can anybody come to my resque here. am having difficulties following the interpolation here. why are we taking 75% of openibg point and taking 25% of end period?
For the policy year starting 1st Oct 2007, the mid-point of the policy year is 1st April 2008. This is 1 quarter of the way between GT figures as at 1/1/08 and 1/1/09. Therefore we apply a 0.75 weight to the 1/1/08 figure (1909) and a 0.25 weight to the 1/1/09 figure (1970).
Is it appropriate to consider the GT as being equivalent to an earned premium measure of exposure, e.g. consider value 1,909 to be exposure at end of 2007 and 1,970 to be that at end of 2008, so that exposure (GT) for policy commencing 01/10/2007 is 0.25*1,909+0.75*1,970? This seems reasonable given for part of the policy term at end 2007 exposure was around 1,909 level.
This one is the correct one: "For the policy year starting 1st Oct 2007, the mid-point of the policy year is 1st April 2008. This is 1 quarter of the way between GT figures as at 1/1/08 and 1/1/09. Therefore we apply a 0.75 weight to the 1/1/08 figure (1909) and a 0.25 weight to the 1/1/09 figure (1970)." This is using linear interpolation to find the GT at the midpoint of each policy year.
Hi, I don't understand the logic, can you please help? if it is "1 quarter of the way between GT figures as at 1/1/08 and 1/1/09", i.e. from 1/1/08 until 1st April 2008, that's a 3 months gap, it makes more sense to attach a quarter to the 2008 figure, no? why would you attach 0.75 to the 2008 figure please? Thanks.
This is straightforward linear interpolation. To interpolate between (x(0),y(0)) and (x(1),y(0)) to find x(n) the general formula is: y(n)=y(0)+[(x(n)-x(0))/(x(1)-x(0))]*(y(1)-y(0)) In this case x(0)=0 and x(1) = 1 and n=0.25, so y(0.25)=y(0)+0.25*(y(1)-y(0)))=0.75*y(0)+0.25*y(1)
