CT6-2005-September Q9

Hi Jia

I've now had a good look through this question.

The BF method enables us to estimate the claims that have yet to emerge / be paid (called the emerging liability or o/s claims amount).

To calculate the emerging liability for 2004 using the BF method, we start with an initial estimate of the ultimate claims (the total claim amount that we think we will end up paying in 2004) ...

... this initial estimate is based on the loss ratio ...

... then we use the development ratios from to work backwards to decide what we think should have been paid in each of the previous development years.

The initial estimate of the ultimate claim amount is the premium * loss ratio = 5,250 * 0.75 = 3937.50.

Therefore, if we believe that the loss ratio is accurate, we expect to pay 3937.50 in total in respect of accident year 2004.

The development ratios were calculated on the previous page of the Examiners' Report, these are:

DY0-1 1.73783
DY1-2 1.28434
DY2-3 1.13207

(I'm assuming you're ok with the calculation of these?)

With the basic chain ladder method we use these to project forwards. However, with BF, we use them to project backwards - ie if we believe 3937.5 is the correct ultimate claim figure, then what do we think the claims figures would have been in the previous development years? Instead of multiplying up by the development ratios, we divide by them to get estimates of the cumulative claims paid in each of the development years:

_______DY0______DY1______DY2______DY3 (Ultimate)
2004__1558.32___2708.10__3478.13___3937.5

For example, to get the DY2 figure I have done 3937.5 / 1.13207 = 3478.13.
And to get the DY2 figure, I have done 3937.5 / (1.13207 * 1.28434).

These figures are still cumulative. We need to make them incremental in order to apply future inflation (inflation is only ever applied to the incremental figures). Taking the four figures above and disaccumulating them gives:

_______DY0______DY1______DY2______DY3 (Ultimate)
2004__1558.32__1149.78____770.03___459.37

For example, to get the DY2 figure, I have done 3478.13 - 2708.10 = 770.03.

Note that the three figures in DY1, DY2 and DY3 give us an estimate of the claims yet to emerge, ie the outstanding claims.

Then the examiners' report goes on to apply the future inflation to these three figures to give us the face value of the amounts to be paid in the future years. These are then summed to give the total outstanding claims.

Is this ok now?
Anna