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Judge how much credit risk derivative contracts involve.

FRM® Part II · Credit Risk Measurement and Management · Credit Risk · FRM2.CR.12.a

The idea

A derivative creates credit risk only when it has, or can acquire, a positive value to you. If the counterparty defaults you lose what it owes you, but you still owe what you owe it. Let V be the contract's current value to you. Because only a positive value is at risk, the credit exposure to the counterparty at any time is: Exposure = max(V, 0). Unlike a loan, the amount at risk is uncertain and moves with market variables. A contract that is always an asset to you, such as a bought option, carries one-sided risk. An option you have written and been paid for carries none. Forwards and swaps can change sign and so carry two-sided risk. Exchange-traded contracts have little credit risk because the clearing house margins both sides. Currency swaps are riskier than interest rate swaps of equal size because principal is exchanged at the end and exchange rates are volatile. Exam point: measure exposure by the positive replacement value, not by the notional.

Formulas

Credit exposure on a derivative

exposure = max(V, 0)

V
the current mark-to-market value of the contract to you

Exposure is the positive replacement value, never the notional. A contract that is a liability to you carries no credit exposure.

A practice question

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

A bank sells a European option to a corporate client and receives the full premium at inception. Which statement about credit risk on this contract is correct?

  1. The bank has no credit exposure to the client, because the client owes it nothing further, while the client is exposed to the bank. - correct
  2. The bank is exposed to the client for the option notional, since the client could default on its obligations under the contract and the bank would then lose the whole notional.Why not: Treats the notional as the amount at risk and ignores that the premium has already been paid.
  3. The exposure is two-sided, because every derivative can switch between being an asset and a liability.Why not: Applies two-sided risk to a contract that can only ever be a liability to the writer.
  4. The bank and the client have the same exposure, because each holds one side of the same contract.Why not: Ignores that credit exposure arises only for the party to whom the contract has a positive value.

Once the premium is paid, the writer's position can only be a liability, so its replacement value is never positive and it has no exposure. The buyer holds an asset and bears the risk.

A harder one

A company holds a long forward to buy an asset at USD 50 in six months. The forward price for delivery on that date is now USD 56, and the continuously compounded risk-free rate is 4% per year. If the counterparty defaulted today, what is the credit exposure of the long party and of the short party (closest values)?

  1. 6.00 for the long party and zero for the short party.Why not: Omits discounting of the gain (56 - 50) over six months.
  2. Zero for the long party and 5.88 for the short party.Why not: Reverses the parties: the short party owes the gain and is the one with a negative value.
  3. 5.88 for the long party and zero for the short party. - correct
  4. 5.88 for both parties.Why not: Treats exposure as two-sided at the same moment; only one party can have a positive value at a time.

Long forward value = (56 - 50) x exp(-0.04 x 0.5) = 5.88. That is positive for the long party, so it is that party's exposure; the short party's value is negative, so its exposure is max(V, 0) = 0.

The hardest tier

A dealer enters a swap with Client X (current value to the dealer: +USD 4.0 million) and hedges it with an offsetting swap with Dealer Y (current value to the dealer: -USD 4.0 million). Client X defaults and recovers 30% of its claim, while Dealer Y performs. Ignoring discounting and collateral, what is the dealer's loss?

  1. USD 2.8 million. - correct
  2. Zero, because the two swaps offset each other.Why not: Assumes netting across different counterparties; the hedge with Y still has to be paid in full.
  3. USD 1.2 million.Why not: Counts only the recovery received from X rather than the loss left after recovery.
  4. USD 4.0 million.Why not: Ignores the 30% recovery on the claim against X.

The dealer receives only 30% x 4.0 = 1.2 from X but still pays 4.0 to Y, so the loss is 4.0 - 1.2 = 2.8 (equivalently 4.0 x (1 - 0.30)). Netting works only within one counterparty's agreement.

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