CVA on a Single-Name Oil Producer: Collateral, Wrong-Way Risk and an Index Hedge
A bank has a single netting set with an oil-and-gas producer rated BBB. The set is a 5-year USD interest-rate swap in which the bank pays fixed; the net mark-to-market in the bank's favour is USD 180m. Modelled expected exposure is flat at USD 150m per year for five years. The counterparty's 5-year CDS trades at 240bp, recovery is 40%, and the bank discounts at a flat 3%. The CSA has a USD 50m threshold, no minimum transfer amount, daily margining, and no downgrade trigger. The counterparty operates in a commodity-linked economy where policy rates and the oil price are strongly positively correlated. The credit desk proposes hedging the resulting CVA by buying protection on a broad investment-grade CDS index, arguing the hedge 'removes the mark-to-market volatility of the CVA book'.
1. Compute the unilateral CVA ignoring collateral, showing the hazard rate, marginal default probabilities and discounting.
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Hazard rate from the spread: lambda = s / (1 - R) = 0.024 / 0.60 = 4.0% per year.
Marginal default probabilities (survival to start of year times lambda):
| Year | Marginal PD | DF at 3% | PD x DF |
|---|---|---|---|
| 1 | 3.92% | 0.9709 | 0.0381 |
| 2 | 3.77% | 0.9426 | 0.0355 |
| 3 | 3.62% | 0.9151 | 0.0331 |
| 4 | 3.48% | 0.8885 | 0.0309 |
| 5 | 3.34% | 0.8626 | 0.0288 |
| Sum | 0.1664 |
CVA = LGD x EE x sum(PD x DF) = 0.60 x 150 x 0.1664 = USD 15.0m.
Sanity check without discounting: 5-year cumulative PD = 1 - exp(-0.04 x 5) = 18.13%, so 0.60 x 150 x 0.1813 = USD 16.3m. The discounted figure of USD 15.0m is the one to report.
Note the units of the exposure assumption: the number is only as good as the flat-EE simplification. A real EE profile that peaks in years 2-3 would shift the CVA materially because the early-year discount factors are the largest.
2. The CSA threshold is USD 50m. Explain how collateral changes the CVA and why the reduction cannot simply be computed as a linear scaling of the uncollateralised figure.
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Mechanics. With daily margining and a USD 50m threshold, the counterparty posts collateral equal to exposure above USD 50m. Residual secured exposure is therefore capped near USD 50m rather than USD 150m, and a naive linear scaling gives CVA of roughly 15.0 x (50/150) = USD 5m, i.e. the CSA removes about two thirds of the charge. That is directionally right but optimistic in three ways:
- Margin period of risk. Collateral is posted against exposure as measured, not against where exposure moves before the next effective exchange (10 business days for a derivative netting set). With meaningful rates volatility, a 10-day move can add tens of millions of uncovered exposure above the threshold, and that tail is where the remaining CVA sits.
- Posting failure. The protection is only as good as the counterparty's willingness and ability to post. In stress - a downgrade, a liquidity squeeze, a dispute over valuation - collateral stops arriving and the 'secured' exposure becomes unsecured at the worst moment. CVA must be stressed on an assumption of zero collateral received for the MPoR, not on the contractual assumption.
- No downgrade trigger. The CSA has no ratings-based threshold or additional-collateral requirement, so a two-notch downgrade changes the credit quality of the exposure without changing the collateral protection at all.
Conclusion. Report USD 5m as a point estimate, but pair it with a stress CVA assuming no collateral for the MPoR. The residual is concentrated in the tail, which is precisely where the capital is needed.
3. The credit desk wants to hedge with a broad investment-grade CDS index. Assess whether that hedge addresses the risk that actually matters here.
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The position is wrong-way. The bank pays fixed, so it has positive mark-to-market when rates fall. In a commodity-linked economy, rates and oil are positively correlated: a fall in oil drags rates down, which is exactly the state in which the bank's exposure rises - and it is also the state in which an oil producer's cash flow and rating deteriorate. Exposure and default probability are positively correlated. The independent-exposure CVA of USD 15m therefore understates the true charge; correcting it requires a joint simulation of rates, oil and default, not a separate EE and a separate PD.
Why the index hedge misses it. A broad IG index hedges the systematic component of the name's spread - its beta to the IG market. The component that is dangerous here is oil-linked idiosyncratic deterioration, which is roughly orthogonal to the index. The bank would end up with a smooth, well-hedged CVA book that still carries a concentrated jump-to-default on one name. There is also basis risk: the index spread and the single-name spread do not move one-for-one, so the hedge introduces its own P&L volatility.
What would actually address it:
- A bespoke or energy-sector CDS on the name, if liquidity allows.
- An oil-price-linked hedge that tracks the driver of joint deterioration.
- A collateral redesign: lower threshold, ratings-based threshold schedule with a downgrade trigger, and a minimum transfer amount small enough to be irrelevant in stress.
- Failing all of the above, a smaller sector and single-name limit - the cheapest hedge of all.