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CFA Level II · CFA Level II Exam

Credit Analysis Models for CFA Level II

Credit analysis models estimate the chance a borrower defaults, how much you lose if it does, and how that risk is priced in a bond. You solve them by finding PD, LGD and discount rates in the vignette, then applying the right model: structural, reduced-form or CVA.

What this chapter covers

This chapter is about measuring and pricing credit risk. You start with the building blocks: probability of default (PD), loss given default (LGD), exposure at default and expected loss. Then you meet two modelling families. Structural models treat a firm's equity as an option on its assets. Reduced-form models treat default as a random event driven by a hazard rate.

The second half is about valuation. You value risky bonds by discounting cash flows with default risk included, and you compute credit valuation adjustment (CVA), the present value of expected loss. You also read credit spreads, spread curves and the term structure of credit.

The chapter connects to Fixed Income, where spreads and yield curves are core, and to Derivatives, where counterparty risk matters. It also uses option pricing ideas and the time value of money. In the exam, it appears inside an item set with a vignette and exhibits that may give PDs, recovery rates and discount factors.

Fixed Income carries a 10-15% weight, and credit analysis models give you calculation-based questions that are very scoreable once you know the steps. The maths is mostly multiplication, discounting and simple option logic. Candidates who practise the setup lose few points here, while those who only memorise definitions struggle when the vignette hides the data in an exhibit. There is no penalty for wrong answers, so always attempt every question.

Credit Analysis Models: topics in the order to study them

  1. 1Basics of Credit Risk and Credit AnalysisIt defines PD, LGD, exposure and expected loss, which every later model uses.
  2. 2Structural Models of Credit RiskIt builds on option logic and shows why equity behaves like a call on firm assets.
  3. 3Reduced-Form Models of Credit RiskIt contrasts with structural models, so learn it right after to see the differences clearly.
  4. 4Valuing Risky Bonds and Credit Valuation AdjustmentIt applies PD and LGD in discounting and needs both model families fresh in mind.
  5. 5Credit Spreads, Term Structure and Credit MeasuresIt links model outputs to market spreads and curves, so it works best as the final synthesis.

How to prepare Credit Analysis Models

Treat this chapter as a set of repeatable calculations plus a few conceptual contrasts. Build the calculations first, then the comparisons.

  1. Write the core definitions on one page: PD, LGD, recovery rate, exposure and expected loss. Use expected loss = PD × LGD × exposure, and LGD = 1 − recovery rate. Exposure can change over time, so note the exposure at each date.
  2. Study structural models with the option analogy. Be able to say who holds the call and who holds the put, and what happens to equity and debt value when asset volatility rises.
  3. Learn reduced-form models by contrast. Note what drives default in each model and what data each one needs.
  4. Practise risky bond valuation with two separate methods. Method 1: discount the promised cash flows at risk-free rates, then subtract CVA, the present value of expected losses on those cash flows. Method 2: discount the promised cash flows at the risky yield, which is the risk-free rate plus the credit spread. Do CVA as a sum of discounted expected losses. For each period, expected loss = exposure at that date × marginal (unconditional) PD × LGD. Exposure may differ by date, for example the bond's remaining value, so read it for each date.
  5. Work through item sets under time. For each vignette, first list the given PDs, recovery rates and discount factors, then answer.
  6. Finish with spread and term structure questions. Practise explaining why spreads widen or narrow, and how to read the credit spread term structure from the data in the vignette.
  7. Keep an error log. Review it two days before the exam and again the day before.

Common mistakes in Credit Analysis Models

  • Using cumulative PD where the period's marginal PD is needed

    Fix: Label each PD as annual, marginal or cumulative before you calculate, and use the one that matches the cash flow date.

  • Using recovery rate in place of LGD

    Fix: Write LGD = 1 − recovery rate every time, and check which figure the vignette gives.

  • Mixing up the option positions in structural models

    Fix: Equity holders are long a call on the firm's assets, so they gain from higher asset volatility. Lenders are short a put on the assets, so they lose from higher asset volatility. Use this to check your positions.

  • Forgetting to discount expected losses in CVA

    Fix: Multiply each period's expected loss by the discount factor for that date, then sum them.

  • Confusing what drives default in structural versus reduced-form models

    Fix: Remember: structural links default to asset value falling below debt; reduced-form treats default as a surprise at a random time governed by a default intensity (hazard rate), and is typically calibrated to market data such as bond or CDS spreads rather than the firm's balance sheet.

  • Reading the question without scanning the exhibits first

    Fix: Scan for numbers and definitions in the exhibits before reading the question, then match each given input to a formula term.

Last-day revision: Credit Analysis Models

  • Expected loss = exposure × PD × LGD, with LGD = 1 − recovery rate.
  • Structural models view equity as a call option on firm assets.
  • In structural models, risky debt equals a risk-free bond minus a put option on assets.
  • Equity holders are long the call and gain from higher asset volatility. Lenders are short the put, so higher volatility raises the put value, lowers risky debt value and raises its spread.
  • Reduced-form models treat default as a surprise that occurs at a random time, governed by a (possibly stochastic) default intensity, also called the hazard rate.
  • Structural models need firm asset value and volatility; reduced-form models are typically calibrated to observable market data such as bond or CDS spreads.
  • Risky bond value = PV of promised cash flows at risk-free rates minus CVA, where CVA is the PV of expected losses on those cash flows. Alternatively, discount the promised cash flows at the risky yield (risk-free rate plus credit spread).
  • CVA is the sum of discounted expected losses across periods.
  • Compute each period's expected loss as exposure at that date × marginal (unconditional) PD for that period × LGD. Do not use the cumulative PD. Exposure may differ by date. Marginal PD = probability of surviving to the prior period × conditional probability of default in that period.
  • Wider credit spreads compensate for higher expected loss and risk premium.
  • Know the PD types. Cumulative PD is the probability of default by a date. Marginal (unconditional) PD is the probability of default in one period, seen from today. Conditional PD is the probability of default in a period given survival to its start. Match the type to the period you are using.
  • Answer every question; there is no penalty for wrong answers.

Credit Analysis Models in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Credit Analysis Models: frequently asked questions

What is the difference between structural and reduced-form credit models?

Structural models link default to the firm's asset value relative to its debt, using option theory. Reduced-form models treat default as a random event with a hazard rate, and often use market data rather than the firm's balance sheet.

How do I calculate credit valuation adjustment?

For each period, multiply the exposure at that date, the marginal (unconditional) PD for that period and LGD to get expected loss. Exposure can differ by date. Marginal PD is the probability of surviving to the prior period times the conditional probability of default in that period. Discount each expected loss to today and add them up. The sum is CVA, and subtracting it from the risk-free value gives the risky value.

Is this chapter calculation-heavy?

Yes, in part. The calculations are mostly multiplication and discounting, but the vignette setup takes care. You also need to explain model differences and spread movements in words.

How should I use the vignette for credit questions?

Scan the exhibits for PD, recovery rate, exposure and discount factors first. Then read each question and decide which model or formula applies before you calculate.