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Describe how CVA can be stress tested.

FRM® Part II · Credit Risk Measurement and Management · The Evolution of Stress Testing Counterparty Exposures · FRM2.CR.21.e

The idea

CVA is the market value of counterparty credit risk. It is approximately LGD times the sum, over time buckets, of discount factor × expected exposure × marginal default probability. Because CVA is marked to market, a CVA stress test measures a P&L hit that occurs without any default. Its drivers are counterparty credit spreads, recovery rates and the market factors that drive expected exposure. A full test shocks both sides, preferably in one coherent scenario, because the two interact multiplicatively and may be wrong-way correlated. Two approaches are used. Full revaluation re-simulates exposure under the stressed factors and spreads. Sensitivity-based estimates use CS01 and delta and gamma terms, including cross terms. They are fast but weaker for large shocks. Counterparties without liquid CDS use proxy spread curves, which must be stressed too. The CVA hedges must be included in the test, with their basis and jump-to-default risk.

Formulas

Sensitivity estimate of the CVA stress loss

ΔCVA = CS01 × Δs + δ × Δx + cross term

CS01
the change in CVA per basis point of counterparty spread
Δs
the spread move, in basis points
δ
the CVA sensitivity to the market factor
Δx
the market factor move
cross term
the extra effect of spreads and market factors moving together

A first-order approximation: fast but weaker for large shocks. Leaving out the cross term understates the loss, and hedge gains, such as CDS CS01 × Δs, are subtracted.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which inputs does a complete stress test of CVA shock?

  1. Counterparty credit spreads and recovery assumptions, together with the market factors that drive expected exposure - correct
  2. Only counterparty credit spreads, because expected exposure is a fixed contractual profileWhy not: Ignores that expected exposure moves with market factors.
  3. Only market risk factors, because credit spreads are observable constantsWhy not: Spreads move sharply in stress and drive the PD term of CVA.
  4. Only the notional amounts of trades, which scale CVA linearlyWhy not: Notional is not the scenario variable; CVA depends on revalued exposure and spreads.

CVA = LGD x sum of DF x EE x marginal PD. EE depends on market factors and PD on spreads, so both must be shocked, along with recovery.

A harder one

A dealer's CVA to a counterparty has a CS01 of USD 45,000 per basis point. It holds CDS protection with a CS01 of USD 30,000 per basis point against it. Using a linear sensitivity approach, what is the net stress loss on CVA for a parallel 200 bp widening of the counterparty's spread, ignoring other factors?

  1. USD 9.0 millionWhy not: Ignores the CDS hedge and takes 45,000 x 200 only.
  2. USD 6.0 millionWhy not: Counts only the hedge gain (30,000 x 200) instead of the net position.
  3. USD 3.0 million - correct
  4. USD 15.0 millionWhy not: Adds the hedge sensitivity to the CVA sensitivity instead of subtracting it.

CVA loss = 45,000 x 200 = 9.0 million; CDS gain = 30,000 x 200 = 6.0 million. Net loss = 3.0 million. Linear approximations are quick but miss convexity for large moves.

The hardest tier

A dealer pays an emerging-market currency and receives USD in cross-currency swaps with local banks. An analyst runs two separate stress tests: a 300 bp spread widening with exposures unchanged, and a 30% devaluation of the local currency with spreads unchanged. What is the main weakness?

  1. The tests miss that the devaluation raises exposure and widens spreads at the same time for the same counterparties, so the combined loss is understated - correct
  2. The tests are too severe, because a local-currency devaluation and a spread widening on local banks never occur together in practiceWhy not: In emerging-market crises devaluations and spread widening are positively linked.
  3. The spread shock should have been applied only to the dealer's own spreadWhy not: The own spread drives DVA; counterparty spreads drive CVA.
  4. Currency moves are irrelevant to CVA because CVA depends on credit spreads onlyWhy not: Exposure, and therefore CVA, depends on the revalued swaps and so on FX.

A devaluation raises the USD claim measured in local currency and weakens local banks' credit. Exposure and PD rise together and multiply in CVA, so separate tests understate the joint stress loss.

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