How Probability of Default Is Actually Calculated in the Real World (And why it’s much simpler than you think)

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If you have ever tried to understand Probability of Default (PD), chances are you’ve been told things like:

  • “PD comes from complex statistical models”

  • “You need logistic regression”

  • “You need advanced mathematics”

  • “This is only for quants”

That framing scares people away.

The truth is simpler.

In the real lending world, PD starts with a very basic question:

Out of all loans that are performing today, how many of them will become 90+ days past due within the next 12 months?

That’s it.

Everything else comes later.

Let’s walk through this step by step, using plain data and plain logic.

First, let’s fix the definition in your head

In most retail lending setups:

  • Default = loan reaching 90+ DPD

  • 12-month PD = probability that a loan which is currently below 90 DPD will migrate to 90+ DPD within the next 12 months

PD is not:

  • Recovery

  • Loss

  • Write-off

  • Provision

PD is only about migration to default status.

Once this clicks, everything else becomes easier.

Step 1: What data do you actually need?

You don’t need fancy model outputs to start.

You need just three columns:

  1. Loan ID

  2. DPD bucket today

  3. DPD bucket exactly 12 months later

For example:



Important points:

  • You only look at live loans in April 2012

  • You observe where the same loans land in April 2013

  • Closed loans are tracked separately

This is the raw material of PD.

Step 2: Convert raw data into a migration matrix

Now comes the most important step.

You cross-tabulate the starting bucket against the ending bucket.

That gives you a From–To migration matrix.

Simplistic Illustration:

 


This matrix answers one question very clearly:

Where did loans move over the next 12 months?

Step 3: Where is PD hiding in this table?

Now comes the “aha” moment.

👉 PD is simply the 90+ column.

Let’s convert the above table into percentages row-wise.


That’s your bucket-wise 12-month PD.

No regression.
No black box.
No confusion.

Just migration.

Step 4: Repeat this for every month

Now repeat the same exercise:

  • May 2012 → May 2013

  • June 2012 → June 2013

  • …

  • March 2013 → March 2014

For one financial year, you will end up with 12 such PD matrices.

Each one answers:

What was the 12-month PD starting from this particular month?

These are called Point-in-Time (PIT) PDs.

Step 5: Average PD (still simple)

Now do something very practical.

For each bucket:

  • Average the 12 monthly PDs within the year

Example:


You now have average PDs.

Step 6: Through-the-cycle PDs

Repeat this process across multiple years.

Then take an average across years.

That gives you Through-the-Cycle (TTC) PDs.

Conceptually:

  • PIT PD = what you observe right now

  • TTC PD = what you expect over a full credit cycle

This distinction becomes crucial once you enter ECL modelling.

Step 7: Forward-looking PD (where modelling starts)

Till now, everything has been observational.

Forward-looking PD begins when you ask:

How will PD change if the economy worsens or improves?

That’s where:

  • Macro overlays

  • Stress scenarios

  • Forecast adjustments

come in.

But notice something important:

👉 You cannot do forward-looking PD unless you first understand raw migration-based PD.

Most confusion happens because people jump straight to Step 7.

Step 8: From 12-month PD to lifetime PD

ECL does not stop at 12 months.

You need:

  • 12-month PD

  • 24-month PD

  • 36-month PD

  • … up to loan maturity

This is where:

  • Survival matrices

  • Cumulative probability rules

come into play.

Example intuition:


The mechanics are simple.
The discipline is not.

The one idea you should take home

If you remember nothing else from this article, remember this:

PD is nothing but loans migrating from any bucket below 90 DPD into the 90+ DPD bucket over a defined time horizon.

Everything else is layering.

  • LGD is a different question

  • EAD is a different question

  • Provisioning is a different question

PD is migration.

Where this naturally leads next

This article intentionally stops here.

Because once you understand:

  • Bucket-wise PD

  • PIT vs TTC

  • 12-month vs lifetime PD

The next natural questions are:

  • How does PD flow into ECL?

  • How does staging actually work?

  • How do PD, LGD, and EAD talk to each other?

  • How do behavioural assumptions change provisions?

  • How do you stress PDs without breaking logic?

That is exactly what we build, step by step, in the ECL course.

If this article made PD feel clear instead of scary, you are ready for it.

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