Lifetime PD and the PD term structure

Lifetime ECL needs a PD for every year of an asset's life, not just the next 12 months, and the three ways of expressing those PDs are easily confused. This guide explains the PD term structure, shows how to move between conditional, marginal and cumulative PDs, and builds a five-year curve.

By Hamza Fida, Chartered Accountant. Reviewed by Mirza Fahad Baig, Chartered Accountant. 3 minute read.

Short answer

A lifetime PD is the probability that a borrower defaults at any time over an asset's remaining life. It is built from a PD term structure: a probability of default for each future year. The term structure can be expressed as conditional PDs, the chance of defaulting in a year given survival to it; marginal PDs, the chance of defaulting in that year and not before; or cumulative PDs, the chance of defaulting by the end of it. Lifetime ECL multiplies each year's marginal PD by that year's LGD, EAD and discount factor. In this guide's example, a five-year lifetime PD is 9.43%.

At a glance

12-month PD
Year 1 of the term structure
Lifetime PD
Cumulative PD to maturity
Marginal PD
Default in that year, not before
Conditional PD
Default in a year given survival
Survival
1 minus cumulative PD
Excel
PD term structure model
Lifetime PD and the PD term structure12-month PD: Year 1 of the term structure; Lifetime PD: Cumulative PD to maturity; Marginal PD: Default in that year, not before; Conditional PD: Default in a year given survival; Survival: 1 minus cumulative PD; Excel: PD term structure model.KEY FACTS AT A GLANCELifetime PD and the PD term structure12-month PDYear 1 of the termstructureLifetime PDCumulative PD to maturityMarginal PDDefault in that year, notbeforeConditional PDDefault in a year givensurvivalSurvival1 minus cumulative PDExcelPD term structure modelTax BakersLifetime PD and the PD term structure12-month PD: Year 1 of the term structure; Lifetime PD: Cumulative PD to maturity; Marginal PD: Default in that year, not before; Conditional PD: Default in a year given survival; Survival: 1 minus cumulative PD; Excel: PD term structure model.KEY FACTS AT A GLANCELifetime PD and the PD termstructure12-month PDYear 1 of the term structureLifetime PDCumulative PD to maturityMarginal PDDefault in that year, not beforeConditional PDDefault in a year given survivalSurvival1 minus cumulative PDExcelPD term structure modelTax Bakers
Key facts at a glance, as set out in this guide.

What are conditional, marginal and cumulative PDs?

  • Conditional PD (also called the hazard rate): the probability of defaulting in year t, for a borrower that has survived to the start of year t.
  • Marginal PD: the probability, seen from today, of defaulting in year t and not before. Marginal PD = survival to the start of year t x conditional PD.
  • Cumulative PD: the probability of defaulting at any time up to the end of year t, the sum of marginal PDs to that year. The lifetime PD is the cumulative PD at maturity.

Building a lifetime PD from a five-year term structure

A lender's model gives conditional PDs that rise over time, as is typical for newly originated loans to average-quality borrowers.

YearConditional PDSurvival at startMarginal PDCumulative PD
11.5%100.00%1.500%1.50%
21.8%98.50%1.773%3.27%
32.0%96.73%1.935%5.21%
42.2%94.79%2.085%7.29%
52.3%92.71%2.132%9.43%
Marginal PD by yearMarginal PD by year2Year 12Year 22Year 32Year 42Year 5Marginal PD, %
Conditional PDs rise each year, but marginal PDs rise more slowly as fewer borrowers survive.

Read down the marginal PD column to see the curve the lifetime ECL calculation uses. The 12-month PD is 1.5%; the five-year lifetime PD is 9.43%, less than the 9.8% you would get by adding the conditional PDs, because borrowers who default in an early year cannot default again later. The Term structure sheet of the PD term structure model (Excel) builds this curve for up to 10 years.

How do you convert a cumulative curve into marginal PDs?

Rating agency studies and many credit models give cumulative PDs. Marginal PD for year t is cumulative PD at t minus cumulative PD at t - 1; conditional PD is that marginal PD divided by survival to the start of year t, which is 1 minus the previous cumulative PD. With cumulative PDs of 0.5% after one year and 1.2% after two, the year 2 marginal PD is 0.7% and the conditional PD 0.7% / 99.5% = 0.70%.

What shapes do PD term structures take?

A migration matrix explains why. Strong borrowers usually have low conditional PDs that rise over time, because their credit quality can only drift down. Weak borrowers often have high early PDs that fall for survivors, because those who get through the first years are the stronger ones. Mortgages and consumer loans show seasoning: defaults peak a few years after origination. A flat conditional PD is a simplifying assumption, useful for small portfolios with little data to support a more detailed shape.

How are forecasts built into the term structure?

Lenders adjust PDs for their economic forecasts over the reasonable and supportable period, the horizon over which they can forecast with evidence, typically two to five years, then revert to long-run average PDs. Each economic scenario has its own term structure, and ECL is calculated for each and weighted. See probability of default for the point-in-time adjustment.

Why does the term structure matter for staging?

The SICR test compares lifetime PD for the remaining term today with the lifetime PD expected at origination for the same remaining term. A term structure is needed to make that comparison like for like; see significant increase in credit risk.

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Questions people ask

What is a lifetime PD?

The probability that a borrower defaults at any time over the asset's remaining life: the cumulative PD at maturity.

What is the difference between marginal and conditional PD?

Conditional PD is the chance of default in a year given survival to it; marginal PD is the chance, seen from today, of default in that year and not before.

How do you calculate lifetime PD from annual PDs?

Multiply each year's conditional PD by survival to that year to get marginal PDs, then add the marginal PDs.

What is a PD term structure?

A probability of default for each future period, used to calculate lifetime ECL year by year.

Sources

Every fee, date and rule on this page was taken from these official and primary sources.

  1. IFRS Foundation: IFRS 9 Financial Instruments

Rules and fees change. If you are reading this long after October 4, 2026, confirm the figures with the source before you rely on them.

ECLProbability of default (PD)ECLHow to calculate ECL, step by stepECLPD from external credit ratings

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This guide is general information. It is not tax or legal advice for your situation.