9 Probability to Default Modelling

This section provides information about the PD modeling feature.

PD Modelling

OFS Loan Loss Forecasting and Provisioning PD Modelling accurately predicts the number of defaults by omitting optimism or conservatism. Adjustments are made on regulatory capital models to remove inherent conservatism. Estimated PDs are point-in-time. These are adjusted, where necessary, to reflect the effects of the current economic conditions. The PD estimates are recalibrated based on the current representative sample regularly. PD is calculated using a sufficient sample size and historical loss data covers at least one full credit cycle.

PD model segments consider drivers in respect of borrower risk, transaction risk, and delinquency status. The PD models are representative of the portfolio segments. The data used for calibration is consistent with the IFRS 9 default definition throughout. Techniques used to determine lifetime PD measures do not introduce bias into the calculation. Future projected macroeconomic factors are used in the computation of lifetime PD's. The risk of default is higher when the expected life of the instrument considering cumulative probability is longer.

The LLFP application calculates Cumulative PD and Final Marginal PD using a conditional probability logic. The PD calculation can be performed as mentioned in the following processes:

· Calculation of Marginal PD whenever Cumulative PD is provided as a download using a Conditional Probability Logic.

· Computation of the Factor - Lambda, Geometric factor, or Arithmetic factor, depending on the Interpolation technique, using the given formula.

· Computation of Intermediate Cumulative PD using the given formula.

· Computation of Intermediate Marginal PD using the conditional probability approach, for each block of time.

· Computation of Final Cumulative PD by using the conditional probability approach, cumulating across periods till the max maturity bucket. This value is used for the Cash Flow approach.

· Computation of Final Intermediate PD by subtracting each cumulative PD with the preceding Cumulative PD. This value is used for the Forward Exposure approach.

The whole PD modeling process consists of the following processes:

· Transition Matrix Definitions

· Economic Scenarios

· PD Model Process

· Survival Model

· User Group Mapping for Sandbox

· PD Model Execution Parameters

NOTE:

Segmentation (Portfolios) is a mandatory prerequisite for these three processes.

The Transition Matrix definition is an optional process. You can also use the transition Matrices generated through the Historical Transition Matrix Run.

Transition Matrix Definitions

This section provides information about the Transition Matrix Definitions.

Access Transition Matrix Definitions

You can access the Transition Matrix Definitions module by clicking the Transition Matrix Definitions link in the LHS menu of the OFS Loan Loss Forecasting and Provisioning application. Upon clicking this link, the Transition Matrix Definitions window is displayed with the Search table and the Transition Matrix Definitions table.

Figure 10: The Transition Matrix Definitions Page

Title: Description of transition_matrix-definitions.png follows - Description: This illustration shows the Transition Matrix Definitions window that can be accessed by clicking the Transition Matrix Definitions link in the LHS menu of the application.

The Transition Matrix Definitions window displays all the existing Transition Matrix definitions under the Transition Matrix Definitions table. The definitions are displayed with details such as Definition Name, Transition Matrix ID, Portfolio, Matrix Type, Frequency, Computed Matrix, Roll Rate, and Modified Date.

Definition Search

The Search table enables you to perform a search for existing Transition Matrix definitions. Perform the following steps to search for an existing Transition Matrix definition from the Search table:

1. Enter the value for one or many of the following search parameters, in the respective fields:

The Transition Matrix Definition Search Form
Field Name	Description
Definition Name	Enter the full or partial name of the definition that you want to search for.
Created Date	Select less than or greater than, or = from the drop-down list and click the Calendar to specify the date, to search for definitions that are created before, after, or on the specified date.
Portfolio	Select the Portfolio from the drop-down list.
Frequency	Select the required value for frequency from the drop-down list. Available options are: · Annually · Half Yearly · Quarterly · Monthly
Matrix Type	Select the required matrix type from the drop-down list. Available options are: · Credit Rating · Dates Past Due

2. Click Search.

The search operation is performed with the entered parameter values and the results are displayed in the Transition Matrix Definitions table.

You can make use of the pagination options to decide the number of definitions per page or to navigate between pages.

Creating a Transition Matrix Definition

Perform the following steps to create a Transition Matrix definition:

1. In the Transition Matrix Definitions table, click Add to open the Transition Matrix window.

Figure 11: The Transition Matrix Window

Title: Description of process_selection.png follows - Description: This illustration shows the Transition Matrix window that can be accessed from the Transition Matrix Definitions pane. You must enter details for the Name, Description, Matrix Type, Frequency, Portfolio, Applicable for Roll Rate. Computation Basis and MIS Date fields, and then click Save.

2. Populate the Transition Matrix form as tabulated.

The Transition Matrix Form
Field	Description
Name	Enter a name for the Transition Matrix definition.
Description	Enter a short description of the Transition Matrix definition.
Matrix Type	Select the matrix from the drop-down list. Available options are: · Credit Rating · Days Past Due
Frequency	Select the frequency from the drop-down list. Available options are: · Annually · Half Yearly · Quarterly · Monthly
Portfolio	Select the portfolio from the drop-down list. Available options are: · Corporate - Overdraft · Corporate - Guarantee · Retail - Lease · Corporate - Others · Corporate - Loans · Retail - Guarantee · Retail - Others · Corporate - Lease · Retail - Loans · Retail - Overdraft
Applicable for Roll Rate	Select either Yes or No from the drop-down list.
Computation Basis	Select the computation basis from the drop-down list. Available options are: · Count Movement · Value Movement
MIS Date	Select the MIS date by clicking the Calendar adjacent to the MIS Date field and by picking the required date.

3. Enter the values in the matrix. As you enter the values, the Row Totals and Column Totals fields in the matrix are auto-updated.

4. Click Add Matrix. The entered transition matrix is saved for the selected MIS date.

You can also click View Matrix to view the added transition matrices and Delete to remove unwanted transition matrices of a selected MIS date.

5. Click Save to save the definition details.

The saved definition is displayed under the Transition Matrix Definitions table in the Transition Matrix Definitions window.

The Audit Trail section at the bottom of the Multiple Rating window displays the metadata related to the definition and contains the fields Created By, Creation Date, Last Modified By, and Last Modification Date with a System ID. The User Comments section facilitates you to add or update additional information as comments.

Viewing a Transition Matrix Definition

The View feature enables you to view the details of an existing Transition Matrix definition. Perform the following steps to view the definition details:

Select the checkbox adjacent to the Transition Matrix definition name, which you want to view, in the Transition Matrix Definitions table.

1. Click View to open the Transition Matrix Definition window.

In View mode, you cannot add or edit any of the fields.

2. Click Cancel to return to the Transition Matrix Definitions page.

Editing a Transition Matrix Definition

The edit feature enables you to update the details of an existing Transition Matrix definition. Perform the following steps to edit an existing Transition Matrix definition:

1. In the Transition Matrix Definitions table, select the checkbox adjacent to the Transition Matrix definition name that you want to edit.

2. Click Edit to open the Transition Matrix Definition window.

You can only update the Description and Applicable for Roll Rate fields in Edit mode. Additionally, you can click View Matrix and view transition matrices for different dates.

3. Update the required fields of the definition.

4. Click Save to save the definition details.

The saved definition is displayed under the Transition Matrix Definitions table in the Transition Matrix Definitions window.

Checking Dependencies of a Transition Matrix Definition

You can check the dependency information of individual Transition Matrix definitions from the Transition Matrix Definitions window.

Perform the following steps to check the dependency information of an existing Transition Matrix definition:

1. In the Transition Matrix Definitions window, select the checkbox adjacent to the Transition Matrix definition for which you want to check the dependency information.

2. In the Transition Matrix Definitions table, click Check Dependency.

The dependency information of the selected definition is displayed in the Dependency Information window with the details such as Child Object Name, Child Object Type, Folder, Parent Object Name, Parent Object Type, and Folder.

Deleting a Transition Matrix Definition

You can delete an existing Transition Matrix definition from the Transition Matrix Definitions window.

Perform the following steps to delete one or more existing Transition Matrix definitions:

1. In the Transition Matrix Definitions window, select the checkbox(s) adjacent to the Transition Matrix definitions that you want to delete.

2. Click Delete .

A warning dialog is displayed.

3. Click Yes.

The selected definitions are removed from the Transition Matrix Definitions window.

Economic Scenarios

This section provides information about economic scenarios.

Access Economic Scenarios

You can access the Economic Scenarios module by clicking the Economic Scenarios link in the LHS menu of the OFS Loan Loss Forecasting and Provisioning application. Upon clicking this link, the Economic Scenario Definitions window is displayed with the Search table and the Economic Scenario Definitions window.

Figure 12: The Economic Scenario Definitions Window

Title: Description of process_selection.png follows - Description: This illustration shows the Economic Scenario Definitions window that can be accessed by clicking the Economic Scenarios link in the LHS menu of the application. You must enter details for the Name and Description fields and select the Add field to add a new Time Sequence and Cycle Factor and then click Save.

The Economic Scenario Definitions window displays all the existing Economic Scenario definitions under Economic Scenario Definitions table. The definitions are displayed with details such as Name, Description, Frequency, Created By, and Created Date.

Definition Search

The Search table enables you to perform a search for existing Economic Scenario definitions. To search for an existing Economic Scenario definition from the Search table, enter the name of the definition you want to search and click Search. The search operation is performed with the entered keyword and the results are displayed in the Economic Scenario Definitions table.

You can make use of the pagination options to decide the number of definitions per page or to navigate between pages.

Creating an Economic Scenario Definition

Perform the following steps to create an Economic Scenario definition:

1. In the Economic Scenario Definitions table, click Add to open the Economic Scenario Definition window.

Figure 13: The Economic Scenario Definition window

Title: The Economic Scenario Definition window - Description: In the Economic Scenario Definitions table, click Add to open the Economic Scenario Definition window.

2. Populated the Economic Scenario Definition form as tabulated.

The Economic Scenario Definition Form
Field	Description
Name	Enter a name for the Economic Scenario definition.
Description	Enter a description for the Economic Scenario definition.
Frequency	The value in this field is set to Annually and is non-editable.
Add	Add a new Time Sequence and Cycle Factor.

3. Enter the required time sequence values in the From field.

4. Enter the required cycle factor values in the Cycle Factor field.

As you enter values in From and Cycle Factor fields, the To field of the Time Sequence is auto-generated.

You can also select the checkbox adjacent to a Time Sequence and click Delete to remove a Time Sequence.

5. Click Save.

The saved definition is displayed in the Economic Scenario Definitions table.

Editing an Economic Scenario Definition

The edit feature enables you to update the details of an existing Economic Scenario definition. Perform the following steps to edit an existing Economic Scenario definition:

1. In the Economic Scenario Definitions table, select the checkbox adjacent to the Economic Scenario definition name that you want to edit.

2. Click Edit to open the Economic Scenario Definition window.

3. Update the available fields of the definition.

4. Click Save.

The saved definition is displayed under the Economic Scenario Definitions table in the Economic Scenario Definitions window.

Viewing an Economic Scenario Definition

The View feature enables you to view the details of an existing Economic Scenario definition. Perform the following steps to view the definition details:

1. In the Economic Scenario Definitions table, select the checkbox adjacent to the Economic Scenario definition name that you want to view.

2. Click View to open the Economic Scenario Definition window.

In View mode, you cannot add or edit any of the fields.

Checking Dependencies of an Economic Scenario Definition

You can check the dependency information of the individual Transition Matrix definition from the Economic Scenario Summary window.

Perform the following steps to check the dependency information of an existing Economic Scenario Matrix definition:

1. In the Economic Scenario Summary window, select the checkbox adjacent to the Economic Scenario definition for which you want to check the dependency information.

2. Click Check Dependency.

Deleting an Economic Scenario Definition

You can delete an existing Economic Scenario definition from the Economic Scenario Definitions window.

Perform the following steps to delete one or more existing Economic Scenario definitions:

1. In the Economic Scenario Definitions window, select the checkbox(s) adjacent to the Economic Scenario definitions that you want to delete.

2. Click Delete.

A warning dialog is displayed.

3. Click Yes.

The selected definitions are removed from the Economic Scenario Definitions window.

PD Model Process

This section provides information about the PD Model Process.

Functional Overview

From the average transition matrix, the transition (migration) from a given Rating or Delinquency band to the Default band represents Probability of Default for that Rating or Delinquency band, for the corresponding period. On projecting this transition matrix year on year, an asset may transition from one grade to another. The probability of transition to default at the end of each year is the Through the Cycle (TTC) Probability of Default (cumulative). When such Probability of default is adjusted for changes in macroeconomic variables, the Probability of Default is Point in Time (PIT).

Access the PD Model Process

You can access the PD Model Process module by clicking the PD Model Process link in the LHS menu of the OFS Loan Loss Forecasting and Provisioning application. Upon clicking this link, the PD Model Process window is displayed with the Search table and the PD Model Process table.

Figure 14: The PD Model Process Window

Title: Description of pd_model_process_summary.png follows - Description: This illustration shows the PD Model Process window that can be accessed module by clicking the PD Model Process link in the LHS menu of the application. You can enter details for the Name field and select a Portfolio from the Segment drop-down list then click Search.

The PD Model Process window displays all the existing PD Model Process definitions under the PD Model Process table. The definitions are displayed with details such as Name, Created By, Created Date, and Portfolio.

Definition Search

The Search table enables you to perform a search for existing PD Model Process definitions. To search for an existing PD Model Process definition from the Search table, enter the name of the definition you want to search and or select a required Portfolio from the drop-down list before clicking Search. The search operation is performed with the entered parameters and the results are displayed in the PD Model Process table.

You can make use of the pagination options to decide the number of definitions per page or to navigate between pages.

Creating a PD Model Process Definition

Perform the following steps to create a PD Model Process definition:

1. In the PD Model Process table, click Add to open the PD Model Stitching Process window.

Figure 15: The PD Model Stitching Process Window

The PD Stitching window displays the PD Model Stitching Process and Name & Description tables. The PD Model Stitching Process table displays processes such as Name and Description, Matrix Selection, and Scenario Selection. By default, the Name and Description process is selected.

2. Populate the PD Model Stitching Process form as tabulated.

The PD Model Stitching Process form
Field	Description
Name	Enter a name for the PD Model Process definition.
Description	Enter a description for the PD Model Process definition.
Choose Portfolio	Select the portfolio from the drop-down list.
FIC MIS Date	Select the MIS Date by clicking the Calendar .
Frequency	The Frequency is set to Annually, by default.
Transition Base	Select the transition base from the drop-down list. Available options are: · Credit Rating · Days Past Due
Merton R-Value	Select this checkbox if you want to enter the Merton R-Value. If you select this checkbox, then the Metron R-Value field is enabled.

3. Select the checkbox adjacent to the Apply Model Flag field if you want to apply the model flag.

4. Click Next.

5. Click the Matrix Selection process from the PD Model Stitching Process table to open the Matrix Selection table.

6. Click Add from the Matrix Selection table.

7. Enter the values in From and To fields of the Computation Sequence pane.

If you have created multiple Computation Sequences, the To field of all the sequences except the final sequence is auto-populated with the previous number to what is entered in the From field of the next sequence.

8. Click the drop-down list in the Assign Matrix field and select the required value.

You can also select the checkbox adjacent to a Computation Sequence and click Delete to remove a matrix.

9. Click Save to save the changes.

10. Click the Scenario Selection process from the PD Model Stitching Process table.

The Scenario Selection table is displayed.

11. Click Add to add a new Scenario Selection row.

12. Click the drop-down list under the Select Scenarios column and select the required scenario from the list of available scenarios.

13. Enter the weight values corresponding to the selected Scenarios in the text fields in the Weights column.

The cumulative number of weights is displayed under the Weights column against the Total field.

You can also select the checkbox adjacent to a Scenario and click Delete to remove the same.

14. Click Save to save the definition details.

The saved definition is displayed under the PD Model Process table in the PD Model Process window.

Editing a PD Model Process Definition

The edit feature enables you to update the details of an existing PD Model Process definition. Perform the following steps to edit an existing PD Model Process definition:

1. In the PD Model Process table, select the checkbox adjacent to the PD Model Process definition name that you want to edit.

2. Click Edit to open the PD Stitching window.

3. Update the required fields of the definition.

4. Click Save.

The saved definition is displayed under the PD Model Process table.

Viewing a PD Model Process Definition

The View feature enables you to view the details of an existing PD Model Process definition. Perform the following steps to view the definition details:

1. In the PD Model Process table, select the checkbox adjacent to the PD Model Process definition name that you want to view.

2. Click View to open the PD Model Process window.

3. Click Cancel to return to the PD Model Process page.

Deleting a PD Model Process Definition

You can delete an existing PD Model Process definition from the PD Model Process window.

Perform the following steps, to delete one or more existing PD Model Process definitions:

1. In the PD Model Process window, select the checkbox(s) adjacent to the PD Model Process definitions that you want to delete.

2. Click Delete .

A warning dialog is displayed.

3. Click Yes.

The selected definitions are removed from the PD Model Process window.

Survival Model

The survival model is used to compute the probability of default. Lifetime Probability of Default is then used as an input to compute the Expected Credit Loss. The survival Model enables financial institutions to understand, how long will customers take before they default. The survival time describes the amount of time that a customer takes before they default.

Access Survival Model

You can access the Survival Model module by clicking the Survival Model link in the LHS menu of the OFS Loan Loss Forecasting and Provisioning application. Upon clicking this link, the Survival Model Summary window is displayed with the Search section and the Survival Model pane.

Figure 16: The Survival Model Pane

Title: Description of process_selection.png follows - Description: This illustration shows the Process Selection window that can be accessed from the Origination Date Cash-flow Process window. You must enter details for the Folder and Generate Cash Flow fields and select a process from the Process Selection field, and then click Apply.

The Survival Model Summary window displays all the existing Survival Model definitions under the Survival Model table. The definitions are displayed with details such as Definition Name, Created By, and Created Date.

Definition Search

The Search table enables you to perform a search for existing Survival Model definitions. To search for an existing Survival Model definition from the Search table, enter the name of the definition you want to search and click Search. The search operation is performed with the entered keyword and the results are displayed in the Survival Model table.

You can make use of the pagination options to decide the number of definitions per page or to navigate between pages.

Creating a Survival Model Definition

Perform the following steps to create a Survival Model definition:

1. In the Survival Model table, click Add to open the Survival Model Definition window.

Figure 17: The Survival Model Definition Window

2. Populate the Survival Model Definition form as tabulated.

The Survival Model Definition Form
Field	Description
Name	Enter a name for the Survival Model definition.
Description	Enter a description for the Survival Model definition.
Product Code	Select the required product code from the drop-down.
Region	Select the required region from the drop-down list.
Term	Enter the required terms for the definition. Note: Ensure that the Product Code and Region that you selected in the Survival Model Definition window is entered in the Value field of the product. id and country.id parameters in the Input Parameters window, before the model execution. Users must add the respective Product ID and Country ID that they have used when defining the Survival Model.
Customer Type	Select either Retail or Corporate.

3. In the Available Attributes pane of the Account Attributes table, click the required attributes to select or deselect them to the Selected Attributes pane.

4. In the Available Variables pane of the Economic Variables table, click the required variables to select or deselect them to the Selected Variables pane.

5. Click Save.

The saved definition is displayed in the Survival Model table.

Editing a Survival Model Definition

The edit feature enables you to update the details of an existing Survival Model definition. Perform the following steps to edit an existing Survival Model definition:

1. In the Survival Model table, select the checkbox adjacent to the Survival Model definition name that you want to edit.

2. Click Edit to open the Survival Model window.

3. Update the required fields of the definition.

4. Click Save.

The saved definition is displayed in the Survival Model table.

Viewing a Survival Model Definition

The View feature enables you to view the details of an existing Survival Model definition. Perform the following steps to view the definition details:

1. In the Survival Model table, select the checkbox adjacent to the Survival Model definition name that you want to view.

2. Click View to open the Survival Model window.

3. Click Cancel to return to the Survival Model Summary window.

Copying a Survival Model Definition

The Copy feature enables you to use an existing Survival Model definition to create a new one. Perform the following steps to copy an existing definition and create a new one:

1. In the Survival Model table, select the checkbox adjacent to the Survival Model definition name that you want to copy.

2. Click Copy to open the Survival Model window.

3. Update the required fields of the definition.

4. Click Save.

The saved definition is displayed under the Survival Model table in the Survival Model Summary window.

Deleting a Survival Model Definition

You can delete an existing Survival Model definition from the Survival Model window.

Perform the following steps to delete one or more existing Survival Model definitions:

1. In the Survival Model window, select the checkbox(s) adjacent to the Survival Model definitions that you want to delete.

2. Click Delete .

A warning dialog is displayed.

3. Click Yes.

The selected definitions are removed from the Survival Model window.

User Group Mapping for Sandbox

Only those users who are mapped to the Modeler and Modelling Administrator Groups can execute models under the sandbox.

PD Model Execution Parameters

Following are the PD Model execution parameters:

The PD Model Execution Parameters
Sl. No.	Parameter	Details	Values to be provided in Sandbox	Values to be provided While Deploying to Atomic Schema
1	FIC MIS DATE	Refers to the execution Date of the Sandbox Population.	Provide the Date for which the data is available in the Sandbox Schema.	Before deploying the PD Model definition to the atomic schema, the FIC_MIS_DATE needs to be updated as -1 in the PD Model Creation Window Definition. The model can be authorized and requested for deployment after this change.
2	SEGMENT ID	This refers to the segments or portfolios that need to be considered for PD model executions.	the SEGMENT ID (It can be referred to from the FSI_PERIOD_TM_MAP_MST Table). It also supports the value -1.	The value must be the SEGMENT ID (It can be referred to from the FSI_PERIOD_TM_MAP_MST Table). It also supports the value -1.
3	Apply Merton	Allows the PD model to know if the Merton R-value needs to be considered to adjust TTC to PIT PD.	The value can be either Y or N depending on whether you want the Merton R-value to be considered by the PD Model. If made N, the Model shall not consider the Merton R provided, irrespective of the APPLY MERTON R flag selection in the UI. If made Y, the model will take the input from APPLY MERTON R flag selection in the UI (either Yes or No).	The value can be either Y or N depending on whether you want the Merton R-value to be considered by the PD Model. If made N, the Model shall not consider the Merton R provided, irrespective of the APPLY MERTON R flag selection in the UI. If made Y, the model will take the input from APPLY MERTON R flag selection in the UI (either Yes or No).
4	Years to TTC	Number of Years for Smoothing the PD Values - Used to define the number of years over which the PD values have to be smoothened from the PIT values to TTC values post the application of Economic Scenarios. For example: If the total PD term structure is for 10 years and the Economic scenarios have been provided for 3 years, with Years to TTC as 4. The model output will have PIT PDs for 3 years, smoothened PD values for years 4 to 7, and TTC PDs for years 8 to 10.	Any number based on the bank's requirement.	Any number based on the bank's requirement.
5	Overwrite.DefaultRow	Value must be �Y� If user wants to make default state as absorption state. Else 'N'	Value must be 'Y' If the user wants to make the default state as absorption state. Else 'N'	The value must be 'Y' If user wants to make the default state as absorption state. Else 'N'

The probability to Default (PD) Term Structure

Oracle's LLFP application enables you or the customer to provide a series of Probability of Default (PD) values across multiple periods - a PD Term Structure either as a download or compute the same through the seeded model. This PD term structure is used in computations of Expected Cash flows and Expected Credit Loss. The PD values are generally outputs of models that are specific to a set of product portfolios wherein they generate a series of PD values for different Ratings or DPD bands.

PD Term Structure through Staging

The LLFP application provides a staging area to obtain the PD term structures, which are expected as a download from the bank. These values can either be Marginal PD or Cumulative PD. If the bank is providing Cumulative PD, the application calculates the Marginal PD value, at the given frequency.

A series of PD values, across multiple periods, and for different Ratings or DPD bands can be loaded into the staging tables under a given PD Term Structure ID. Multiple such PD Term structures can be provided by you to be consumed by the application, maybe across different portfolios - for example, different PD Term Structures for different Portfolios. Additionally, the staging tables can also accept different PD Term structures at different frequencies.

The staging tables are required to be updated only when there is a change in the parameter values, such as Frequency, new Term structures, and so on, or when the PD values change. The PD-related Staging tables need not be updated for every MIS Date.

PD Term Structure through Seeded PD Models

If you prefer to generate PD values using the seeded PD model, the application stores the results, PD term structures - one for each defined segment, in a specific output table, called FSI IFRS9 PD Term Structure Model Output.

Movement of Data from Staging or PD Output Table to Processing Tables

The data movement from the Stage or the PD Model output tables to the Processing tables happens through an SCD batch, which needs to be executed only when fresh data is loaded into the Stage tables. PD data moving into the Processing table are generally stored over time, thus it contains historic data.

During the execution of the Interpolation batch, the application considers only the new PD term structures that have been loaded into the Processing area.

NOTE:

The number of periods for which the Probability of Default values are provided must be constant across dates, forgiven term structure ID.

Interpolation of PD Values to Buckets

The interpolation logic is part of a Batch. The first step in the process is to identify if any new PD term structures have been loaded as part of the SCD, this includes new PD Term Structure IDs or existing IDs but new dates. The interpolation logic kicks in only if there are new term structures. The next step in the process is the determination of the maximum number of buckets for which the PD values have to be interpolated and calculated for a given ID - Rating or ID-DPD band combination. The application looks up the Application Preferences table to determine the maximum period to which the PD values need to be extrapolated and the Setup Parameter table to determine the frequency, bucket frequency, to which the values are to be interpolated.

NOTE:

If the bucket frequency is greater than the PD Term structure frequency, the PD values are not calculated or interpolated.

Once the total buckets are determined, the PD values are then calculated against each of the bucket IDs.

NOTE:

If the bucket frequency as part of the setup parameter is changed, then all historical data is removed and all the term structures, historical, current, and new, are interpolated to the new bucket frequency.

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.