April 2010 Q5 iv)

[LastHurdles]

Could someone kindly explain the logic of extrapolation in the solution to this part of the question?

For the lower limit ILF, regardless of whether you choose to reconstruct the ILF table on 2012 terms (by inflating limits) or reconstructing the ILF table on 2009 terms (by deflating limits), i would have just interpolated for the ILF(86.384) as:
0.864=1x(86.384/100) for the deflating approach
or for the inflating approach taken ILF(100) as
1x(100/115.763)

If this is also correct, how would my assumption differ?

I think i just dont understand the extrapolating part!

 

[Darren Michaels]

Hi Last Hurdles

Both approaches (your approach and linear extrapolation of the ILF curve below 100,000) were given as valid alternatives in the Examiners' Report.

Linear extrapolation means that we are extending the shape of the curve between 100,000 and 200,000 to values below 100,000.

In your case you are effectively assuming that the ILF curve is a straight line between 0 and 100,000. So your assumption is that the ILF below the lowest limit reduces in proportion to the limits.

N.B. You can still apply wither method by either inflating or deflating the limits.

 

[LastHurdles]

Thank you for the response Darren

 

[r_v.s]

The contract is said to start on 1-Jan-2011. and the ILF table is as at 2009. Why is the inflation factor cube of 1.5? Shouldn't we be counting Starting from 1.7.2009 - 1-7-2010 and then 1-1-2011? Why does it go on till 2012?

 

[Darren Michaels]

Because the question asks you to price a three year contract starting on 1 January 2011. Average date of claim from the contract is therefore 30 June 2012. Average date of claim from ILF table for 2009 is 30 June 2009. Hence 3 years of inflation adjustment required.

 

[r_v.s]

Oh! thanks so much! I was under the impression it was the start and the premium determined was for the first year!