# PD and LGD for ECL calculations needs to be time dependent?

I'm studying the implementation of an expected credit loss (ECL) model. I have encountered a complication. Do I need to calculate a probability of default (PD) and loss given default (LGD) with a time dependency of the staging position, i.e. for a specific portfolio the parameters needs to be: $$PD_{t,i}$$ and $$LGD_{t,i}$$, where $$t$$ is the time the account is on the respective staging and $$i$$ is the staging value (1,2 or 3). Or I can simply have $$PD_{i}$$ and $$LGD_{i}$$ only depending on the portfolio and the staging.

Thank you very much in advance.

I assume that you calculate ECL in the context of IFRS9 -correct?

market practice often follows the following appraoch:

1. estimate a TTC PD/LGD (TTC = through the cycle). This corresponds to your lifetime estimate (e.g. one marginal PD value for each year of the life of your exposure) in the average of the economic cycle.
2. But for IFRS9 provisioning you have to reflect current information. Thus usually a PiT (point in time) model is developed on top of the TTC component. In this step you model how your PD/LGD estimate depends on macro economic variables. Later when you calculate provisions you perform (or just retrieve) a forecast of the macros and adjust your PD or LGD values according to this forecast and the sensitivity modeled in the PiT part. Usually forecasts are only used for ~2 years. Noone expects you to forecast further into the future.

In summary you have one time dimension in the sense of marginal PDs for each year (or even month) of the duration of your exposures. Another time dimension is how the forthcoming years adjust these estimates.

• First of all Thank you very much, I do understand but, for example I have a segmentation in stage 2 with where the contracts have different Lifetimes, I can apply an average PD for the average Lifetime of that portfolio or I need to apply a PD for the specific lifetime of each account in the portfolio? Feb 21 '20 at 10:37

You are building a model - the question you are asking is a trade off between accuracy and complexity.

If the accuracy only improves in a minor capacity and the extension is considered complex you can ask the question "is it really necessary"?

If the accuracy greatly improves then whether the extension is considered complex or not I suspect that for whatever purpose it is probably more beneficial to include it.

Most of the time I have seen an LGD kept constant with the PD being flexible to vary over time, but models do vary across firms and purposes.

Time evolution in each staging area might be more relevant. If it is the IFRS stage definition then stage 3 (loans in default) are already in default so time is irrelevant, otherwise stage 2 is probably most sensitive to time in the stage, becuase they are in transition between stage 1 and stage 2 if a further default event occurs.

• But for stage 2 it is needed to calculate a "curve" of the PD Lifetime depending on time? Feb 21 '20 at 10:38

To answer your question in the commentary above: IFRS 9 requires each financial instrument to be measured individually