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Explain the way netting enters the computation of CVA.

FRM® Part II · Credit Risk Measurement and Management · CVA · FRM2.CR.20.h

The idea

Netting enters CVA at the exposure. If a legally enforceable netting agreement covers a set of trades, the claim on default is the net value. Exposure at each date is therefore the net value floored at zero, rather than the sum of the positive parts of each trade, and it is given by Exposure = max(V1 + V2 + ..., 0). CVA is then computed from the expected netted exposure, using the same LGD times discounted EE times marginal PD formula. Since the maximum of a sum is at most the sum of the maxima, netted CVA is never above the sum of standalone CVAs. The benefit is largest when trades offset one another, for example a payer and a receiver swap. Netting applies only within one netting agreement and only if it is enforceable, so trades outside it are added gross. CVA is therefore not additive across trades.

Formulas

Exposure of a netting set

Netted exposure = max(ΣVᵢ, 0)

Vᵢ
the value to the bank of each trade in the enforceable netting set

Only under a legally enforceable netting agreement. Trades outside it are added gross, so netted CVA is never above the sum of standalone CVAs.

A practice question

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

Compared with the sum of the CVAs of each trade calculated on a standalone basis, the CVA of a netting set is:

  1. greater when the trades are in opposite directions, because each side carries its own exposure.Why not: Offsetting trades are the case where netting helps most, not where it hurts.
  2. never greater, and lower whenever trades in the set can offset one another. - correct
  3. always equal, because CVA is additive across trades.Why not: CVA is not additive: max(sum of values, 0) is below the sum of the individual positive parts.
  4. always greater, because netting concentrates exposure on one counterparty.Why not: Confuses netting with concentration; netting only reduces the amount owed on default.

Because max(a + b, 0) <= max(a, 0) + max(b, 0), the netted exposure never exceeds the gross exposure, so netted CVA never exceeds the sum of standalone CVAs.

A harder one

Two trades with the same counterparty are covered by one netting agreement. At a future date there are four equally likely scenarios for the values of Trade 1 and Trade 2 to the bank (USD million): (12, -5), (6, -9), (-3, 7) and (-8, 10). Default probability over the interval is 5% and loss given default is 60%; exposure and default are independent. The CVA at this date with netting is closest to:

  1. USD 75,000Why not: Uses the average net value without flooring each scenario at zero, so negative net values offset positive ones across scenarios.
  2. USD 97,500 - correct
  3. USD 135,000Why not: Uses only the larger standalone expected exposure rather than the expected net exposure.
  4. USD 262,500Why not: Ignores netting and adds the two standalone expected exposures.

Net values by scenario: 7, -3, 4, 2. Floored at zero: 7, 0, 4, 2, so EE = 3.25. CVA = 0.6 x 0.05 x 3.25 million = USD 97,500. Gross EE would be 8.75.

The hardest tier

Two trades with a counterparty are in one netting set. At a future date there are three scenarios (probability; Trade 1 value; Trade 2 value, USD million): (50%; 8; -7), (30%; -7; 4) and (20%; 15; -10). Exposure and default are independent. Compared with the sum of standalone CVAs, netting reduces the CVA at this date by about:

  1. 82% - correct
  2. 18%Why not: Reports netted exposure as a fraction of gross exposure, rather than the reduction.
  3. 15%Why not: Assumes only the smaller trade's exposure is eliminated by netting.
  4. 93%Why not: Treats the net value as exposure without flooring at zero in each scenario, overstating the benefit.

Standalone EEs: 7.00 and 1.20 (sum 8.20). Net values are 1, -3 and 5, so net EE = 0.5 x 1 + 0 + 0.2 x 5 = 1.50. Reduction = 1 - 1.50 / 8.20 = 82%. CVA scales with EE, so CVA falls by the same percentage.

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