Expected Credit Loss with Bond Default Protection and Counterparty Risk
Summary
The document asks how to estimate credit losses on a bond paired with default protection when both the bond issuer and protection seller can default. It provides the bond notional, default probabilities, joint default probability, and recovery assumptions, then highlights a limitation of the simple probability-times-loss-given-default-times-exposure formula: the protection’s market value and replacement cost are not specified.
One response separates outcomes into bond-only default, counterparty-only default, joint default, and no default. It explains that the joint case creates loss on the unrecovered asset and that other scenarios can depend on the protection’s mark to market. A second response treats only simultaneous default as loss-bearing and calculates an expected loss from the joint probability and unrecovered asset value. These answers differ because of their assumptions about payoff valuation; the prompt lacks enough information to determine the protection’s exposure or resolve default timing, so the simple result is conditional rather than complete.
Key ideas
- Credit protection reduces bond default loss only if the protection seller can perform.
- Joint default probability is central to the loss scenario when the protected asset and seller can fail together.
- The protection contract’s mark to market and replacement cost affect exposure but are not supplied.
- A scenario analysis exposes assumptions that a single expected loss formula can hide.
- The simplified expected loss calculation assumes only simultaneous default creates loss.
Tags
Full text
# Expected Loss on a Portfolio, which contains an asset and a default protection contract, due to credit defaults # Expected Loss on a Portfolio, which contains an asset and a default protection contract, due to credit defaults A portfolio consists of one (long) 100 million asset and a default protection contract on this asset. The probability of default over the next year is 10% for the asset, 20% for the counterparty that wrote the default protection. The joint probability of default for the asset and the contract counterparty is 3%. Estimate the expected loss on this portfolio due to credit defaults over the next year assuming 40% recovery rate on the asset and 0% recovery rate for the contract counterparty. If expected loss of a portfolio is: ``` Default Probability x Loss Given Default x Exposure at Default ``` How can I use this formula to solve this problem? Or can this equation be used if we are not given an exposure amount for the contract? ## Answer by Dimitri Vulis (score 1) https://quant.stackexchange.com/a/59972 Assuming "asset" means a credit-risky bond, and "protection" is a standard credit default swap on the same notional. Ignoring the coupons and interest payments, there are 4 scenarios: Probablity 10%-3% = 7% : the bond has a credit event. The credit protection seller has not defaulted. You put the defaulted bond to the credit protection seller and receive the notional. Your P&L is the notional (the face value of the bond) that you receive, minus the mark to market of the credit protection. Probability 3%: both the bond and the credit protection seller have credit events simultaneously. Your defaulted bond is now worth 40% (recovery) * 100 mil (notional). Your protection is worthless, so you lose the mark to market of the protection with 0% recovery. We don't know how much that was worth. (In reality, they are unlikely to defalt simultaneously. What matters is which one of them defaults first.) Probablity 20%-3% = 17% : only the credit protection seller has a credit event. You lose the mark to market of the protection. We don't know how much that was worth. You still have a performing credit-risky bond. We don't know what it may be trading at. You may want to buy replacement credit protection from someone else. Probability 100%-10%-17%=73% neither the bond not the protection seller have a credit event, so no credit losses. We don't know what the asset may be trading at, nor the mark to market of the credit protection. ## Answer by Anonymous (score 0) https://quant.stackexchange.com/a/70956 Some irrelevant and unclear info in the Q. If asset defaults and counterparty does not, we are covered for the full value => no loss If counterparty defaults and asset does not, we lose nothing bar the cover (as asset is fine) => no loss We're only caught in the case that both default (3% chance). Even in this case we would still recover 40% of the value of the asset (40,000,000). Effectively, 3% of the time we lose $60,000,000 Expected loss = (100,000,000-40,000,000) * 0.03 = $1,800,000
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