1. Delay between claim event and claim settlement date.
2. The ultimate claim cost will only be known after some time.
3. Must set up reserves in respects of those claims to be settled.
ELEMENTS OF RESERVES
1. Known Claims consist of reopened claims reserves, development on known claims & case reserve.
2. Unknown Claims consists of claims in transit and incurred but not reported (IBNR)
3. IBNR consists late reported claims & development on known Claims (IBNER)
SHORT TAIL VS LONG TAIL
1. The size of IBNR is largely dependent on the tail(Short Tail Business and Long Tail Business) which depends on speed of claim.
CHAIN LADDER (PAID)
1. Ultimate Claims can be estimated via Paid to Date * Cumulative LDF or Paid to date / %Paid
2. Step 1 - Gather Cumulative Claims Paid by development year
AY
|
Development Year
|
|||
1
|
2
|
3
|
4
|
|
2009
|
6000
|
10500
|
13700
|
13820
|
2010
|
7000
|
12500
|
16500
|
|
2011
|
8500
|
15000
|
||
2012
|
10500
|
3. Step 2 - Compute LDF, Compute Cumulative LDF and % Paid
AY
|
Development Year
|
|||
1-2
|
2-3
|
3-4
|
Tail
|
|
2009
|
1.75
|
1.3
|
1.01
|
|
2010
|
1.79
|
1.32
|
||
2011
|
1.76
|
|||
2012
|
||||
Average
|
1.77
|
1.31
|
1.01
|
1
|
CUM LDF
|
2.34
|
1.32
|
1.01
|
1
|
% Paid
|
43%
|
76%
|
99%
|
100%
|
i. Assuming tail factor is 1.00
ii. LDF1-2 (2010) = 12500/7000 =1.79
iii. CUM LDF 1-2 = 1.75 *1.3*1.01 = 2.34
iv. Paid 1-2 = 1/2.34 = 43%
4. Compute Projected Ultimate. O/S Liability, IBNR
AY
|
Paid to Date
|
Inc To date
|
Cumulative LDF
|
Projected Ultimate
|
O/S Liability
|
Case Reserve
|
IBNR
|
2009
|
13,820
|
13,820
|
1
|
13,820
|
-
|
-
|
-
|
2010
|
16,500
|
16,600
|
1.01
|
16,665
|
165
|
100
|
65
|
2011
|
15,000
|
17,000
|
1.32
|
19,800
|
4,800
|
2,000
|
2,800
|
2012
|
10,500
|
13,500
|
2.34
|
24,570
|
14,070
|
3,000
|
11,070
|
TOTAL
|
55,820
|
60,920
|
-
|
74,855
|
19,035
|
5,100
|
13,935
|
Note:
i. Projected ultimate Paid to date * CLDF
ii. O/S Liability = Projected Ultimate - Paid to Date
iii. IBNR = O/S Liability - Case Reserve
CHAIN LADDER (INCURRED)
1. Same process applies to Claims incurred but this time only using incurred data.
AY
|
Development Year
|
|||
1
|
2
|
3
|
4
|
|
2009
|
8000
|
11500
|
16600
|
13820
|
2010
|
9500
|
13500
|
16500
|
|
2011
|
12000
|
17000
|
||
2012
|
13500
|
|||
AY
|
Development Year
|
|||
1-2
|
2-3
|
3-4
|
Tail
|
|
2009
|
1.44
|
1.20
|
1.01
|
|
2010
|
1.42
|
1.23
|
||
2011
|
1.42
|
|||
2012
|
||||
Average
|
1.43
|
1.21
|
1.01
|
1
|
CUM LDF
|
1.75
|
1.22
|
1.01
|
1
|
% Paid
|
57%
|
82%
|
99%
|
100%
|
AY
|
Paid to Date
|
Inc To date
|
Cumulative LDF
|
Projected Ultimate
|
O/S Liability
|
Case Reserve
|
IBNR
|
2009
|
13,820
|
13,820
|
1
|
13,820
|
-
|
-
|
-
|
2010
|
16,500
|
16,600
|
1.01
|
16,766
|
266
|
100
|
166
|
2011
|
15,000
|
17,000
|
1.22
|
20,740
|
5,740
|
2,000
|
3,740
|
2012
|
10,500
|
13,500
|
1.75
|
23,625
|
13,125
|
3,000
|
10,125
|
TOTAL
|
55,820
|
60,920
|
-
|
74,951
|
19,131
|
5,100
|
14,031
|
COMPARISON PL PAID VS INCURRED
1. The IBNR reserve for a portfolio is usually calculated on the basis of both the run-off triangle of paid losses and the run-off triangle of incurred losses.
2. Problem arises when the projection based on paid losses is far different than the projection based on incurred losses.
3. Paid losses may yield a higher ultimate loss projection than incurred losses in one accident year, but in the next accident year, the situation may be entirely reversed, with incurred losses yielding the higher projection of ultimate loss.
4. Suggests further reading on Munich Chain Ladder Method
4. Suggests further reading on Munich Chain Ladder Method
