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Counterparty credit exposure

Your loss when a counterparty defaults is the replacement cost of the trade (the positive mark-to-market), not the notional. Collateral and netting shrink it further.

On a derivative the other side can default any time the trade has positive value to you. You then have to replace the hedge at market, so your exposure is max(V, 0), a small fraction of the notional. Move the mark-to-market, the future-exposure add-on, and the collateral, and watch the exposure bar against the notional.

Current exposure max(V, 0)
A$8.0m
Exposure at default (EAD)
A$10.0m
Expected loss PD·LGD·EAD
A$0.12m
Exposure as % of notional
10.0%
NOTIONAL A$100mcontract face value — NOT your lossEXPOSURE BUILD-UP max(V,0) + add-onEXPOSURE AT DEFAULT A$10.00m (10.0% of notional)← this thin sliver is your loss
CE = max(V, 0) = max(A$8.0m, 0) = A$8.0m
EAD = max( CE + add-on − collateral, 0 )
EAD = max( A$8.0m + A$2.0mA$0.00m, 0 ) = A$10.0m
EL = PD · LGD · EAD = 2.00% · 60.0% · A$10.0m = A$0.12m
Notional A$100.0mAdd-on (PFE) A$2.0mCollateral applied A$0.00mEAD ÷ notional 10.0%

With a Credit Support Annex, posted collateral nets against the exposure. Without one, collateral does not apply and you are an unsecured creditor.

NotionalA$100.0m
Mark-to-market V (to you)A$8.0m
Future-exposure add-on (% of notional)2.0%
Collateral / variation marginA$0.00m
CREDIT PARAMETERS
Probability of default (PD)2.0%
Loss given default (LGD)60%
Exposure is the replacement cost, not the notional. On A$100.0m notional your exposure at default is A$10.0m (10.0% of notional) and the expected loss is A$0.12m. To rebuild the hedge you must replace the trade at current market prices.
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DISCUSSION

A US$100 million notional swap can produce a US$2 to US$5 million loss rather than a US$100 million loss. Why is the notional the wrong number for credit risk, and how do daily variation margin under a CSA and central clearing each push the exposure at default toward zero? When does the future-exposure add-on still matter even after today's mark-to-market is fully collateralised?

Assumption: a single-trade, single-period view in the Hull (2022) §24 spirit. EAD = max(CE + PFE add-on − collateral, 0), with the add-on a stylised percent of notional rather than a full simulated potential future exposure. PD and LGD are taken over one horizon.