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Outline credit value adjustment (CVA) and contrast CVA with credit limits as tools for assessing and reducing counterparty risk.

FRM® Part II · Credit Risk Measurement and Management · Counterparty Risk and Beyond · FRM2.CR.15.e

The idea

Credit value adjustment, CVA, is the market price of counterparty risk. It is the difference between the risk-free value of a portfolio and its value allowing for counterparty default. In each period, DF is the discount factor, EPE the expected positive exposure and PD the marginal default probability, while LGD is the loss given default. The probabilities are market-implied (risk-neutral) ones, taken from credit spreads. Approximately, CVA = LGD × the sum over periods of DF × EPE × PD. Because it is a price, it enters the deal's pricing and the accounts and can be hedged with credit default swaps. Credit limits are different. They cap the potential future exposure at a high confidence level for a counterparty. They set a quantity rather than a price, ignore the cost of the risk and do not respond to spreads. Limits control concentration, while CVA prices expected loss. Exam point: use risk-neutral probabilities for CVA that will be hedged, historical ones for capital or reserves.

Formulas

Credit value adjustment

CVA = LGD × Σ (DFₜ × EPEₜ × PDₜ)

LGD
loss given default, one minus the recovery rate
DFₜ
the discount factor to date t
EPEₜ
the expected positive exposure at date t
PDₜ
the risk-neutral marginal default probability for the period ending at t

For a CVA that will be charged and hedged, use market-implied default probabilities. Historical ones belong in capital or reserves.

CVA approximated from the credit spread

CVA = s × EPE × T

s
the counterparty's CDS spread a year, as a decimal
EPE
the average expected positive exposure
T
the maturity in years

An approximation that ignores discounting. CVA moves in proportion to the spread, which a credit limit does not.

A practice question

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

Which statement correctly contrasts CVA and credit limits as tools for counterparty risk?

  1. CVA caps the maximum exposure to a counterparty, while credit limits price the expected loss.Why not: Reverses the two: limits cap exposure and CVA prices the expected loss.
  2. A credit limit caps potential future exposure to a counterparty without pricing the risk, while CVA puts a price on the expected loss that can be charged and hedged. - correct
  3. Both CVA and credit limits are priced from the counterparty's credit default swap spread, so each rises and falls with the market's view of the counterparty's credit quality.Why not: Limits are set on exposure measures and not priced from spreads.
  4. Credit limits are hedged with credit default swaps, whereas CVA cannot be hedged.Why not: CVA can be hedged, partly with CDS; limits are not instruments that can be hedged.

Limits are a quantity control and do not respond to spreads, while CVA is a price. A trader can pass CVA on to the client and hedge it.

A harder one

A bank estimates the expected positive exposure to a counterparty at three annual dates as USD 10 million, 14 million and 8 million. The risk-neutral marginal default probabilities for the three years are 1.0%, 1.5% and 2.0%, the discount factors are 0.97, 0.94 and 0.91, and loss given default is 60%. Using CVA = LGD x sum of discount factor x EPE x marginal PD, the CVA is closest to:

  1. USD 282 thousandWhy not: Omits the discount factors.
  2. USD 176 thousandWhy not: Multiplies by the recovery rate of 40% instead of the loss given default of 60%.
  3. USD 264 thousand - correct
  4. USD 452 thousandWhy not: Uses cumulative default probabilities (1.0%, 2.5%, 4.5%) where marginal probabilities are required.

Terms: 10 x 1.0% x 0.97 = 0.0970; 14 x 1.5% x 0.94 = 0.1974; 8 x 2.0% x 0.91 = 0.1456. Sum = 0.44 million; x 60% = 0.264 million.

The hardest tier

A bank has uncollateralised exposure to two counterparties. Both have an average expected positive exposure of USD 20 million over a three-year horizon, and both are within a PFE-based credit limit of USD 40 million. Counterparty A has a CDS spread of 100 basis points and counterparty B 400 basis points. Using CVA = spread x average EPE x maturity, ignoring discounting, the difference between the two CVAs is closest to:

  1. USD 1.8 million - correct
  2. USD 0 millionWhy not: Treats equal exposure and equal limit usage as equal risk cost; the limit ignores credit quality.
  3. USD 2.4 millionWhy not: Gives B's CVA alone instead of the difference between B's and A's.
  4. USD 1.08 millionWhy not: Multiplies the difference by LGD of 60% again, though the spread already incorporates loss given default.

A: 1.00% x 20 x 3 = 0.6. B: 4.00% x 20 x 3 = 2.4. Difference = 1.8. A limit treats the two names the same, while CVA reflects that B costs four times as much to carry.

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