Case 041Counterparty risk and CVAHard

A bank is quoting a five-year cross-currency swap to a steel company. Given the expected exposure profile, default probability and recovery, compute the CVA and decide whether a 15 basis point upfront credit charge covers it.

The situation

Jhelvora Steel wants a five-year cross-currency swap with your bank on Rs 300 crore of notional: it will pay dollars and receive rupees. The swap is uncollateralised. Your exposure model gives expected positive exposure at the end of years 1 to 5 of Rs 8, 12, 14, 12 and 6 crore.

Jhelvora's default probability is 3% a year, loss given default is 60% and your discount rate is 8%. The sales desk proposes an upfront credit charge of 15 basis points of notional, Rs 45 lakh. Jhelvora imports most of its coking coal in dollars.

Your task

What is the CVA, does the charge cover it, what is the breakeven charge, and what else about this counterparty should worry you?

Quick check

Before computing: is 15 basis points enough?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The CVA is about Rs 71 lakh, so a Rs 45 lakh charge covers only about 63% of it. Each year's exposure times the chance Jhelvora first defaults that year, times 60% loss, discounted at 8%, sums to Rs 71.1 lakh, a breakeven of about 24 basis points. The number is also likely too low: Jhelvora pays dollars and buys coal in dollars, so a weaker rupee raises the exposure just as it weakens Jhelvora. Reprice, or ask for collateral.

Step 1What is CVA actually pricing?

A shop that sells on credit to a customer who might go bust should charge a little more for the goods, enough to cover the expected bad debt. CVACredit valuation adjustment: the market value of the expected loss from a counterparty defaulting while it owes you money on a derivative. is that expected bad debt on a derivative: in each period, what you would be owed, times the chance the counterparty defaults then, times the share you would lose, discounted to today. The exposure matters because a swap is only a loss if the counterparty owes you at the moment it fails.

Expected exposure on the Jhelvora swap rises from Rs 8 crore to a peak of Rs 14 crore in year 3 and runs off to Rs 6 crore, while the chance of Jhelvora first defaulting in each year eases from 3.00% to 2.66% as fewer years of survival remain.

Step 2How do you compute it year by year?

The chance of a first default in year t is the chance of surviving to it times 3%: 3.00% in year 1, 2.91% in year 2 and so on. Multiply each year's exposure by that probability, by 60% loss and by the discount factor, then add: the total is Rs 71.1 lakh. Year 3 contributes most, because it combines the largest exposure with a still-high default chance. Using a flat 3% every year, ignoring survival, gives Rs 75.1 lakh, a small overstatement worth mentioning but not worth arguing over.

The relationship

\text{CVA} = \text{LGD} \sum_{t=1}^{5} \text{EPE}_t \,(1-p)^{t-1} p \,\frac{1}{(1+r)^t} \approx 0.711\text{ crore}

\text{EPE}_t	expected positive exposure at the end of year t
p	yearly default probability, 3%
\text{LGD}	loss given default, 60%
r	discount rate, 8%

What it says in wordsCVA adds up, year by year, the exposure times the chance of first default in that year times the loss rate, discounted to today.

Year	Exposure, Rs cr	First default	Discount factor	Expected loss, Rs lakh
1	8	3.00%	0.926	13.3
2	12	2.91%	0.857	18.0
3	14	2.82%	0.794	18.8
4	12	2.74%	0.735	14.5
5	6	2.66%	0.681	6.5
CVA				71.1

Each year's expected loss is exposure times the chance of first default that year times 60%, discounted at 8%; the five years sum to a CVA of Rs 71.1 lakh.

The discounted expected losses sum to a CVA of Rs 71.1 lakh against a proposed charge of Rs 45 lakh, a shortfall of about Rs 26 lakh; covering it needs about 24 basis points upfront.

Step 3Why is the true cost probably higher still?

The calculation assumes exposure and default are independent. Here they are not. Jhelvora pays dollars on the swap and buys its coal in dollars, so a sharp fall in the rupee raises what it owes you at the same moment it squeezes its margins. That is wrong-way riskWhen exposure to a counterparty tends to rise exactly when that counterparty becomes more likely to default., and it means the exposure that matters, the one on the day Jhelvora fails, is larger than the average the model gives. The fix is not a bigger spreadsheet; it is a stressed exposure profile, a higher charge, or collateral.

Step 4What would you do with the trade?

Three options, in order of preference. A collateral agreement with a low threshold cuts expected exposure to a fraction and makes most of the CVA disappear. Failing that, charge at least 24 basis points plus a margin for wrong-way risk, and remember that capital and funding costs sit on top of CVA. A mutual break clause at year 3 caps the tail. Taking the trade at 15 basis points means giving away about Rs 26 lakh of expected value on day one, which a counterparty risk manager should say plainly to the desk.

Where candidates lose it

The usual mistake is to multiply the peak exposure by the default probability and stop, or to use the notional of Rs 300 crore as the exposure. A swap's exposure is its replacement value, a small and changing fraction of notional, which is why the profile is given.

The second is to miss the wrong-way risk. The question tells you Jhelvora buys coal in dollars for a reason: the counterparty is weakest in exactly the scenario where it owes the most.

What the interviewer asks next

How much would a collateral agreement with a Rs 2 crore threshold cut the CVA?
Should the bank also account for its own default risk, and what is that adjustment called?
Jhelvora's credit spread widens sharply next month. What happens to the CVA and to the desk's P&L?

Company names and figures are illustrative.