## ICAAP Submissions: Probability of Default (PD) Calculation

*in*Basel II and III

In order to quantify credit risk for the internal ratings based approach of the Internal Capital Adequacy and Assessment Process (ICAAP) the bank would need to be able to calculate the probability of default (PD). The post below presents one methodology of calculating PD which is based on historical data. It is based on the article “Sound Calculation for Probability of Default (PD)” by Alexander Dorfmann (Finance Trainer- March 2004).

# Calculation of Probability of Default

One method of estimating Probability of Default (PD) is to use historical time series data. The data are grouped by rating grade and a PD estimate is derived for each rating grade. The PD therefore gives the likelihood for obligors with a particular rating grade at the start of a given time period defaulting within that time period.

When calculating the probability of default the following must be considered:

- A consistent definition of what constitutes as a default event across the data pool being analysed and over the time period being analysed. Differing definitions could lead to misleading results.
- Basel 2 require 1-year estimates of PD that are based on long run averages to ensure that there is less variability in the PD estimates over time. This means that the data should consist of long term time series data. The average PD would be the weighted average of the one year PDs where the weights are the number of obligors in each time period.
- The current ratings of the customer are reflective of their status (current or default). This means that applicable ratings are assigned to the obligors on a timely basis and are updated regularly. Delays in assigning ratings could lead to misleading results for PDs.
- As the PD estimate measures the proportion of obligors with a particular rating grade who default during a given period, it is important that for that given period the pool being examined remains static, i.e. there are no late additions to the pool.

Extensions to the 1-year PD estimate model are:

- The computation of transition probabilities where instead of computing the likelihood of default, the likelihood of moving from the given rating grade to another rating grade during the given time period is calculated.
- The computation of a cumulative multiyear PD estimate for each rating grade.

Limitations to the model are:

- There may not be sufficient data to get adequate granularity in the results making the estimation process more volatile.
- If the calculation of PD is done only on an annual basis it is possible that the process of quantifying the credit risk of the portfolio will not be reflective of current data. A solution to this is a rolling monthly estimation process of 1-year PDs and a monitoring process whereby year on year estimates are compared and tracked.

We have reviewed a methodology for deriving PD’s based on the historical data. In the next few posts we consider some methodologies for stress testing Credit Risk.