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Give worked cases of compressing derivative positions, find the net notional exposure figure and say which counterparty ends up holding the net contract position.

FRM® Part II · Credit Risk Measurement and Management · Netting, Close-out and Related Aspects · FRM2.CR.16.e

The idea

In a compression exercise all the trades must have the same terms: product, maturity, fixed rate and floating index. The direction of each is recorded as who pays fixed to whom. Bilaterally, offsetting trades between two parties collapse into one trade for the difference in notional, held in the direction of the larger one. If A pays fixed on 100 to B and B pays fixed on 70 to A, the result is A paying fixed on 30. Multilaterally, compute each participant's net position as notional received less notional paid. The minimum remaining gross notional equals the sum of the positive net positions, which equals the sum of the negative ones. The participants with net payments are paired off with those with net receipts. A participant with a zero net position drops out entirely. Check that each firm's net market position is unchanged, because compression changes gross, not net.

Formulas

Minimum gross notional after multilateral compression

Minimum gross notional = Σ positive net positions

positive net positions
each participant's notional received less notional paid, where that is above zero

Trades must share all terms. The sum of positive net positions equals the sum of negative ones, and a participant at zero drops out.

A practice question

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

Two interest rate swaps with identical maturity, fixed rate and floating index are held between A and B. A pays fixed to B on notional 100, and B pays fixed to A on notional 70 (both in USD million). After bilateral compression, what remains?

  1. A pays fixed to B on notional 30 - correct
  2. B pays fixed to A on notional 30Why not: Reverses the direction; the larger trade, in which A pays fixed, determines who holds the net position.
  3. A pays fixed to B on notional 70Why not: Cancels the 100 trade and keeps the 70 notional instead of netting the two.
  4. A pays fixed to B on notional 170Why not: Adds the notionals instead of offsetting them.

Net notional = 100 - 70 = 30, held in the direction of the larger trade, so A is the net fixed-rate payer.

A harder one

A and B have three identical fixed-for-floating swaps: A pays fixed to B on 120, B pays fixed to A on 45, and B pays fixed to A on 30 (USD million). After bilateral compression, what is the position?

  1. B pays fixed to A on 45Why not: Reverses the direction of the net position; A holds the larger fixed-payer side.
  2. A pays fixed to B on 45 - correct
  3. A pays fixed to B on 75Why not: Offsets only one of the two smaller trades (120 - 45) and forgets the third.
  4. A pays fixed to B on 195Why not: Adds all three notionals instead of netting them.

Net = 120 - 45 - 30 = 45 in A's favour as a fixed payer: A remains the net fixed-rate payer on 45.

The hardest tier

Identical swaps are held among four dealers. Each entry shows the fixed-rate payer, receiver and notional (USD million): A pays B 80, B pays C 50, C pays D 70, D pays A 30, A pays C 20. After multilateral compression to the minimum gross notional, which dealer is left with no position and what is the remaining gross notional?

  1. Dealer C; notional 140Why not: Adds the absolute values of all net positions, counting each notional twice.
  2. Dealer B; notional 70Why not: Picks the dealer with the smallest net position (30) rather than the one with a zero net.
  3. Dealer C; notional 70 - correct
  4. Dealer C; notional 110Why not: Cancels only C's trades and leaves the others untouched, instead of re-pairing net positions.

Net positions: A -70, B +30, C 0, D +40. C has zero net position and drops out. Remaining gross = 70, for example A pays B 30 and A pays D 40, down from 250.

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