Describe bilateral CVA (BCVA) together with debt value adjustment (DVA).
The idea
Bilateral CVA recognises that the institution can default as well as the counterparty. Debit (debt) value adjustment, DVA, is the value to the institution of the possibility that it defaults on what it owes. Here ENE is the discounted expected negative exposure at each date, PDown is the institution's own marginal default probability, and V is the risk-free value. Using those inputs, the adjustment at each date is DVA = LGDown × Σ ENE × PDown, summed over all of the dates. The bilateral value of the position to the institution, starting from the risk-free value, is Value = V − CVA + DVA. The net charge to the institution, which is positive when the counterparty's risk outweighs its own, is BCVA = CVA − DVA. The counterparty sees the mirror image: its CVA is your DVA and its DVA is your CVA, so the two bilateral valuations are symmetric and sum to zero. DVA increases when your own spread widens, a gain from deteriorating credit that is hard to realise or hedge, which is the main criticism. Do not mix up the exposure measures or whose PD is used.
Formulas
Bilateral value of a derivative portfolio
Bilateral value = V − CVA + DVA
- V
- the risk-free value
- CVA
- the adjustment for the counterparty's default
- DVA
- the adjustment for the institution's own default
CVA is a cost and DVA a benefit. The counterparty's bilateral value uses the same two numbers with roles swapped, so the two values sum to zero.
A practice question
Debit (debt) value adjustment (DVA) in a bilateral valuation reflects:
- the benefit to the institution of its own possible default on amounts it owes. - correct
- the cost to the institution of posting collateral to the counterparty and funding it.Why not: Confuses DVA with a funding or collateral cost; it is a credit-risk adjustment.
- the cost to the institution of the counterparty possibly defaulting on amounts owed to it.Why not: Describes CVA, the cost of counterparty default, not DVA.
- the maximum amount the institution could be required to pay at a high confidence level.Why not: Describes a potential future exposure style measure, not an expected valuation adjustment.
DVA is the mirror image of CVA: it is the value to the institution of the possibility that it defaults when it owes money, and it is computed from the expected negative exposure and the institution's own default probability.
A harder one
A bank holds a derivative asset position with a corporate counterparty. Only the bank's own CDS spread widens; the counterparty spread and the exposure are unchanged. What happens to the bank's bilateral valuation of the position?
- The valuation is unchanged, because DVA applies only to liabilities and the position is an asset.Why not: Overlooks that the position can turn into a liability in future; DVA depends on the expected negative exposure.
- The valuation falls, because the bank's wider spread reduces the discount factors.Why not: Mixes credit spread into the risk-free discount factors, which are unaffected by DVA.
- The valuation rises, because DVA increases while CVA is unchanged. - correct
- The valuation falls, because the bank's weaker credit raises the CVA on the counterparty.Why not: CVA depends on the counterparty's spread, not the bank's own.
DVA = LGD_own x discounted ENE x own marginal PD. A wider own spread raises own PD, so DVA rises and value rises, which is why DVA gains in bad times are controversial.
The hardest tier
A bank's swap with a counterparty has a risk-free value of USD 5.0 million to the bank, a CVA of USD 1.2 million and a DVA of USD 0.7 million. The counterparty values the same swap bilaterally using the same inputs, so its own CVA is the bank's DVA and its DVA is the bank's CVA. What is the counterparty's bilateral value of the swap?
- Minus USD 6.9 millionWhy not: Adds both adjustments to the position's magnitude, ignoring that CVA is a deduction for the party that is owed.
- Minus USD 4.5 million - correct
- Minus USD 3.1 millionWhy not: Subtracts both adjustments from the magnitude of the position, ignoring that DVA adds value.
- Minus USD 5.5 millionWhy not: Uses the bank's CVA and DVA unswapped as the counterparty's own CVA and DVA, so the roles are not reversed.
Bank: 5.0 - 1.2 + 0.7 = 4.5. Counterparty: -5.0 - (its CVA = 0.7) + (its DVA = 1.2) = -4.5. Bilateral valuation is symmetric: the two values sum to zero.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
Start free →More in CVA
- Account for why pricing counterparty risk is wanted and what makes it hard.
- Explain the concept of CVA, the adjustment made to a derivative's value for credit risk.
- Work out CVA, plus its expression as a spread, in the simple setting where wrong-way risk, netting and collateralization are all absent.
- Judge how shifts in credit spread and recovery rate assumptions affect CVA.
- Account for how unilateral CVA (UCVA) differs from BCVA, and how unilateral DVA (UDVA) differs from BCVA.
- Work out the DVA and the BCVA, then restate BCVA as a spread.
- Explain the way netting enters the computation of CVA.
- State what incremental CVA and marginal CVA are, compute them and show how CVA is turned into a running spread.
- Show how the CVA figure changes once collateralization is built in, paying attention to initial margins, thresholds and the margin period of risk.
- Spell out wrong-way risk and set right-way risk against it.
- Identify illustrations of right-way risk as well as wrong-way risk.
- Review how collateral bears on wrong-way risk.
- Identify cases that illustrate collateral exposed to wrong-way risk.
- Weigh up how wrong-way risk bears on CCPs (central counterparties).
- Outline the methods for modelling wrong-way risk: hazard rate, structural, parametric and jump approaches.
- Account for what central clearing means for wrong-way risk.