Rate table with interpolated rate factor

In a rate table with interpolated rate factors, PolicyCenter computes the rate factor if the policy value falls between two interpolated parameter values. A rate table can have only one interpolated parameter. In addition, the interpolated parameter can be defined as with or without relaxing. To learn how this affects matching, see Rate table with interpolated rate factor.

The data type of the interpolated parameter must be a numeric type: either decimal or integer. The data type of the interpolated factor must also be numeric. The parameter and the factor can have different numeric data types. For example, a rate table has integer parameters because they are discrete end points of a range, but the factors are decimal values. In this example, the policy values can be decimal rather than integer.

The Interpolation Param rate table in the sample data is an example of a rate table with interpolated rate factors. This rate table is for the personal auto line of business.

The following example shows a rate table similar to, but not the same as, the Interpolation Param rate table. (The Row # column does not appear in PolicyCenter.) The rate table has the following content:

Row #	Jurisdiction	Interpolated parameter	Discount code	* Interpolation Factor
1				14
2	New Jersey			13
3	New Jersey	0		10
4	New Jersey	6		8
5	New Jersey	10		6
6	New Jersey	10	Silver	4

Note: In the user interface for rate table content, rate factor columns are marked with an asterisk (*).

Jurisdiction and Discount Code are exact match parameters.

The only way you can match row 6 is with the exact inputs: Jurisdiction is New Jersey, Interpolated Parameter is 10, and Discount Code is Silver. Hereafter, these values are represented as {New Jersey, 10, Silver}.

If the policy values match row 4 exactly or by relaxing parameters, then PolicyCenter matches row 4 and returns the factor of 8. For example, the policy values match row 4 if you have {New Jersey, 6, Silver}. By relaxing the Discount Code parameter, the input values match row 4.

If the policy values are {New Jersey, 8, Silver}, then Discount Code is relaxed. Rows 4 and 5 are the bounds for interpolation because New Jersey matches, and the policy value 8 is between 6 and 10.

If the policy value of the interpolated parameter falls between two rows and matches on the other parameters, then the factor is calculated proportionally. The interpolated factor is computed according to this formula:

IF =  ( 
         ( (PV - IP1) ÷ (IP2 - IP1) )
         X (F2 - F1) 
      ) 
      + F1

Where:

IF – is the interpolated factor
PV – is the policy value of the interpolated parameter
IP1 – is the lower value of the interpolated parameter
IP2 – is the higher value of the interpolated parameter
F1 – is the value of the factor for IP1
F2 – is the value of the factor for IP2

For example, the policy values are {New Jersey, 8, –}. The interpolated factor is computed by using rows 4 and 5 in the rate table. The formula is:

IF = ( ( (8 - 6) ÷ (10 - 6) ) X (6 - 8) ) + 8

Since the formula is a bit complicated, the following lines show in detail how to compute the input factor:

IF = ( ( 2 ÷ 4 ) X (6 - 8) ) + 8
IF = (     ½     X ( -2  ) ) + 8
IF = (          -1         ) + 8
IF = 7

Interpolated parameters with and without relaxing

Interpolated parameters have an additional type of relaxing. When you define an interpolated parameter, you specify it as either with or without relaxing. An interpolated parameter without relaxing requires that both bounds for the input parameter be found at the same level of relaxation. An interpolated parameter with relaxing allows the bounds to be found at different levels of relaxation. With relaxing, the algorithm finds the bound above or below the input parameter at some level of relaxation, then further relaxes the query to find the other bound.

To see how relaxing affects the bounds, the following rate table has an interpolated parameter and an exact match Discount Code. The policy values of the input parameters are {5, Silver}.

Row #	Interpolated parameter	Discount code	* Interpolation Factor
1	0		14
2	10	Silver	12
3	10	Gold	10
4	20	Silver	8
5	20	Gold	6
6	100		4

Without relaxing – If you define the interpolated parameter without relaxing, rows 1 and 6 are the bounds. These rows match at the same relaxation level (by relaxing the Discount Code). Although Silver matches the Discount Code in rows 2 and 4, the Interpolated Parameter 5 is not between 10 and 20. Therefore, these rows are not the bounds. When Discount Code is relaxed, rows 1 and 6 are the bounds. Rows 1 and 6 are the bounds because they do not specify a Discount Code, and 5 falls between the Interpolated Parameter values 0 and 100.

With relaxing – If you define the interpolated parameter with relaxing, rows 1 and 2 are the bounds. On the first pass to find a match, row 2 is the first bound because the Discount Code matches and the Interpolated Parameter value of 10 is greater than 5. To find the second bound, the Discount Code is relaxed, and row 1 provides the second bound.