Long-run Default Rate

From Open Risk Manual

Definition

The Long-run Default Rate is given by the average Default Rate over an entire observation window (typically composed of n equal periods)[1]


\mbox{LRDR}_{t} = \frac{1}{n} \sum_{1}^{T} \frac{N^{D}_t}{N_t}

Regulatory Requirements

The Long-run Default Rate plays an important role in regulatory frameworks for financial institutions and specific regulations and guidance apply[2], [3]

Observation Period

For the purpose of determining the historical observation period referred to in Articles 180(1)(h) and 180(2)(e) of Regulation (EU) No 575/2013, additional observations to the most recent 5 years, at the time of model calibration, should be considered relevant when these observations are required in order for the historical observation period to reflect the likely range of variability of default rates of that type of exposures as referred to in Article 49(3) of the RTS on IRB assessment methodology.

Representativeness

For the purpose of assessing the representativeness of the historical observation period referred to in paragraph 82 for the likely range of variability of one-year-default rates, institutions should assess whether the historical observation period contains a representative mix of good and bad years, and they should take into account all of the following:

  • the variability of all observed one-year-default rates;
  • the existence, lack or prevalence of one-year default rates relating to bad years as reflected by economic indicators that are relevant for the considered type of exposures within the historical observation period;
  • significant changes in the economic, legal or business environment within the historical observation period.


Where the historical observation period is representative of the likely range of variability of the default rates, the long-run average default rate should be computed as the observed average of the one-year default rates in that period.

Where the historical observation period is not representative of the likely range of variability of default rates as referred to in Article 49(4) of the RTS on IRB assessment methodology, institutions should apply the following:

  • where no or insufficient bad years are included in the historical observation period the average of observed one year default rates should be adjusted in order to estimate a long-run average default rate;
  • where bad years are over-represented in the historical observation period, the average of observed one-year default rates may be adjusted to estimate a long-run average default rate where there is a significant correlation between economic indicators referred to in paragraph 83(b) and the available one-year default rates.

References

  1. BCBS, Studies on the Validation of Internal Rating Systems, 2005
  2. ECB guide to internal models - Credit Risk, Sep 2018
  3. EBA Guidelines on PD estimation, LGD estimation and the treatment of defaulted exposures, Nov 2017

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