Understand default and migration risk, separate exposure from notional, and calculate expected credit loss without assuming away exposure and recovery dependence.
Credit risk
Credit risk is the possibility of financial loss when a borrower or counterparty fails to meet its agreed obligations. For a lender, a promised repayment is therefore different from cash already received: the amount at stake, the chance of default and the amount recoverable all matter.
Credit analysis also tracks deterioration before a failure to pay. A bond can lose market value as its issuer becomes less creditworthy, even while every scheduled payment is still being made. This connects credit risk with market risk, without making the two descriptions interchangeable.
Three questions behind a default loss
Question
Credit-risk input
How likely is default over the stated horizon?
Probability of default (PD)
What claim is exposed when default occurs?
Exposure at default (EAD)
What fraction of that exposure is lost after recovery?
Loss given default (LGD)
PD is a probability; LGD is a loss fraction; EAD has currency units. A PD needs a horizon and a definition of default. The relevant contract, legal setting and modelling purpose determine what counts as default and how exposure and recovery are measured. A late payment does not automatically trigger identical consequences across all instruments.
For a derivative, exposure is generally a positive replacement claim, rather than the contract's full notional amount. Its value can change with market conditions before the counterparty defaults. That is the central issue in counterparty credit risk.
Two possible losses, one mean
Take a synthetic one-period default-loss model with:
fixed EAD of USD 1,000,000;
stipulated PD of 5% over the period;
fixed LGD of 60%, measured on the same valuation basis as EAD.
All amounts are expressed at one common valuation date in USD; recovery timing and any discounting are already absorbed into the stipulated LGD. This is a model of loss from default only. It excludes interest income, fees and changes in market value without default. The inputs are assumptions, not estimates for an issuer.
If default occurs, the loss is 1,000,000×0.60=600,000 USD. Otherwise, default loss is zero. The expected value is
E[L]=0.95×0+0.05×600,000=30,000 USD.
A synthetic one-period model has 95% probability of zero default loss and 5% probability of USD 600,000 default loss. The weighted mean is USD 30,000, which is neither possible realised outcome.
Original synthetic one-period model in USD, with fixed EAD of USD 1,000,000 and fixed LGD of 60%. Amounts share one valuation basis. Loss is positive; no-default market losses, income and fees are excluded.
USD 30,000 is 3% of EAD, but it is neither a certain cost nor the loss if default happens. In this model, the realised default loss is either zero or USD 600,000. The mean alone cannot describe the severity of adverse outcomes or determine a capital buffer.
When the familiar product needs care
With fixed EAD and LGD, the example reduces to the familiar expression PD×EAD×LGD. If exposure and recovery are uncertain, first define the loss in each state, then average it.
Let D be default during the period, and let 1D equal one on default and zero otherwise. On a consistent currency and valuation basis,
L=1DEADLGD,E[L]=P(D)E[EADLGD∣D].
The conditional expression applies when default has positive probability; if its probability is zero, default loss is zero. It averages exposure times loss fraction in the default states. Multiplying unconditional average exposure by unconditional average LGD and PD generally does not give that result. Even multiplying the two default-conditional averages requires zero conditional covariance or another sufficient restriction, such as one component being fixed.
The financial concern is concrete: a distressed borrower may draw more of a credit line just when collateral values fall. Both the amount exposed and the fraction lost can then be high in the same default states. For derivatives, adverse dependence between exposure and counterparty credit quality is wrong-way risk. A joint loss model preserves those connections.
Deterioration is not default
Credit migration means movement between credit-quality states, including upgrades and downgrades. A downgrade can increase estimated future default risk without being a default itself. A credit rating is an assessment on a particular scale; a letter grade alone is not an exact default probability.
Deterioration can also widen a bond's credit spread, reducing its marked value before maturity. A default-only model like the one above intentionally omits that channel. A credit portfolio model may need both migration-related revaluation and losses at default.
The probability measure matters too. A physical PD aims to describe default frequency under a real-world model. A risk-neutral probability is used within a pricing model. A market-implied pricing probability is not automatically a forecast of realised default frequency.
Credit limits, diversification, collateral, enforceable netting and credit protection can reduce particular exposures. Their effect depends on the structure: collateral can lose value, netting needs legal enforceability, and a protection seller creates its own counterparty exposure. The Basel Committee's credit-risk principles consequently treat contract terms, exposure profiles, collateral or guarantees and default potential together.
For a worked next step, Exposure profiles builds positive claims from future derivative values and separates expected exposure from exposure quantiles. It has a public preview; membership is required for the full lesson.
Sources
McNeil, Frey and Embrechts, Quantitative Risk Management: Concepts, Techniques and Tools, revised edition, Princeton University Press, 2015, §1.1.2, pp. 5–6; §10.1.5, pp. 372–373; and §10.2.1, pp. 374–375: risk categories, PD/LGD/EAD, their dependence and rating migration. The numerical model and figure here are original.
Basel Committee, Principles for the management of credit risk, April 2025, Principle 4, paragraphs 24–26, and Principle 11, paragraph 49: loss absorption, limits of collateral and netting, and exposure-sensitive measurement. These are banking supervisory principles; the synthetic model does not calculate regulatory capital or an accounting provision.
