PDA

View Full Version : Reproducing exhibit 6.14 - Basic Ratemaking

smilehoe
02-02-2011, 04:33 AM
4th ed, Pg 111,
There are two tables on the page, the first one listing frequency, severity and pure premium for 12 months ending each quarter year. In the second table, it shows the exponential fit of the data. What formula did the author used to arrive at the values in the second table. Any help? Attached is the excel file with the two tables in it.

Vorian Atreides
02-02-2011, 10:31 AM
I doubt that they'll ask for an exponential fit of the data on an Exam question. In practice, an exponential fit is likely to be used, but it's calculation is not all that nice w/o some data transformation.

Replicating the exhibit with your own calculator, what you need is the TI-30X II, and enter the relevant data as if you were going to do a linear fit to the data, except use ln(y) instead of just y.

The regression slope would be the quarterly trend (since the X values are quarterly).

To get an annual trend, you need to take e^{4 times the regression slope} - 1.0 to get the trend value.

I've attached an Excel file to show the details more clearly.

smilehoe
02-02-2011, 10:57 AM
Thanks! That was very clear. Especially the excel calculation steps.

arthapasc
11-13-2015, 09:17 AM
Thanks !

Abelian Grape
11-13-2015, 09:31 AM
anytime dawg

x_chuck_x
11-13-2015, 12:34 PM
4th ed, Pg 111,
There are two tables on the page, the first one listing frequency, severity and pure premium for 12 months ending each quarter year. In the second table, it shows the exponential fit of the data. What formula did the author used to arrive at the values in the second table. Any help? Attached is the excel file with the two tables in it.

In practice (that is exam questions) I've seen them give different exponential fits for different times (4, 8, 12, 16 months or quarters) and you have to choose one and just give a valid rationale for having chosen that one based on the other information in the problem. I don't think the calculation of the fit is practical for an exam problem. How long would it take? Last exam had 25 problems. 24 problems is just 10 minutes each on average.