It is a common approach to model the point-in-time PD (PiT PD; meaning that the PD depends on the current or lagged economy) by regressing default rates on current or past macro variables (such as GDP or unemployment rate). The specific functional form (e.g., regression of logits) is not relevant for my question. Let us assume that we found a model of the following form: $$ DR_{t+1} = f(DR_t, \Delta GDP_{t-5}) $$ where $t$ measures quarters. This means that the default rate of the following year depends on the current default rate (a sensible assumption) and the change of GDP five quarters ago.

In order to incorporate forward looking information into our PiT-PD estimate of the following year we consider $\Delta GDP$ forecasts for $t+1, \ldots, t+4$. Looking at the above equation and due to the lag in the reaction, these forcasts have, according to our model, impact on $$ DR_{t+7}, DR_{t+8}, DR_{t+9} \text{ and } DR_{t+10}. $$ Finally, this means that the whole PiT-PD for the coming year is indpendent of the forecast and is rather a deterministic calculation using observed GDP changes from $t-5$ until $t-1$.

While this looks simple, we can not use this for the following use cases for the coming year:

  • incorporating various forward looking forecasts (scenarios) to get different PDs in these scenarios.
  • Stresstesting by assuming that a future GDP decrease impacts next years default rate in our portolio.

My question, thus, is:

  • Can we use PiT-models with lagged relations of more than one year at all for PiT-modelling. It looks as this then only helps for the lifetime view.
  • Should we restrict feasible models to such where a timely reaction is assumed?

Happy to read any comments on this.


1 Answer 1


I will try to provide an answer, even if it should most likely be refined with the detailed case you are working on:

  1. It is reasonnable to use PiT models with lagged relations of more than one-year. To predict the PiT PD, you can perfectly integrate lagged events older than a year. However, as you identified, the effectiveness of such model is stronger for TTC PDs as it then fully captures the long term impact of changes in the macro-economic environment. Performing time-series regression, GAMs analysis or even recursive models, is a way to model the seasonality and LT trends and identify temporal confounders for investigating the lagged periods.
  2. If the goal is to capture the impact of a recent change in the environment, then indeed, it is preferable to restrict to models limited to short lags. If the model aims at capturing the evolution of the ECL and the changes in estimated PDs, including from past events, it is reasonable to include lagged events for more than a year in the PiT PD analysis.

I hope this helps...

  • $\begingroup$ Thank you for your answer. However, I don't fully understand. In point 1 you mention the use of macros for TTC models ... I don't know such approaches. I only know TTC approaches that work on the portfolio only (and consider long enough averages). $\endgroup$
    – Richi Wa
    Dec 6, 2023 at 19:52
  • $\begingroup$ What puzzles me is the case of ECL. There we have to consider 3 scenarios. If most of the impact is lagged by more than one year, then the 3 scenarios only materialize in the rather far future. The coming year is rather a function of the past (1 scenario) than a function of the scenario forecasts ... this looks suboptimal :) $\endgroup$
    – Richi Wa
    Dec 6, 2023 at 19:54
  • 1
    $\begingroup$ Macros for TTC : it is true that traditional TTC models focus on long-term averages and are typically built on portfolio data, they can be enhanced by incorporating macroeconomic variables. This allows the model to capture broader economic trends and cycles, providing a more holistic view of credit risk. I hope this clarifies my initial answer on your first comment $\endgroup$ Dec 7, 2023 at 11:14
  • $\begingroup$ For your question 2, let me try to clarify: For ECL calculation under IFRS 9, indeed, we need to consider multiple scenarios. If most of the impact is lagged by more than one year, then the scenarios will materialize in the future. However, this doesn’t necessarily mean that the coming year is only a function of the past. The idea is that these scenarios represent different possible paths the economy might take, and the ECL is a weighted average of credit losses under each scenario. $\endgroup$ Dec 7, 2023 at 11:17
  • $\begingroup$ Continued - The weights are the probabilities of each scenario occurring, which should be updated as new information becomes available. So, even if the impact of a scenario is lagged, its probability can change based on recent events, and this will affect the ECL. $\endgroup$ Dec 7, 2023 at 11:17

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