Interpolation Logic

The next step is the population of Marginal PD from the given term structure data to the max bucket for each period. This is populated as follows:

• Considering bucket frequency is monthly - If the input data is yearly, the marginal PD of every year is populated to the 12th monthly bucket of every period. That is Buckets 12, 24 36, and so on.
• Considering bucket frequency is Quarterly - If the input data is half-yearly, the marginal PD of every half-year is populated to the 2nd Quarterly bucket of every period - 2, 4, 6, and so on.

Note:

If the PD term structure is of a lesser period than the total number of buckets applicable, then the Marginal PD of the last period is repeated for all further buckets.

For example: If the total number of buckets is 36 (monthly) but the PD term structure was given for only 2 years, the second-year value is populated for the third year as well, that is PD of Year 2 PD from the term structure is populated for 24th bucket and 36th bucket.

The next step is to interpolate the PD values for the intermediate buckets in each period. One of the following interpolation techniques is used to interpolate the PD values from the given frequency to the bucket frequency:

• Poisson process
• Arithmetic process
• Geometric process.

The interpolation technique gives the intermediate cumulative PD values for every bucket within the given period, which is the Cumulative PD for buckets 1 to 12, 13 to 24, 25 to 36, and so on, assuming input PD is yearly and bucket frequency is monthly.

The intermediate Marginal PD is calculated from the Intermediate Cumulative PD values.

The final step is the calculation of the final cumulative PD against every bucket ID, for every given combination of ID and Rating or DPD.

The interpolation batch ends here.