FINC6023 Chap.11 Credit Risk: Credit Exposure & Credit VaR
Credit Risk: Credit Exposure & Credit VaR
Credit Risk: Credit Exposure and Credit VaR combines the chance of default with the amount that would be lost. Exposure depends on contract value at the time of default. A long option has non-negative value to its holder, while a short option is a liability rather than a credit exposure.
A forward or swap can move between positive and negative value, so only the positive replacement value is exposed to counterparty default.
Exposure is not necessarily independent of credit quality. Wrong-way risk occurs when exposure rises as the counterparty becomes more likely to default. Right-way risk occurs when exposure falls as credit quality weakens.
Netting, collateral, margining, downgrade triggers, and central clearing can reduce exposure, though each control introduces operational, liquidity, or legal considerations that must be understood.
Expected credit loss is the probability-weighted mean built from default probability, exposure, and loss given default.
Linearity of expectation means marginal default probabilities determine this mean even when defaults are correlated. Credit VaR concerns the tail of the loss distribution. Positive default correlation makes joint losses more likely and can increase the worst credit loss at a confidence level without changing expected loss.
Under the course convention, Credit VaR subtracts expected credit loss from that worst credit loss.
The available final paper devotes several multiple-choice questions and a full Part B question to this material. For two bonds, enumerate both default, only the first, only the second, and neither.
Calculate each probability and loss, sort by loss severity, cumulate probabilities, select the confidence quantile, and subtract expected loss. Never apply a normal approximation to a small discrete distribution when its exact states are available.
What this chapter covers
- 01
Exposure by contract type (always-asset, always-liability, can-be-either)
- 02
Greatest exposure when the contract is in-the-money to you
- 03
Wrong-way vs right-way risk
- 04
Mitigation: netting, collateral, downgrade triggers; CVA
- 05
Expected credit loss E[CL] = Σ PD·EAD·LGD (independent of correlation)
- 06
Credit VaR = WCL − ECL; default correlation raises unexpected loss, not expected loss
- 07
Two-bond Credit VaR and the joint-default ↔ correlation inversion [OFF-SHEET]
Worked example · free
Two-bond Credit VaR with a given joint-default probability
- 1Loss given default: A loses LGD_A = 1 − 0.40 = 0.60 → $360,000; B loses LGD_B = 1 − 0.25 = 0.75 → $300,000.
- 2Expected credit loss ECL = PD_A·EAD_A·LGD_A + PD_B·EAD_B·LGD_B = 0.05(360,000) + 0.08(300,000) = 18,000 + 24,000 = $42,000.
- 3Build the loss outcomes. Both default: p = 0.01, loss = 360,000 + 300,000 = $660,000. Only A: p = 0.05 − 0.01 = 0.04, loss = $360,000. Only B: p = 0.08 − 0.01 = 0.07, loss = $300,000. Neither: p = 1 − 0.01 − 0.04 − 0.07 = 0.88, loss = $0.
- 2Sort by severity and cumulate: P(loss ≤ 0) = 0.88; P(≤ 300,000) = 0.95; P(≤ 360,000) = 0.99; P(≤ 660,000) = 1.00.
- 1The 97.5th percentile worst credit loss is the smallest loss with cumulative ≥ 0.975, which is $360,000. Credit VaR = WCL − ECL = 360,000 − 42,000 = $318,000.
Key terms
- Credit exposure (EAD)
- The amount at risk if the counterparty defaults. It depends on contract type: a long option is always an asset (exposed), a short option never is, and a forward or swap can be either depending on its mark-to-market.
- Wrong-way / right-way risk
- Wrong-way risk is when the exposure rises exactly as the counterparty's PD rises (e.g. AIG); right-way risk is when exposure falls as PD rises. Wrong-way risk inflates the effective exposure.
- Expected credit loss (ECL)
- Σ PD·EAD·LGD — the mean credit loss. It depends on default probability and exposure but NOT on default correlation.
- Credit VaR
- The worst credit loss at a confidence level minus the expected loss, Credit VaR = WCL − ECL. It is highly skewed and lengthens with horizon; default correlation increases it by fattening the tail.
- Default correlation / joint default
- The tendency of counterparties to default together. The covariance of the two default indicators is p(A and B) minus PD_A times PD_B, and dividing that covariance by their two default-indicator standard deviations recovers correlation (off-sheet).
- Netting
- Netting combines eligible positive and negative contract values with the same counterparty so credit exposure is based on the net amount rather than gross positive positions.
- Wrong-way risk
- Wrong-way risk occurs when exposure increases as the counterparty's probability of default rises, making the credit loss channel more severe than an independence assumption suggests.
Credit Risk: Credit Exposure & Credit VaR FAQ
Why does default correlation affect Credit VaR but not expected credit loss?
Expected loss is a sum of marginal expectations, Σ PD·EAD·LGD, and expectation is linear — it does not care whether defaults happen together. Default correlation changes the SHAPE of the loss distribution: positive correlation makes simultaneous defaults more likely, fattening the tail and raising the worst-case loss (and hence Credit VaR) while leaving the mean unchanged.
How do I build a two-bond Credit VaR?
Enumerate the four states — both default, only A, only B, neither — with their probabilities and dollar losses, sort the outcomes by loss size, cumulate the probabilities, read off the worst credit loss at the required confidence, and subtract the expected credit loss. If only a correlation is given, first convert it to a joint-default probability.
What gives the greatest credit exposure on a swap?
You lose when the counterparty defaults while the contract is IN-THE-MONEY to you (it has positive value), because that positive value is what you fail to collect. A contract that is out-of-the-money to you carries no credit loss on default.
Why does a long option create credit exposure?
A long option has non-negative value to its holder because exercise is optional. If that positive value is owed by a counterparty, default can destroy the replacement value. A short option is a liability to its writer rather than a positive exposure, while swaps and forwards can move between asset and liability states.
How does the available final weight this chapter?
It includes several Part A items on collateral, exposure, expected loss, credit-loss shape, and Credit VaR, followed by a full Part B Credit VaR question. Preparation should therefore combine fast state identification with complete loss-distribution construction and a short firm-level discussion of interactions among market, credit, and operational risk.
Exam move
Separate exposure from loss probability before doing arithmetic. For each contract, ask whether its current or future value can be positive to the institution and identify any wrong-way relationship with counterparty quality. For a two-name Credit VaR problem, use a four-row state table every time: both default, only the first, only the second, and neither.
Derive exclusive probabilities from marginal and joint probabilities, attach loss given default to each exposure, and verify that probabilities sum to one. Sort by loss, build the cumulative distribution, locate the requested quantile, and subtract expected credit loss only after the worst credit loss is identified.
Recompute expected loss independently from the marginal formula; it should not change when only default correlation changes. Practise explaining that correlation moves probability mass into joint tail states while linearity preserves the mean. Because this topic dominates the available paper, alternate short exposure and expected-loss multiple-choice items with full written Credit VaR solutions.
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