Credit and Counterparty Risk

Introduction and Context

Credit risk is the possibility that a borrower, issuer, trading counterparty, or other obligor will fail to meet contractual obligations, causing financial loss. It is one of the oldest banking risks and remains central to lending, bond investment, derivatives trading, insurance, trade finance, and treasury management.

Counterparty risk is a specific form of credit risk arising in a transaction whose value may change over time. In a derivative contract, for example, the amount at risk is uncertain because the replacement cost of the contract fluctuates with market prices. A bank may therefore face credit risk both from traditional loans and from the future positive value of swaps, forwards, options, and securities-financing transactions.

Effective credit-risk management connects quantitative measurement with underwriting, pricing, collateral, documentation, portfolio diversification, capital allocation, monitoring, and recovery processes. The central analytical decomposition is:

where EL is expected loss, PD is probability of default, EAD is exposure at default, and LGD is loss given default. This relationship is a useful foundation, but it does not capture every dependence, extreme event, or model limitation.

Learning Objectives

By the end of this chapter, the reader should be able to:

1. Distinguish credit risk from counterparty credit risk.
2. Estimate and interpret PD, EAD, LGD, expected loss, and unexpected loss.
3. Explain credit ratings, rating migration, and credit-spread information.
4. Analyse concentration risk, collateral, guarantees, and close-out netting.
5. Explain wrong-way risk and its effect on exposure.
6. Compare major credit-portfolio models.
7. Apply credit-risk concepts to lending and derivatives decisions.
8. Evaluate governance, regulatory, ethical, and model-risk considerations.

1. The Structure of Credit and Counterparty Risk

A credit exposure exists when one party has a claim on another party. Examples include a bank loan, a corporate bond, an unpaid invoice, a repurchase agreement, or a positive-value interest-rate swap.

Default and credit events

Default is not always identical to bankruptcy. A contract, accounting policy, or regulatory framework may define default through events such as:

• failure to pay principal or interest within a specified period;
• bankruptcy, insolvency, or administration;
• restructuring that disadvantages creditors;
• breach of a financial covenant;
• cross-default under related obligations.

The exact definition matters because PD estimates, recovery data, and capital requirements depend on the event being measured.

Credit risk versus counterparty risk

Traditional credit risk is often relatively predictable. A five-year loan has a contractual balance, although repayments, drawings, and prepayments may change it. Counterparty risk is dynamic: exposure depends on market variables and may become positive or negative before maturity. In a derivatives portfolio, the institution may be exposed to a counterparty when the contract has positive replacement value, but the same contract may later have negative value.

Counterparty risk also has a bilateral character. If both parties can owe money at different times, each may have exposure to the other. For a collateralized derivative, exposure is additionally affected by margin frequency, thresholds, minimum transfer amounts, collateral haircuts, disputes, and liquidation time.

2. Core Measurement Quantities

Probability of default

PD is the probability that an obligor defaults over a specified horizon, commonly one year or the remaining life of an exposure. A one-year PD and a lifetime PD must not be treated as interchangeable.

A rating-based estimate may be obtained from historical default frequencies. A market-based estimate may use bond spreads or credit-default-swap spreads, but market prices include liquidity, risk premia, recovery assumptions, and other influences. Statistical models may use financial ratios, payment history, industry conditions, macroeconomic variables, and borrower characteristics.

For a discrete one-year event, the expected default indicator D satisfies:

PD should be defined consistently with the population, observation period, default definition, and economic conditions. A through-the-cycle PD seeks stability across the business cycle; a point-in-time PD is more responsive to current conditions.

Exposure at default

EAD is the amount subject to loss when default occurs. For a fully drawn, uncollateralized loan, EAD may approximate the outstanding principal plus accrued interest. For a revolving credit facility, the borrower may draw additional funds before default. A common formulation is:

CCF is the credit conversion factor, between zero and one in ordinary applications, representing the expected proportion of the unused commitment drawn before default. The formula assumes that the undrawn commitment and its conversion factor are measured consistently.

For derivatives, current exposure is commonly related to positive mark-to-market value:

where V is the current replacement value of the contract or netting set and C is eligible collateral after applicable adjustments. If V ≤ C, current exposure is zero, although future exposure, operational risk, and collateral liquidation risk may remain.

Future exposure is uncertain. Potential future exposure (PFE) estimates a high percentile of possible exposure over a chosen horizon. Expected positive exposure (EPE) is the time-weighted average of expected positive exposure:

T is the horizon, V(t) is the future value at time t, C(t) is collateral, and E denotes expectation under the exposure simulation measure. The integral representation is conceptual; practical systems use discrete time steps. EPE is not itself a loss estimate because it does not include PD or LGD.

Loss given default and recovery

LGD is the proportion of EAD not recovered after default. If R is the recovery rate, measured as the present value of recoveries divided by EAD, then:

Recovery may come from cash, collateral, guarantees, asset sales, litigation, or restructuring. Recovery values must account for timing and costs. A recovery received later is worth less than an immediate recovery, so discounting and workout expenses are important.

LGD is influenced by seniority, collateral quality, jurisdiction, industry, default cycle, loan-to-value ratio, and the availability of guarantees. It can be lower for senior secured debt than for subordinated unsecured debt, but this is not guaranteed in every case.

Expected loss

Expected loss is the probability-weighted average loss over a specified horizon:

The formula assumes that PD, EAD, and LGD are appropriately defined for the same exposure, horizon, and default event. In a more general setting, EAD and LGD may vary by scenario and may be correlated with default; then the expected loss is better represented as:

where 1_default equals one if default occurs and zero otherwise. The simple product is a useful approximation when inputs are treated as suitable averages.

Worked example: a revolving facility

A company has drawn $6 million on a $10 million facility. The one-year PD is 3%, the CCF on the undrawn amount is 40%, and LGD is 45%.

Undrawn commitment = $10m − $6m = $4m.

Therefore:

The result is an expected one-year loss of $102,600, subject to the assumptions used for PD, CCF, and LGD. It is not a prediction that exactly $102,600 will be lost.

Unexpected loss

Actual losses vary around their expected value. Unexpected loss (UL) represents loss volatility, especially adverse outcomes in the tail of the loss distribution. A simplified standard-deviation description is:

where L is portfolio loss. Capital is generally intended to absorb severe but plausible unexpected losses, while pricing and provisions address expected loss. The distinction is conceptual: accounting provisions, regulatory capital, and economic capital may use different definitions and confidence levels.

For a single exposure with deterministic EAD and LGD and a Bernoulli default event, the variance is:

This formula assumes fixed EAD and LGD and only default/no-default uncertainty. It is not a complete portfolio-risk formula because it ignores dependence between obligors and variation in recovery and exposure.

3. Credit Ratings and Migration

Credit ratings communicate an assessment of relative credit quality. Agencies commonly use letter grades, while banks often use internal grades linked to default frequencies. A rating is an opinion or classification, not a guarantee of repayment.

Rating systems

A sound rating system should have:

• clear definitions for each grade;
• documented approval and override procedures;
• evidence that grades differentiate risk;
• regular validation against realized defaults and losses;
• controls against conflicts of interest;
• governance over data, models, and expert judgment.

External ratings can support investment mandates and risk limits, but institutions should not rely mechanically on them. Internal analysis remains necessary because ratings may lag market developments and may not capture transaction-specific collateral, covenants, or concentration.

Rating migration

Migration is movement between credit grades, including upgrades, downgrades, and default. A transition matrix records the probability of moving from an initial rating i to rating j over a fixed horizon:

For each initial rating i, the probabilities across all mutually exclusive ending states should sum to one:

A bond portfolio can lose value even without default if issuers are downgraded and credit spreads widen. Thus, credit risk includes both default loss and mark-to-market loss from migration. Transition matrices may be historical, through-the-cycle, or conditioned on a macroeconomic scenario. They are not constant laws of nature: migration probabilities vary by industry, geography, cycle, and definition.

4. Concentration and Dependence

Diversification reduces idiosyncratic risk only when exposures are not excessively dependent. Concentration may arise by:

• single borrower or connected group;
• industry or economic sector;
• country or region;
• product, maturity, or collateral type;
• common guarantor;
• currency or supply chain;
• correlated macroeconomic driver.

A portfolio of many loans to unrelated small firms may be safer than a portfolio of many loans to companies dependent on the same commodity price. The number of names alone is therefore an inadequate diversification measure.

Dependence is important because defaults can cluster during recessions, financial crises, natural disasters, or geopolitical events. Portfolio models commonly use a latent systematic factor to represent shared economic conditions. Correlation estimates are uncertain and often increase in stress, making diversification benefits smaller precisely when they are most needed.

5. Collateral, Guarantees, and Netting

Collateral

Collateral reduces loss if it is legally enforceable, liquid, properly valued, and available when needed. Examples include cash, government securities, receivables, inventory, property, and margin posted under a derivatives agreement.

A collateral valuation should consider:

• current market value;
• volatility and appropriate haircut;
• liquidation time;
• currency mismatch;
• legal control and perfection;
• concentration and wrong-way risk;
• maintenance and operational costs.

If collateral has market value M and haircut h, its recognized value may be approximated by:

The haircut is expressed as a decimal. This formula is a simplified risk-control calculation, not a universal regulatory rule. For example, $2 million of securities with a 10% haircut provide recognized value of $1.8 million.

Guarantees and credit protection

A guarantee transfers or shares credit risk, but it does not eliminate it. The guarantor’s own PD, legal capacity, correlation with the borrower, documentation, and ability to perform must be assessed. Credit derivatives such as credit-default swaps can transfer default risk, but introduce counterparty, basis, liquidity, legal, and collateral risks.

Close-out netting

Without netting, positive and negative transactions may be assessed separately. Enforceable close-out netting permits transactions under a master agreement to be terminated and replaced by a single net amount after default. For transactions with values V₁, V₂, …, Vₙ, the net replacement amount is:

Current net exposure before collateral is:

Netting reduces exposure only if the legal agreement is valid in the relevant jurisdictions and applies to the relevant transactions. Operational records must correctly identify the netting set, collateral, valuation time, and close-out terms.

6. Wrong-Way Risk

Wrong-way risk occurs when exposure to a counterparty increases as that counterparty’s credit quality deteriorates. General wrong-way risk arises from broad economic dependence; specific wrong-way risk arises from a direct relationship between the counterparty and the exposure.

For example, a bank may lend to an oil producer while accepting oil-related collateral. A fall in oil prices may reduce the borrower’s ability to repay and simultaneously reduce collateral value. Similarly, a derivative may have positive value to the bank precisely when the counterparty is under stress.

Wrong-way risk violates the intuition that exposure and default probability can be treated as independent. If default indicator D and exposure E are dependent:

cannot generally be replaced accurately by PD × E[E] × E[LGD]. Risk managers should identify causal links, apply limits, stress joint movements, impose collateral requirements, and avoid inappropriate diversification assumptions.

7. Credit-Portfolio Models

Expected-loss approach

The simplest portfolio approach sums expected losses:

It is transparent and useful for pricing and provisioning, but it does not measure loss variability or default dependence.

Structural models

Structural models link default to the value of a firm’s assets. In the basic intuition, equity resembles a call option on asset value: shareholders receive value after debt obligations are met. Default occurs when asset value falls below a debt threshold at a relevant maturity. These models connect leverage, asset volatility, interest rates, and maturity to default risk. Their limitations include uncertain asset values, complex liabilities, changing capital structures, and unrealistic assumptions about continuous markets and observable inputs.

Reduced-form models

Reduced-form, or intensity, models treat default as a stochastic event driven by a hazard rate. If λ(t) is a deterministic hazard rate, survival probability to time T is:

If λ is constant, this becomes S(T) = e^(−λT). The formula assumes the specified hazard process adequately represents default timing and that the model’s recovery and pricing conventions are consistent. Hazard rates inferred from credit spreads include risk premia and liquidity effects; they are not automatically physical default probabilities.

Credit portfolio simulation

Simulation models generate correlated default, migration, exposure, and recovery outcomes. A simplified factor model may represent an obligor’s latent credit variable as:

where Z is a common systematic factor, εᵢ is an obligor-specific factor, and ρᵢ lies between zero and one. Default occurs when Xᵢ falls below a threshold calibrated to PD. The model illustrates how common economic conditions create clustered defaults. It does not eliminate the need for validation of factor choice, correlation, thresholds, recovery, and exposure assumptions.

8. Accounting, Regulation, and Governance

Credit-risk measurement supports several different purposes. Financial reporting may require forward-looking expected-credit-loss estimates over 12 months or the remaining life of an exposure, depending on credit deterioration and the applicable accounting standard. Regulatory capital generally focuses on solvency under prescribed risk-weighting, stress, and capital rules. Economic capital seeks a firm-specific measure of severe loss. These measures should not be assumed identical.

Strong governance includes independent credit approval, segregation of duties, documented limits, exception escalation, watch lists, covenant monitoring, collateral audits, model validation, data-quality controls, and independent internal audit.

Ethical issues include fair borrower treatment, responsible use of alternative data, explainability of automated decisions, privacy, discrimination, conflicts of interest in ratings, and avoiding the concealment of deteriorating exposures through repeated refinancing. A model that predicts default accurately but systematically denies credit to protected groups may still be unacceptable.

Technology can improve monitoring through automated covenant extraction, transaction analysis, anomaly detection, and early-warning indicators. Artificial-intelligence systems require representative data, explainability, human challenge, cybersecurity, access controls, drift monitoring, and documented accountability. Automation should support—not replace—professional judgment and governance.

9. Applied Case: Northbridge Bank and an Energy Derivatives Counterparty

This is an illustrative case, not a report of an actual institution.

Background

Northbridge Bank has a five-year interest-rate swap with Delta Energy. The swap currently has a positive value of $12 million to Northbridge. Delta has posted $8 million of eligible cash collateral. Northbridge also has a $20 million revolving loan to Delta, of which $14 million is drawn. The undrawn commitment is $6 million.

The credit team estimates a one-year PD of 4%, LGD of 50%, and a CCF of 50% for the revolving facility. Delta’s revenues and collateral are strongly linked to natural-gas prices. A fall in gas prices could reduce both Delta’s repayment capacity and the value of related collateral.

Problem

The bank must estimate exposure, identify concentration and wrong-way risk, and decide whether existing limits and collateral are adequate.

Analysis

The current derivative exposure after collateral is:

The loan EAD is:

If the loan and derivative are legally enforceable within the same netting set, their values and collateral may be assessed under the applicable agreement. If they are separate legal agreements or products, the bank cannot assume cross-product netting merely because the same counterparty is involved.

A simple expected loss for the loan is:

This excludes the derivative’s future exposure and assumes independent, stable inputs. The bank should simulate the swap’s potential future exposure, stress gas prices and interest rates jointly, and assess Delta’s liquidity under those scenarios.

Approach and solution

Northbridge should:

1. confirm legal enforceability of master agreements and collateral rights;
2. define the correct netting sets and collateral eligibility;
3. stress the joint decline in Delta’s credit quality, gas prices, collateral value, and derivative exposure;
4. set a counterparty limit based on stressed exposure rather than current exposure alone;
5. require additional margin or reduce the loan if the stress result breaches risk appetite;
6. monitor covenant headroom, liquidity, collateral concentration, and rating migration;
7. document model assumptions and obtain independent validation.

Outcome

The bank concludes that the $4 million current derivative exposure understates risk because future exposure can rise and because energy-price declines create specific wrong-way risk. It tightens the limit, increases margin frequency, applies a collateral haircut to energy-linked assets, and establishes an escalation trigger for rating downgrade or gas-price stress.

Learning points

Current exposure is not the same as potential future exposure. A low current net amount does not remove legal, liquidity, concentration, or wrong-way risk. Expected loss is useful for average pricing and provisioning, while stress testing and portfolio models are needed to assess severe outcomes.

10. Limitations and Best Practices

No single metric captures credit risk completely. PD estimates can be unstable, recovery data may be sparse, EAD can change rapidly, and market-implied measures include risk premia. Historical data may not include the next crisis. Correlations can rise in stress, collateral can become illiquid, and legal assumptions can fail across jurisdictions.

Best practice is therefore to combine:

• borrower analysis and experienced credit judgment;
• robust internal ratings and independent validation;
• scenario analysis and reverse stress testing;
• exposure simulation for derivatives;
• legally reviewed netting and collateral documentation;
• concentration and wrong-way-risk limits;
• conservative data and model controls;
• regular back-testing against defaults, migrations, exposure, and recoveries;
• board-level risk appetite and timely escalation.

Chapter Summary

Credit risk is the possibility of loss caused by failure to perform, while counterparty risk concerns dynamically changing exposure in transactions such as derivatives. The core quantities are PD, EAD, LGD, expected loss, and unexpected loss. The basic expected-loss relationship is EL = PD × EAD × LGD, but dependence between default, exposure, and recovery may require a more general expectation.

Credit ratings classify relative quality, while migration captures upgrades, downgrades, and default. Concentration and correlation can cause clustered losses even in portfolios with many obligors. Collateral, guarantees, and close-out netting can reduce exposure, but only when they are enforceable, liquid, properly valued, and operationally controlled. Wrong-way risk is especially important because exposure can rise as credit quality deteriorates.

Portfolio models range from simple expected-loss aggregation to structural, reduced-form, and simulation approaches. Each depends on assumptions that require validation and stress testing. Effective practice combines quantitative models with underwriting, governance, legal analysis, ethical safeguards, technology controls, and professional judgment.

Key Terms

Probability of default: Likelihood that an obligor defaults over a defined horizon.

Exposure at default: Amount exposed to loss when default occurs.

Loss given default: Proportion of exposure not recovered after default.

Recovery rate: Present value of recoveries expressed as a proportion of exposure.

Expected loss: Probability-weighted average credit loss.

Unexpected loss: Volatility or adverse deviation of loss around expected loss.

Counterparty risk: Risk that a transaction counterparty fails while owing a positive amount.

Potential future exposure: Estimate of possible exposure at a future confidence level.

Expected positive exposure: Average expected positive exposure over a time horizon.

Credit conversion factor: Estimated proportion of an undrawn commitment drawn before default.

Credit rating: Classification of an obligor’s relative credit quality.

Rating migration: Movement between credit grades over time.

Transition matrix: Probabilities of moving from each initial rating to each ending rating.

Credit concentration: Excessive exposure to a borrower, sector, geography, or common risk factor.

Collateral: Asset or cash pledged to reduce loss after default.

Haircut: Reduction applied to collateral value to reflect risk.

Close-out netting: Contractual aggregation of reciprocal obligations after default.

Wrong-way risk: Risk that exposure increases as counterparty credit quality worsens.

Structural model: Default model linked to the value and volatility of an obligor’s assets.

Reduced-form model: Default model based on a stochastic intensity or hazard rate.

Review Questions

Short Answer Questions

1. Define PD, EAD, and LGD.
2. Why is counterparty risk dynamic in a derivatives transaction?
3. What is the purpose of a credit-rating transition matrix?
4. Explain how a collateral haircut affects recognized collateral value.
5. What is wrong-way risk?

Long Answer Questions

1. Explain the expected-loss framework and discuss why PD × EAD × LGD may be insufficient when variables are dependent.
2. Compare current exposure, potential future exposure, and expected positive exposure.
3. Discuss how concentration and default correlation affect a credit portfolio.
4. Explain the benefits and limitations of collateral and close-out netting.
5. Compare structural, reduced-form, and simulation-based credit-portfolio models.

Analytical / Application Questions

1. A $15 million facility has $9 million drawn, a 50% CCF, 5% PD, and 40% LGD. Calculate EAD and one-year expected loss.
2. A derivative has a current value of $18 million and eligible collateral of $11 million. Calculate current exposure and explain two reasons why future exposure may be higher.
3. A bank lends to a commodity producer and accepts the same commodity as collateral. Analyse the wrong-way risk and recommend three controls.

Multiple Choice Questions with Answers

Question 1

Which expression represents the basic expected-loss relationship?

A. PD + EAD + LGD

B. PD × EAD × LGD

C. PD ÷ EAD × LGD

D. EAD − PD − LGD

Correct Answer: B. PD × EAD × LGD

Question 2

A facility has $8 million drawn, $5 million undrawn, and a 40% CCF. What is EAD?

A. $8.0 million

B. $9.0 million

C. $10.0 million

D. $13.0 million

Correct Answer: B. $9.0 million

Question 3

A derivative has a positive value of $10 million and eligible collateral of $7 million. What is current exposure under the simplified formula?

A. $0 million

B. $3 million

C. $7 million

D. $17 million

Correct Answer: B. $3 million

Question 4

If the recovery rate is 35%, what is LGD?

A. 35%

B. 50%

C. 65%

D. 135%

Correct Answer: C. 65%

Question 5

Which statement best describes rating migration?

A. Movement between credit grades over time

B. The market value of collateral after liquidation

C. The amount drawn on a revolving facility

D. The legal aggregation of derivative contracts

Correct Answer: A. Movement between credit grades over time

Question 6

Which situation is an example of wrong-way risk?

A. Exposure falls when a counterparty’s credit quality improves

B. A borrower defaults after an unrelated operational error

C. A borrower’s repayment ability and collateral value both fall when the same commodity price declines

D. A loan is repaid before maturity

Correct Answer: C. A borrower’s repayment ability and collateral value both fall when the same commodity price declines

Question 7

What is the principal purpose of close-out netting?

A. To increase gross contractual exposure

B. To aggregate reciprocal obligations into a net amount after default

C. To eliminate all market risk

D. To guarantee recovery at 100%

Correct Answer: B. To aggregate reciprocal obligations into a net amount after default

Question 8

A $2 million collateral asset has a 10% haircut. What is its recognized value under the simplified formula?

A. $1.0 million

B. $1.8 million

C. $2.1 million

D. $2.2 million

Correct Answer: B. $1.8 million

Question 9

Which model treats default as a stochastic event driven by a hazard or intensity rate?

A. Reduced-form model

B. Inventory model

C. Duration-only model

D. Accounting depreciation model

Correct Answer: A. Reduced-form model

Question 10

Why does unexpected loss matter to a financial institution?

A. It measures only administrative expenses

B. It represents variability and severe outcomes around expected loss

C. It is always equal to zero for diversified portfolios

D. It replaces the need to estimate PD

Correct Answer: B. It represents variability and severe outcomes around expected loss