Credit risk is the possibility that a borrower or counterparty will not meet its obligations as expected. The resulting loss depends on whether default occurs, how much is exposed at that time and how much is ultimately recovered. A mortgage, a credit card and a corporate loan can therefore require different assumptions even when the same high-level loss formula is used.

The opening lessons introduce probability of default, loss given default, exposure at default and portfolio behaviour. You will examine dependence, concentration and migration to understand why an average expected loss does not fully describe a portfolio’s risk. The modelling lessons then explain how candidate variables are selected, how data leakage can produce misleading results, and how discrimination, calibration and stability are assessed.

The accounting section introduces IFRS 9 expected credit losses, staging and significant increases in credit risk. It explains the difference between a loss associated with defaults possible in the next twelve months and losses over the remaining lifetime. Scenario weights, effective-interest discounting, revolving facilities and credit-impaired assets are treated separately because they affect the calculation in different ways.

Work through the path in that order if you are new to credit risk. Use the synthetic portfolios and dataset to test explanations rather than memorise a single PD or LGD. The module distinguishes accounting estimates, internal risk measures and regulatory capital concepts, and states where specialist methods or further judgement are needed.

Continue your learning: SA-CCR counterparty exposure · SA-CVA counterparty risk · Treasury risk

Look up a term as you work through the examples. Definitions explain the terminology; the source references and assumptions beside each lesson explain the scope of its calculation.

108 definitions

Absorbing state

An absorbing state is a model state that cannot be left once entered. Treating default as absorbing is a modelling choice that excludes subsequent cures from that transition model.

Accrual

Accrual allocates interest or other income and expense to the period in which it is earned or incurred. Accrued interest can make a settlement amount differ from a quoted clean bond price.

Accrued interest

Accrued interest is interest earned or owed since the last payment date but not yet paid. Its calculation depends on the contract’s day-count and payment conventions.

Amortised cost and carrying amount

Amortised cost is an accounting measurement that updates the recognised amount using the effective-interest method and relevant payments or adjustments. Gross and net carrying amounts differ where a loss allowance is recognised.

Asset

An asset is a resource or contractual right with economic value. For a bank, examples include cash, securities and loans that customers are expected to repay.

Basel, BCBS and IOSCO

The Basel Committee on Banking Supervision develops international prudential standards for banks. IOSCO is the International Organization of Securities Commissions. International standards require the relevant jurisdictional implementation before they can be treated as local rules.

Basis risk

Basis risk arises when two related prices or rates do not move together as assumed. A hedge tied to one benchmark may therefore leave exposure to a different benchmark, location or contract specification.

Binomial distribution

A binomial distribution counts successes in a fixed number of independent trials with the same success probability. It is used here to make probabilities and replication in discrete outcomes easier to inspect.

Calibration

Calibration selects model parameters to match chosen data, market prices or target risk properties. A calibrated model can still be inappropriate if its structure or the selected evidence does not suit the task.

Carry and opportunity cost

Carry is the ongoing income or expense from holding and financing a position. Opportunity cost compares that choice with a specified alternative, whose credit, capital and liquidity risks may differ.

Cash flow

A cash flow is a payment or receipt at a specified time. Its amount, date, currency and legal owner affect both valuation and liquidity.

Censoring

Censoring occurs when a record’s full outcome is not observed within the available follow-up period. Treating all censored borrowers as permanent non-defaults can bias estimated default behaviour.

Collateral

Collateral is cash or another eligible asset provided to secure an obligation. Its protection depends on value, legal enforceability, availability and the time required to realise it.

Concentration

Concentration means that a large share of exposure or funding depends on a small number of sources or common drivers. The Herfindahl–Hirschman Index, or HHI, sums squared shares to measure size concentration but does not by itself measure behavioural dependence.

Conditional, marginal and cumulative PD

Conditional PD applies to borrowers still surviving at the start of an interval. Marginal PD is the probability of first default during that interval from the original population, while cumulative PD is the probability of default by a specified date.

Correlation

Correlation summarises a specified relationship between two variables. A linear correlation does not fully describe joint tail behaviour, and a prescribed regulatory correlation is a model parameter rather than a measured relationship for every portfolio.

Counterparty credit risk

Counterparty credit risk is the risk of loss when the other party to a financial contract fails to perform. For derivatives, exposure can change with market conditions and may be positive for either party at different times.

Coupon

A coupon is an interest payment on a bond or loan. The coupon rate determines the contractual payment; it is not necessarily the yield available to an investor at the current market price.

Credit conversion factor

A credit conversion factor estimates or prescribes how much of an undrawn commitment contributes to exposure. Behavioural estimates and regulatory factors should not be substituted for one another without checking the purpose of the calculation.

Credit spread

A credit spread is the additional yield or premium associated with credit exposure relative to a reference rate. It can reflect default risk, liquidity and other market effects, so it is not a direct default probability.

Data leakage

Data leakage occurs when model development uses information that would not have been available at the actual decision time or that improperly reveals the target. It can make reported performance look strong while producing an unusable model.

Days past due

Days past due counts how long a contractual payment has remained unpaid. IFRS 9 uses rebuttable presumptions in specified circumstances, but a complete credit assessment also considers other relevant evidence.

Deposit beta and lag

Deposit beta measures the proportion of a market-rate change passed into the customer deposit rate. Lag measures the delay before that repricing occurs; neither is a deposit withdrawal rate.

Discount rate

A discount rate is a rate used to value future cash flows in present terms. The appropriate rate depends on the valuation framework and the characteristics of the cash flow.

Discrimination, ROC and AUC

Discrimination measures how well a score orders risk between outcomes. The ROC curve summarises detection rates at different thresholds, and AUC measures the area under that curve. Good ranking does not establish that the probabilities are well calibrated.

Distribution

A probability distribution assigns probabilities to possible values or outcomes. It describes a range of possibilities rather than one realised observation.

Diversification

Diversification is the reduction in aggregate risk that can arise when positions do not experience adverse outcomes together. Its benefit depends on the chosen risk measure, dependence assumptions and any regulatory aggregation rules.

Drift and diffusion

Drift describes the predictable local direction of a stochastic process under a chosen probability measure. The diffusion term determines the magnitude of its continuous random fluctuations.

Effective interest rate

The effective interest rate discounts the relevant estimated contractual cash flows to the carrying amount under the accounting requirements. Credit-adjusted EIR has a distinct role for purchased or originated credit-impaired assets.

Equity

Equity represents an ownership interest. On a bank balance sheet, equity is the residual interest in assets after liabilities; in a market-risk example, an equity position usually means shares in a company.

Expectation

Expectation is an average weighted by the probabilities in a model. Conditional expectation updates that average using specified information and considers only the outcomes consistent with it.

Expected credit loss

Expected credit loss is a probability-weighted estimate of credit cash shortfalls measured under IFRS 9’s applicable requirements. Timing, discounting, reasonable and supportable information, and the relevant measurement horizon matter.

Expected loss

Expected loss is the probability-weighted average loss over a defined set of outcomes. In a simple single-period credit example it is PD multiplied by LGD and EAD, but richer models also account for timing and dependence.

Expected shortfall

Expected shortfall averages losses in a specified worst part of the loss distribution. Its treatment of probability mass at the threshold matters for discrete scenario samples.

Expiry

Expiry is the time at which an option’s exercise right ends. A European option can be exercised only at expiry, while other exercise styles allow different choices.

Exposure at default

Exposure at default is the amount exposed when default occurs under the relevant model or regulatory definition. It can include future drawings or prescribed add-ons and need not equal today’s drawn balance.

Floating rate

A floating rate resets according to a benchmark or contractual rule. Repricing occurs when the rate used to calculate a payment is updated, which need not coincide with repayment of principal.

Forward contract

A forward contract fixes today the terms of a transaction to occur at a future date. The value of an existing forward changes as current market prices and financing conditions change.

Funding and rollover risk

Funding supports assets and payment obligations through deposits, borrowing and other sources. Rollover risk is the risk that maturing funding cannot be replaced at an acceptable cost or at all.

FVOCI, FVTPL and OCI

FVOCI means fair value through other comprehensive income, while FVTPL means fair value through profit or loss. OCI is other comprehensive income, a presentation category whose treatment differs from ordinary period profit or loss.

Hazard rate

A default hazard rate describes the instantaneous rate of default conditional on survival up to that time. A spread divided by LGD is a simplified hazard approximation, not a full credit-curve calibration.

Idiosyncratic and systematic risk

Idiosyncratic risk is specific to a name or position, while systematic risk is driven by factors shared across many positions. The distinction affects diversification assumptions and some regulatory aggregation treatments.

IFRS 9

IFRS 9 is the financial reporting standard covering relevant classification, measurement, impairment and hedge-accounting requirements for financial instruments. The credit module focuses on its expected-credit-loss concepts and distinguishes them from regulatory capital rules.

Implied volatility

Implied volatility is the volatility parameter that makes a selected pricing model match an observed option price. A volatility smile or surface describes how implied volatility varies across strikes and expiries.

Imputation

Imputation supplies a value for a missing observation under a stated rule. The rule should be fitted using appropriate training data and checked for whether missingness itself contains risk information.

Incremental and standalone risk

Standalone risk measures a position by itself. Incremental risk is the change in portfolio risk when the position is added; it can be negative when the new position hedges an existing exposure.

Independence

Variables are independent when learning the value of one does not change the probability distribution of the other. This is stronger than having zero linear correlation.

Interest rate

An interest rate expresses the cost of borrowing or the return on lending over a stated period. Its meaning depends on the currency, term, compounding convention and credit or collateral conditions.

Internal ratings-based approach

The internal ratings-based approach uses approved internal credit-risk inputs within a prescribed regulatory framework. Eligibility, floors and calculation conventions differ from those used to estimate accounting ECL.

Investment grade and high yield

Investment grade and high yield are credit-quality groupings based on the relevant rating or classification rules. Rating labels such as AA and BBB indicate categories, not guarantees of repayment.

Leverage

Leverage increases exposure relative to the capital supporting it, often through borrowing or derivatives. It can magnify gains and losses and create funding pressure even when a position is expected to be profitable.

Liquidity and solvency

Liquidity concerns the ability to meet obligations when due. Solvency concerns the ability of assets and loss-absorbing resources to cover liabilities and losses; a solvent institution can still face a timed cash shortage.

Loan-to-value ratio

The loan-to-value ratio compares a loan exposure with the value of its supporting collateral under a specified convention. Collateral value, enforcement cost and recovery timing still affect the eventual loss.

Logistic regression

Logistic regression maps a linear combination of predictors into a probability through a logistic function. Its coefficients affect log-odds, so a coefficient is not directly a percentage-point change in PD.

Long and short positions

A long position generally benefits from ownership or a rise in the relevant instrument’s value. A short position has the opposite exposure. For complex derivatives, the precise payment and sign convention should always be checked.

Loss allowance and write-off

A loss allowance records the relevant impairment estimate. A write-off reduces the carrying amount when the accounting criteria are met, which is different from deciding that collection or enforcement must always stop.

Markov assumption

The Markov assumption makes the next-state distribution depend on the current state rather than the complete past. A rating-transition model using this assumption can miss additional information in a borrower’s history.

Maturity

Maturity is the date or remaining period until a contract ends or principal becomes due. It can differ from an instrument’s next interest-rate reset or an option’s expiry.

Modification and derecognition

A modification changes contractual terms. Derecognition removes an asset from the accounts when the applicable conditions are met; a modification does not automatically imply derecognition or a cure of credit deterioration.

Multicollinearity

Multicollinearity occurs when predictors contain strongly overlapping information. It can make estimated coefficients unstable even if overall predictions appear adequate.

Netting set

A netting set contains transactions that can be combined under the relevant legally recognised agreement and calculation rules. Economic offsets across different legal sets do not automatically qualify as regulatory or collateral offsets.

Overfitting and regularisation

Overfitting occurs when a model captures sample-specific noise that does not generalise. Regularisation constrains the fitting process, but it does not replace appropriate data separation and validation.

Overlay

An overlay is a documented adjustment used to address relevant risk or information not adequately reflected in a model output. It should not become an unexplained means of reaching a preferred allowance total.

POCI

Purchased or originated credit-impaired assets are already credit-impaired at initial recognition. Their credit-adjusted effective-interest and impairment treatment differs from applying the ordinary Stage 1-to-Stage 3 sequence to a newly performing loan.

Point-in-time and through-the-cycle

A point-in-time estimate reflects current conditions more directly. A through-the-cycle estimate aims to represent risk across the cycle under its definition. Neither label alone specifies a complete calibration method or accounting suitability.

Poisson process

A Poisson process counts randomly timed events with a specified intensity under its assumptions. Adding jumps allows a model to represent discontinuous changes that a purely continuous diffusion cannot generate.

Population stability index

The population stability index compares the distribution of a variable or score across samples using defined bins. It is a diagnostic of distribution change, not a universal proof that model performance has deteriorated.

Portfolio

A portfolio is a collection of positions considered together. Its risk depends on their sizes, relationships and permitted offsets, not just the sum of their standalone risks.

PRA

The Prudential Regulation Authority is the UK prudential supervisor for the firms within its remit. PRA rules, supervisory statements and consultation proposals have different roles and legal status.

Prepayment and CPR

Prepayment occurs when principal is repaid earlier than the expected or contractual schedule. The conditional prepayment rate is an annualised measure applied to the surviving balance under the stated convention.

Present value

Present value is the value today of a future payment or stream of payments under the selected discounting assumptions. A payment received later is converted into today’s value using a discount factor.

Principal

Principal is the amount borrowed or invested before interest. A derivative’s notional principal is a reference amount used to calculate payments and may never be exchanged.

Probability calibration and Brier score

Probability calibration compares predicted probabilities with observed frequencies under the evaluation design. A Brier score averages squared probability errors, combining aspects of accuracy that differ from rank discrimination alone.

Probability of default

Probability of default is the probability that a borrower defaults over a defined horizon and under specified conditions. One-year, remaining-lifetime, market-implied and prudential PDs answer different questions.

Provision matrix

A provision matrix applies estimated lifetime loss rates to grouped receivables under the relevant simplified approach. The rates should reflect suitable segmentation and forward-looking information; they are not automatically annual PDs.

RAROC and economic capital

Risk-adjusted return on capital compares the specified risk-adjusted income with allocated capital. A hurdle is the required return used in the decision. Economic capital is an internal risk-based measure and need not equal regulatory capital.

Rating migration

Rating migration is movement between credit-quality states. A transition matrix records the probabilities of those movements over a stated period, often including an absorbing default state in simplified examples.

Reconciliation

Reconciliation compares records or results and traces differences to their source. For risk calculations, this includes trade population, valuation time, units, currency, mapping, assumptions and model version.

Recovery and LGD

Recovery is the amount obtained after default, taking account of the relevant cash flows and costs. Loss given default, or LGD, is the fraction of exposure lost under the selected timing and discounting convention.

Regulatory capital and RWA

Regulatory capital is eligible loss-absorbing funding measured under the applicable rules. Risk-weighted assets express exposures or requirements on a risk-adjusted basis and are used with capital ratios; an exposure amount is not automatically a capital charge.

Revolving facility

A revolving facility allows borrowing, repayment and further drawing within contractual terms. Its exposure and expected life can depend on customer behaviour and the lender’s ability to mitigate credit risk.

Ridge penalty

A ridge penalty discourages large fitted coefficients by adding a squared-coefficient penalty to the fitting objective. It can improve stability, but the strength of the penalty must be selected and validated.

Risk appetite and limits

Risk appetite describes the types and amounts of risk an organisation is willing to accept under its governance. Limits and early-warning indicators translate that position into monitored measures and escalation triggers.

Risk class and bucket

A risk class groups related risk types, such as interest rates or equities. A bucket is a further prescribed grouping used in aggregation. The definitions differ across FRTB, SA-CVA and SIMM.

Risk-neutral measure

A risk-neutral measure is a pricing probability measure under which suitably discounted traded asset prices are martingales under the model’s conditions. Its probabilities are pricing weights and need not represent a real-world forecast.

Runoff

Runoff describes the amount or fraction of a funding balance assumed to leave over a specified period. A regulatory runoff rate and an internally chosen behavioural stress assumption are different inputs.

Securitisation and tranche

A securitisation allocates cash flows and credit losses from a pool of exposures to securities or positions. A tranche has a specified priority and loss-absorption range, so its risk can differ substantially from the average risk of the pool.

Seniority

Seniority describes a claim’s priority relative to other claims on an issuer. It affects recovery and can determine whether positions are permitted to offset in a default-risk calculation.

Sensitivity

A sensitivity measures how a value changes when a specified input changes, under a stated bump and unit convention. Greeks are familiar option sensitivities such as delta, gamma and vega.

Settlement

Settlement is the completion of a payment or delivery obligation. A settlement lag separates the trade date from completion and can create cash needs and exposure before the exchange is final.

SICR and staging

A significant increase in credit risk can move a qualifying asset from Stage 1 to Stage 2 under IFRS 9’s general approach. Stage 3 concerns credit-impaired assets. Staging reflects the applicable assessment and is not determined by an arbitrary universal PD cutoff.

SME

SME means small or medium-sized enterprise. Accounting, regulatory and modelling classifications can impose specific size or eligibility criteria beyond that general description.

SPPI and business model

SPPI asks whether contractual cash flows are solely payments of principal and interest under IFRS 9’s conditions. Classification also depends on the relevant business-model assessment, rather than on SPPI alone.

Standard deviation

Variance is the probability-weighted squared deviation from a mean. Standard deviation is its square root and is expressed in the original units of the variable.

Standardisation

Standardisation rescales a variable, often by subtracting a training-sample mean and dividing by its standard deviation. Applying the same fitted transformation to later observations avoids using future information.

Standardised fallback and CU

A standardised fallback applies the prescribed standardised treatment to positions or desks that are not eligible for the internal-model route. CU denotes the standardised charge for ineligible desks in the specific FRTB capital example, with its scope stated there.

Stress calibration

Stress calibration uses a defined adverse market period or scenario to set a model’s risk scale. The data window, factor set and aggregation method determine what the resulting stressed measure represents.

Survival probability

Survival probability is the probability that default has not occurred by a specified time. Its decline across an interval gives the probability of first default during that interval under the model.

Training, validation and test samples

Training data are used to fit a model, while validation and test data assess choices or performance outside that fitting process. An out-of-time sample helps test whether performance survives a change in observation period.

Twelve-month and lifetime ECL

Twelve-month ECL concerns lifetime cash shortfalls associated with defaults that are possible in the next twelve months. Lifetime ECL concerns defaults possible over the relevant expected life; twelve-month ECL is not simply the next year’s missed payments.

Underlying

The underlying is the asset, rate, index or other reference quantity on which a derivative’s payments depend. A derivative can depend on more than one underlying risk factor.

Value at Risk

Value at Risk is a loss threshold at a chosen confidence level over a specified horizon. It does not describe how severe losses beyond that threshold may be. A quantile is the corresponding threshold in a probability distribution.

Variable selection

Variable selection chooses the information used by a model based on relevance, availability, stability and validation. A predictive association does not by itself show that a variable causes default or will remain useful after conditions change.

Vintage and cohort

A cohort is a group observed from a common starting condition, such as an origination period. Vintage analysis follows such groups over time to distinguish seasoning and changing lending conditions from other effects.

Weight of evidence and information value

Weight of evidence compares the distribution of outcomes across variable groups under the stated convention. Information value summarises the resulting separation. Their use requires checks for sample size, leakage and stability rather than reliance on a universal cutoff.

Yield

Yield is a rate of return implied by a price and a specified set of cash flows under a stated convention. Different yield definitions and compounding conventions can produce different numerical rates.

Yield

A yield is a rate of return implied by a price and a specified cash-flow convention. Yield to maturity is the single discount rate that equates a bond’s promised payments to its price; realised returns can differ.

Yield curve

A yield curve or term structure describes how rates or discount factors vary with maturity. Projection curves and discount curves can serve different purposes within one valuation.