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Compute DVA and account for how stressing DVA feeds into combined CCR stress tests.

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

The idea

DVA is the mirror image of CVA, and it is the value of the institution's own option to default. ENE is the expected negative exposure, the average of what the institution itself owes. DVA = own LGD × Σ DF(t) × ENE(t) × own marginal PD(t). The bilateral adjustment is CVA minus DVA. In a stress the institution's own spread usually widens, which raises DVA and produces an accounting gain that offsets part of the CVA loss. The net stress loss is the increase in CVA minus the increase in DVA. The gain is weak support in a stress. It can only be realised by default, it is hard to hedge, and Basel III removes DVA gains from CET1 capital. Combined CCR stress results should therefore show the CVA loss gross and the DVA offset separately. The usual errors are netting the whole DVA gain against CVA losses, or adding DVA instead of subtracting it.

Formulas

Debit valuation adjustment

DVA = LGDᵢ × Σ DF(t) × ENE(t) × PDᵢ(t)

LGDᵢ
the institution's own loss given default
DF(t)
the discount factor to date t
ENE(t)
the expected negative exposure at date t, what the institution expects to owe
PDᵢ(t)
the institution's own marginal probability of default between t − 1 and t

The mirror of CVA, built from what the institution owes and its own spread. A wider own spread raises DVA, an accounting gain.

Net stress loss on the bilateral adjustment

net stress loss = ΔCVA − ΔDVA

ΔCVA
the increase in CVA under the scenario
ΔDVA
the increase in DVA under the scenario

Subtract, never add, the DVA increase. For CET1 under Basel III the DVA gain is removed, so report ΔCVA gross with the offset shown separately.

A practice question

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

Which description matches DVA?

  1. The value of the institution's own option to default on its derivative liabilities, computed from expected negative exposure and its own default probability - correct
  2. The expected loss on the institution's receivables from counterparties, computed from expected exposure and the counterparty's own default probabilityWhy not: Describes CVA, the loss on counterparties' positions, not DVA, which relates to own default.
  3. The funding benefit from posting less collateral than the counterparty requiresWhy not: Describes a funding adjustment, not the value of own default.
  4. The reduction in counterparty exposure achieved by close-out nettingWhy not: Describes netting benefit, not an adjustment for own credit risk.

DVA = own LGD x sum of DF x ENE x own marginal PD. It is the mirror image of CVA and is a gain for the institution when its own credit worsens.

A harder one

An institution's expected negative exposure is USD 8 million at year 1 and USD 6 million at year 2. Its LGD is 60%, discount factors are exp(-0.03t), hazard rate = own spread / LGD, and marginal PD for year t = exp(-L(t-1)) - exp(-Lt). Its own spread widens from 150 bp to 450 bp. By how much does DVA rise, closest to?

  1. USD 0.56 millionWhy not: Reports the stressed DVA level rather than the increase.
  2. USD 0.23 millionWhy not: Uses the spread as the hazard rate without dividing by LGD.
  3. USD 0.37 million - correct
  4. USD 0.20 millionWhy not: Reports the base DVA rather than the change under stress.

Base DVA = 0.197; stressed DVA = 0.564. Rise = 0.367. DVA is calculated like CVA but with ENE and the institution's own PD.

The hardest tier

A bank's combined CCR stress test shows an increase in CVA of USD 40 million and an increase in DVA of USD 15 million. For assessing the impact on common equity Tier 1 capital under Basel III, which stress loss figure should be reported?

  1. USD 40 million, since Basel III removes DVA gains from CET1 capital - correct
  2. USD 25 million, netting the DVA gain against the CVA lossWhy not: Nets the DVA gain, although Basel III derecognises own-credit gains in CET1.
  3. USD 55 million, adding the DVA increase to the CVA increaseWhy not: Adds instead of subtracts, and also ignores the DVA treatment.
  4. USD 15 million, the DVA movement aloneWhy not: Reports the DVA movement and ignores the CVA loss that hits capital.

Basel III derecognises unrealised gains from changes in own credit risk, so the DVA gain cannot offset CVA losses in CET1. The CVA loss of 40 is reported gross, with the DVA offset shown separately.

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