CEIOPS' Advice for Level 2 Implementing ... - EIOPA - Europa

Annex A. Example to illustrate the first method of simplification to
calculate the best estimate of incurred but not reported claims
provision.
General formulation.
The final estimate of this technical provision is derived from the following
expression, where just for illustrative purposes a three-year period of
observation has been considered (the adaptation of the formula for longer series
is immediate):
where
and
IBNR reserve year t = C t x N t ,
C t = average cost of IBNR claims, after taking into account inflation
and discounting. This cost should be based on the average cost of
claims reported in the year t. Since a part of the overall cost of
claims reported in the year t comes from provisions, a correction for
the possible bias should be applied.
Nt = Rt * Av, being
AV = [ (Nt-1 / p1) + (Nt-2 / p2) + Nt-3 ] / [ R t-1+R t-2+R t-3 ]
Furthermore, in these expressions
N t-i = number of claims incurred but not reported at the end of the year
t-i, independently of the accident year (to assess the number of IBNR
claims all the information known by the undertaking till the end of the
year t should be included).
P1= percentage of IBNR claims at the end of year t-3 that have been
reported during the year t-2
p2= percentage of IBNR claims at the end of year t-3 that have been
reported during the years t-2 and t-1
R t-i= claims reported in year t, independently of accident year.
It should be noted that the sufficiency of this method should be regularly
checked using run-off results.
Numeric example
Assuming as date of reference of the valuation December the 31 st of 2008, the
undertaking has the following information:
N_2007 = 90
N_2006 = 100
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