University of Sydney · S1 2026 · FACULTY OF BUSINESS & ECONOMICS

FINC6023 · Financial Risk Management

- one subject, every graph, every model, every mark

50% final exam · hurdle14 Chapters6-page Bible

Our own words - no uploaded lecturer files

Built to mirror S1 2026 · updated this semester

Chapter 11 of 12 · FINC6023

Credit Risk: Credit Exposure & Credit VaR

Credit Risk: Credit Exposure & Credit VaR combines default probability with how much is actually at risk. Exposure depends on the contract type (a long option is always an asset and so exposed; a forward/swap can be either), and wrong-way risk arises when exposure rises just as the counterparty weakens. Expected credit loss = Σ PD·EAD·LGD depends on PD but NOT on default correlation, while Credit VaR = WCL − ECL (worst credit loss minus expected) does — correlation fattens the tail without moving the mean. The signature Part-B problem is the two-bond Credit VaR.

In this chapter

What this chapter covers

01Exposure by contract type (always-asset, always-liability, can-be-either)
02Greatest exposure when the contract is in-the-money to you
03Wrong-way vs right-way risk
04Mitigation: netting, collateral, downgrade triggers; CVA
05Expected credit loss E[CL] = Σ PD·EAD·LGD (independent of correlation)
06Credit VaR = WCL − ECL (longer horizon, highly skewed)
07Default correlation raises unexpected loss, not expected loss
08Two-bond Credit VaR and the joint-default ↔ correlation inversion [OFF-SHEET]

Worked example · free

Two-bond Credit VaR with a given joint-default probability

Q [9 marks]. Over one year you hold Bond A (value $600,000, PD 5%, recovery 40%) and Bond B (value $400,000, PD 8%, recovery 25%). The probability that BOTH default is 1%. Find the expected credit loss and the 97.5% one-year Credit VaR.

1 markLoss given default: A loses LGD_A = 1 − 0.40 = 0.60 → $360,000; B loses LGD_B = 1 − 0.25 = 0.75 → $300,000.
2 marksExpected 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.
3 marksBuild 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.
2 marksSort by severity and cumulate: P(loss ≤ 0) = 0.88; P(≤ 300,000) = 0.95; P(≤ 360,000) = 0.99; P(≤ 660,000) = 1.00.
1 markThe 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.

ECL = $42,000 and the 97.5% one-year Credit VaR = $360,000 − $42,000 = $318,000.

Sia tip — ECL ignores default correlation; Credit VaR does not. If the question gives only a correlation ρ instead of the joint probability, recover it first with p(A and B) = ρ·√(PD_A(1−PD_A))·√(PD_B(1−PD_B)) + PD_A·PD_B, then build the {both/one/none} table exactly as above.

Glossary

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 joint probability satisfies p(A and B) = ρ·σ_A·σ_B + PD_A·PD_B with σ = √(PD(1−PD)); the relationship can be inverted to recover ρ (off-sheet).

FAQ

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.

Study strategy

Exam move

Drill the two-bond Credit VaR as a fixed routine (states → losses → sort → cumulate → WCL − ECL) because it is the most likely Part-B credit question. Memorise the joint-default ↔ correlation inversion, and be able to explain in one line why correlation moves the tail but not the mean.

Keep going — explore the course

A+Everything unlocked

Unlocks this Bible + all 191 of your University of Sydney subjects - and 1,000+ Bibles across every Australian university.

Sia - your FINC6023 tutor, unlimited, worked the way the exam marks it

The full 6-page Bible + practice bank with worked solutions

Chrome extension - sync your LMS so Sia knows your deadlines

Bilingual EN / Chinese on every Bible and every Sia answer

$25/ month

30-day money-back · cancel in one tap · how it works