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Economic Modelling · Simple models for credit risk

Credit Risk Basics and Credit Ratings: PD, LGD and Spreads

Updated 11 October 2026 · Fact-checked

Credit risk is the risk that a borrower fails to pay as promised, or that the market price of its debt falls because default looks more likely. You measure expected loss as PD × LGD × EAD. Ratings from agencies rank borrowers by default likelihood. Spreads are the extra yield investors demand.

Understand Credit Risk Basics and Credit Ratings

Credit risk is the risk of loss because a counterparty does not meet its obligations in full and on time. A bond issuer may miss a coupon. A reinsurer may not pay a claim. A borrower may stop repaying a loan. This failure is called default.

There are two main forms. Default risk is the risk that default actually happens. Credit spread risk is the risk that the price of a bond falls because the market demands a higher yield over a risk-free bond, even though no default has happened. The credit spread is the yield on a risky bond minus the yield on a comparable risk-free bond. A wider spread means lower price. Spread pays for expected default losses and also for uncertainty and illiquidity.

Three measures describe the loss from default. Probability of default (PD) is the chance of default over a stated period, usually one year. Exposure at default (EAD) is the amount owed when default happens. Loss given default (LGD) is the fraction of exposure not recovered. Recovery rate = 1 − LGD. Expected loss = PD × LGD × EAD, where PD, LGD and EAD are treated as independent and as point estimates.

Credit rating agencies assess issuers and issues and give grades. For the major international agencies the top grades run AAA, AA, A, BBB and the lower grades BB, B, CCC and below. BBB and above is called investment grade. Below that is sub-investment grade (high yield). Ratings are opinions about relative creditworthiness, not guarantees. Higher grades have lower historical default rates.

A rating transition matrix shows the probability that an issuer in one grade at the start of a period is in each grade at the end, including default. Each row sums to 1. Default is usually an absorbing state, so its row has 1 for staying in default. Moves to a lower grade (downgrade) widen the spread and hurt prices. This links to Markov models, where the next rating depends only on the current one.

Key rules to remember

Expected loss
EL = PD × LGD × EAD
Assumes PD, LGD and EAD are independent point estimates over the same period.
Loss given default
LGD = 1 − recovery rate
Recovery rate is the fraction of exposure recovered, as a proportion of EAD.
Credit spread
s = y(risky) − y(risk-free)
Use yields of the same term and similar features, such as coupon and currency.
Approximate spread from default
s ≈ λ × LGD
Simple approximation where λ is the annual default intensity (or PD for small values). It ignores risk premium and liquidity.
Transition matrix row condition
Σⱼ pᵢⱼ = 1 for each row i
Each row covers all possible end ratings, including default.
n-year transition probabilities
P(n) = Pⁿ
Valid when the rating process is a time-homogeneous Markov chain.

How to solve Credit Risk Basics and Credit Ratings questions

Use this order for any question on credit risk measures, spreads or ratings.

  1. 1Identify what is asked: PD, LGD, EAD, expected loss, spread, or a rating transition probability.
  2. 2Write down the time period of each given figure. Convert if needed, for example annual to two-year.
  3. 3Convert any recovery rate to LGD = 1 − recovery. Check whether LGD applies to EAD or to face value.
  4. 4Apply the formula in notation, for example EL = PD × LGD × EAD, then substitute.
  5. 5For transition questions, identify the starting row and list every path to the target state. Multiply along a path and add across paths.
  6. 6For spread questions, compare risky and risk-free yields of the same term. Say whether the spread covers only expected loss or also risk premium.
  7. 7State the assumptions used, such as independence and a Markov rating process.
  8. 8Check that the answer is reasonable: probabilities between 0 and 1, loss not above EAD.

Quickest way: Fast route for MCQs

When to use it: Use in the multiple-choice section when numbers are given directly and you need one calculation.

  1. Underline PD, LGD or recovery, and EAD in the stem.
  2. If recovery is given, find LGD at once as 1 − recovery.
  3. Multiply the three numbers. Do the percentage part first, then the rupees.
  4. For a two-step rating path, multiply along the path and add paths. Do not build the whole matrix square.
  5. Eliminate options that are probabilities above 1 or losses above EAD.

Common mistakes in Credit Risk Basics and Credit Ratings

  • Using recovery rate in place of LGD in the expected loss formula.

    The question gives recovery, and students multiply the numbers they see.

    Fix: Always write LGD = 1 − recovery first, then substitute.

  • Treating the credit spread as equal to the expected loss rate only.

    Simple textbook examples link spread to PD × LGD, so students assume it is the whole spread.

    Fix: State that observed spreads also include a risk premium and compensation for illiquidity, so they usually exceed the expected loss part.

  • Confusing default risk with credit spread risk.

    Both involve credit quality, so they sound alike.

    Fix: Default risk needs an actual default. Spread risk is a price loss from a wider spread with no default needed.

  • Adding rows or columns of a transition matrix that do not sum to 1, or reading across the wrong direction.

    Students mix up the from-state (row) with the to-state (column).

    Fix: Rows are the starting rating, columns the ending rating. Check each row sums to 1.

  • Using a one-year PD for a multi-year horizon unchanged.

    The time period is skipped in a hurry.

    Fix: For two years with a constant annual PD p and independence, survival is (1 − p)², so default within two years is 1 − (1 − p)².

  • Treating a rating as a guaranteed measure of default.

    Grades look precise.

    Fix: Say a rating is an opinion based on relative default likelihood and can be changed or lag the market.

Worked examples

Example 1

A bank lends ₹50,00,000 to a company. The one-year probability of default is 2%. If default happens, the bank expects to recover 40% of the exposure. Find the expected loss, assuming the three inputs are independent.

Show the solution
  1. EAD = ₹50,00,000.
  2. PD = 0.02.
  3. LGD = 1 − 0.40 = 0.60.
  4. EL = PD × LGD × EAD = 0.02 × 0.60 × 50,00,000.
  5. 0.02 × 0.60 = 0.012.
  6. 0.012 × 50,00,000 = ₹60,000.

Answer: Expected loss = ₹60,000.

Example 2

A one-year rating transition matrix has states A, B and D (default, absorbing). From A: to A 0.90, to B 0.08, to D 0.02. From B: to A 0.10, to B 0.80, to D 0.10. Find the probability that a bond rated A now is in default after two years.

Show the solution
  1. The process is assumed to be a time-homogeneous Markov chain.
  2. Paths from A to D in two steps: A→A→D, A→B→D, A→D→D.
  3. A→A→D: 0.90 × 0.02 = 0.018.
  4. A→B→D: 0.08 × 0.10 = 0.008.
  5. A→D→D: 0.02 × 1 = 0.02.
  6. Add: 0.018 + 0.008 + 0.02 = 0.046.

Answer: The probability of being in default after two years is 0.046, or 4.6%.

Exam tips

  • Write the formula in notation before substituting. Marks go for method even if the arithmetic slips.
  • In written answers, define default risk and spread risk separately, then link them through spread.
  • For transition questions, list the paths in a short table of lines. This avoids missing the absorbing default path.
  • State assumptions such as independence of PD, LGD and EAD, and the Markov property.
  • Check units: PD per year, EAD in rupees, LGD as a proportion.

Practice questions from Simple models for credit risk

Credit Risk Basics and Credit Ratings in other exams

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

Credit Risk Basics and Credit Ratings: frequently asked questions

What is the difference between PD, LGD and EAD?

PD is the chance a borrower defaults over a period. EAD is the amount owed at default. LGD is the share of that amount lost after recoveries. Together they give expected loss.

How is credit spread related to default risk?

The spread is the extra yield a risky bond pays over a risk-free bond. Part of it pays for expected default losses, roughly PD × LGD. The rest pays for risk premium and liquidity.

What is investment grade?

For the main international agencies, BBB and above are investment grade. Grades below that are sub-investment grade, also called high yield, and carry higher default likelihood.

Why is default an absorbing state in a transition matrix?

Once an issuer defaults, the simple model assumes it stays in default. So the default row has 1 in the default column and 0 elsewhere.