens a netting set with RiskAtoms Bank under an ISDA Master Agreement with no CSA. It books four trades:

H1Receive-fixed swap, £60m, 6 years at 4.00% (Harrowden pays fixed to hedge a floating-rate aircraft loan)
H2Pay-fixed swap, £40m, 3 years at 4.00% (Harrowden swapped a fixed-rate bond into floating)
H3Sell $80m forward for pounds in 1 year at 1.28 (Harrowden buys dollars for fuel and leases)
H4Sold Harrowden a one-year call on $40m at 1.25, premium paid upfront

Eight months later a winter of high fuel prices pushes Harrowden into administration. The bank's legal opinion confirms that close-out netting is enforceable against it. Mid-market values to the bank on the day:

Trade	Value to the bank	max(V, 0)
H1	£6.15m	£6.15m
H2	−£1.27m	£0.00m
H3	−£2.95m	£0.00m
H4	−£1.10m	£0.00m

The bank expects to recover 40% of any unsecured claim on Harrowden.

Lessons: L3.4.01: What counterparty credit risk is · L3.4.04: Netting

(a)What is the netting set's replacement cost under close-out netting? Answer in £m.
£m
(b)What does the bank expect to lose on the netting set, after recovery? Answer in £m.
£m
(c)Suppose instead that netting could not be enforced. What would the bank expect to lose then? Answer in £m.
£m
(d)Had Harrowden survived to settle H3, the bank would deliver the $80m and Harrowden would pay the pounds. If the bank's dollars went out and Harrowden failed before its pounds arrived, how much would the bank be owed? Answer in £m.
£m

Problem 2Reading the exposure simulation

L3.4.02

Exposure analyst, risk methodology

Back on the day Harrowden's trades were booked, the risk system simulates the netting set. A small sample of twelve paths gives these values to the bank in one year (£m):

Path	1	2	3	4	5	6	7	8	9	10	11	12
Value, £m	−4.2	1.8	−0.6	5.3	2.4	−2.9	7.6	0.9	−1.5	3.7	11.2	−0.3

PFE uses the book's quantile convention: sort the twelve exposures, and take position $q\,(n - 1)$ counting from 0, interpolating between neighbours. The full simulation gives these expected exposures in the first year (£m):

Date	3 months	6 months	9 months	12 months
EE	1.55	2.90	2.35	2.60

Each quarterly figure stands for its quarter when you average over the year.

Lessons: L3.4.02: Exposure measures

(a)From the twelve paths, what is the expected exposure in one year? Answer in £m.
£m
(b)From the twelve paths, what is the 95% PFE in one year? Answer in £m.
£m
(c)From the full simulation's quarterly EE, what EAD does the internal model method give (α = 1.4)? Answer in £m.
£m

Problem 3The shape of each trade's exposure

L3.4.03 · L3.4.04

Exposure analyst, risk methodology

The credit officer asks how each of Harrowden's trades (Problem 1) adds to exposure over time. Use the book's market: a flat 4.00% GBP rate (annual compounding) with a normal volatility of 90bp a year, and the normal approximation of L3.4.03: Exposure profiles of common trades for an at-market swap:

\text{EE}(t) \approx \varphi(0)\,N\,\sigma\sqrt{t}\,A(t), \qquad A(t) = \sum_{\text{payments left}} 1.04^{-(k - t)}, \qquad \varphi(0) = 0.3989

For the netting benefit, the risk system gives standard deviations of value at six months of £2.04m for H1 and £3.83m for H3, both at market. In the book, the GBP rate and GBPUSD have a correlation of +0.3. Think about which way each trade gains.

Lessons: L3.4.03: Exposure profiles of common trades · L3.4.04: Netting

(a)When does H1's expected exposure peak, by the rule for a swap? Answer in years.
years
(b)What is H1's EE at that date, by the normal approximation? Answer in £m.
£m
(c)At six months, what is the netting benefit of holding H1 and H3 in one netting set, 1 − net EE / gross EE? Answer in %.
%
(d)Which statement about the other trades' exposure profiles is right?
AH3's EE peaks about a third of the way to settlement, like a swap's.BH4, the call the bank sold, has the largest exposure of the four, because options are the most volatile.CH2's EE is zero, because the bank pays fixed on it.DH3's EE keeps rising to settlement, roughly with √t; H4 adds no exposure to Harrowden once the premium is paid.

Problem 4A CSA with the airline

L3.4.05

Collateral manager, operations

After a review, RiskAtoms Bank and Harrowden sign a two-way CSA: threshold £5m each way, minimum transfer amount £0.5m, no independent amount, transfers rounded to £100,000 (up for a delivery, down for a return). Eligible collateral is cash or gilts, with the BCBS-IOSCO schedule's haircuts. Calls are made daily and met the next day.

Valuation date	Value of the netting set to the bank	Collateral the bank holds before the call
Day 1	£11.37m	£4.80m cash
Day 8	£8.94m	after day 1's call
Day 10	£9.32m	after day 8's transfer

Lessons: L3.4.05: Collateral and the CSA

(a)On day 1, how much collateral does the bank call for? Answer in £m.
£m
(b)Harrowden meets day 1's call with gilts maturing in seven years. What market value of gilts must it deliver? Answer in £m.
£m
(c)What moves on day 8? Answer as a signed amount in £m: positive if Harrowden delivers to the bank, negative if the bank returns collateral to Harrowden.
£m
(d)On day 10, after any call is settled, how much of the bank's exposure to the airline is not covered by collateral? Answer in £m.
£m

Problem 5A hedge fund with full collateral

L3.4.06

Counterparty risk analyst, funds coverage

Quillmere Capital LP (invented), a macro hedge fund, trades rates, FX and equity derivatives with RiskAtoms Bank. The CSA has a zero threshold and zero MTA, and collateral is cash, called daily. The risk system puts the standard deviation of the netting set's value over one year at £11.2m; treat changes in value as normal with mean zero, and count 250 business days a year. The netting set has fewer than 5,000 trades, the collateral is liquid, and there have been no disputes.

Lessons: L3.4.06: The margin period of risk

(a)With the 10-business-day margin period of risk for a daily-margined set, what is the expected exposure to Quillmere? Answer in £m.
£m
(b)What is the 95% PFE over the same margin period of risk? Answer in £m.
£m
(c)Quillmere asks to move to weekly margining (every 5 business days). What would the expected exposure be then? Answer in £m.
£m

Problem 6Initial margin, bilateral and cleared

L3.4.07 · L3.4.08 · L3.4.09

Margin analyst, treasury

Bilateral. Quillmere and RiskAtoms Bank are both covered by the uncleared margin rules, so each must post initial margin to the other. Quillmere's uncleared trades with the bank, valued today:

Trade	Schedule class	Notional	Value to the bank
Q1: Interest rate swap, £90m, 8 years	Interest rate, over 5 years	£90.00m	£3.1m
Q2: Interest rate swap, £50m, 4 years	Interest rate, 2 to 5 years	£50.00m	−£0.8m
Q3: FX forward, $120m (£ notional at 1.30)	Foreign exchange	£92.31m	−£1.9m
Q4: Equity index option, £25m notional	Equity	£25.00m	£2.4m

The BCBS-IOSCO schedule: interest rate 2 to 5 years 2% of notional, over 5 years 4%; foreign exchange 6%; equity 15%. Net IM = (0.4 + 0.6 × NGR) × gross IM, where NGR is net replacement cost / gross replacement cost. For a model figure, use the same £11.2m annual standard deviation as in Problem 5, at 99% over 10 business days.

Cleared. RiskAtoms Bank is a member of Wexcombe Clearing House, the module's illustrative CCP for sterling swaps. Its figures, £m:

Resource	£m
Corriemoor Bank AG: initial margin	13.77
Corriemoor: default fund contribution	13.39
Wexcombe's own capital (skin in the game)	5.00
Surviving members' default fund	56.61
… of which RiskAtoms Bank's contribution	4.34
RiskAtoms Bank's initial margin at Wexcombe	4.46

Corriemoor's house position loses £420,000 for each basis point that rates rise. Assessments on surviving members are capped at one more default fund contribution each, shared pro rata. Wexcombe's IM model uses a rate volatility of 90bp a year, and members post a 25% anti-procyclicality buffer on top of the model IM.

Lessons: L3.4.07: Initial margin and the uncleared margin rules · L3.4.08: Central counterparties · L3.4.09: The risks CCPs bring

(a)What initial margin does the schedule require on Quillmere's set? Answer in £m.
£m
(b)What is the model figure, at 99% over ten business days? Answer in £m.
£m
(c)Corriemoor defaults after rates rise 150bp. How much of RiskAtoms Bank's default fund contribution is used? Answer in £m.
£m
(d)Had rates risen 250bp instead, how much would RiskAtoms Bank lose in all, default fund and any assessment? Answer in £m.
£m
(e)In the stress, Wexcombe recalibrates its IM model to a 150bp volatility. How much extra IM does it call from RiskAtoms Bank? Answer in £m.
£m

Problem 7Pricing the airline's credit, and its wrong way

L3.4.10 · L3.4.11

CVA desk

Back on the booking day (no CSA yet), the CVA desk prices Harrowden's netting set. Harrowden's proxy five-year CDS spread is 300bp, recovery 40%; use a flat hazard rate from the credit triangle. The risk system gives expected exposure at mid-year (£m):

Year	1	2	3	4
EE at mid-year	2.6	3.4	3.0	1.9

Use one line a year, as in L3.4.10: CVA basics: CVA ≈ (1 − R) Σ EE(y − ½) × DF(y − ½) × PD(y − 1, y), discounting at 4% a year, with PD(y − 1, y) = $e^{-\lambda(y-1)} - e^{-\lambda y}$ .

Lessons: L3.4.10: CVA basics · L3.4.11: Wrong-way risk

(a)What is the CVA on Harrowden's netting set? Answer in £ thousands.
£k
(b)Revalue at 400bp and estimate CS01 as (CVA at 400bp − CVA at 300bp) / 100. Answer in £ per basis point.
£
(c)Which of Harrowden's trades carries general wrong-way risk?
AH3, the forward: airlines buy fuel in dollars, so a dollar trade with an airline is wrong-way.BNeither: wrong-way risk needs a direct link to the counterparty's own shares or bonds.CH1, the receive-fixed swap: the bank is owed most when rates have fallen, which tends to happen in the downturns that hit air travel.DBoth equally: every trade with a weak counterparty is wrong-way.
(d)To cover exposure, Harrowden offers £12m face value of its own bonds, counted at a 10% haircut. If Harrowden defaults and the bonds trade at the recovery rate, how far short of their counted value do they fall? Answer in £m.
£m

Problem 8The capital number: SA-CCR

L3.4.12

Regulatory reporting, capital

Three months after booking (before the CSA), the bank reports Harrowden's netting set under SA-CCR. The option H4 is left out here (it needs a supervisory delta, covered in M4.4: Counterparty, operational and large exposures). Residual maturities: H1 5.75 years, H2 2.75 years, H3 0.75 years. The three trades are together worth −£4.0m to the bank, and there is no collateral. GBPUSD is 1.30.

\begin{aligned} \text{SD} &= \frac{1 - e^{-0.05 M}}{0.05}, \quad d^{\text{IR}} = N \times \text{SD}, \quad \text{MF} = \sqrt{\min(M, 1)} \\ \text{AddOn}^{\text{IR}} &= 0.5\% \times \sqrt{D_1^2 + D_2^2 + D_3^2 + 1.4 D_1 D_2 + 1.4 D_2 D_3 + 0.6 D_1 D_3} \\ \text{AddOn}^{\text{FX}} &= 4\% \times \Big|\sum \delta\,d\,\text{MF}\Big|, \qquad \text{multiplier} = \min\Big\{1,\ 0.05 + 0.95\,e^{\frac{V - C}{2 \times 0.95 \times \text{AddOn}}}\Big\} \end{aligned}

Buckets: $D_1$ under 1 year, $D_2$ 1 to 5 years, $D_3$ over 5 years, each the sum of $\delta\,d\,\text{MF}$ ; $\delta = +1$ if the trade gains when its risk factor (the rate, or the price of a dollar) rises, −1 if it loses.

Lessons: L3.4.12: Managing counterparty risk

(a)What is the interest rate add-on? Answer in £m.
£m
(b)What is the FX add-on? Answer in £m.
£m
(c)What is the multiplier?
×
(d)What is the SA-CCR exposure at default? Answer in £m.
£m

Score 0 / 310 of 8 problems checked

Back · L3.4.12

Managing counterparty risk

Next module · L3.5.01 · coming soon

Funding liquidity and market liquidity