Page 162 - Contributed Paper Session (CPS) - Volume 7

CPS2051 Mentje G. et al.
(2006)) and the single loss approximation (SLA) method (see e.g. Böcker and
Klüppelberg (2005)). For a detailed comparison of numerical approximation
methods, the interested reader is referred to de Jongh et al. (2016).
2.2 Scenario modelling
The Basel Accord (see BCBS 196, (2011)) suggests the use of scenario
assessments to improve severity distribution estimation. BCBS refers to three
types of scenarios namely the individual scenario approach, the interval
approach and the percentile approach. In the remainder of the paper we
discuss a percentile approach suggested by de Jongh et al. (2015), which we
believe is the most practical of the existing approaches available in the
literature.
As discussed in de Jongh et al. (2015), we advocate the use of the so-called
one-in- year scenario approach. In the one-in- years scenario approach, the
experts are asked to answer the question: ‘What loss level is expected to be

exceeded once every years?’. Popular choices for vary between 5 and 100
and often 3 values for are used. As an example, one bank used = 7, 20 and
100 and motivated the first choice as the number of years of historical data
available to them. In this case the largest loss in the historical data may serve
as a guide for choosing since this loss level has been reached once in 7
7
years. If the experts judge that the future will be better than the past, they may
want to provide a lower assessment for than the largest loss experienced
7
so far. If they foresee deterioration they may judge that a higher assessment
is more appropriate. The other choices of are selected in order to obtain a
scenario spread within the range that one can expect reasonable improvement
in accuracy from the experts’ inputs. Of course the choice of = 100 may be
questionable because judgments on a one-inhundred years loss level are likely
to fall outside many of the experts’ experience. In the banking environment,
they may take additional guidance from external data of similar banks which
in effect amplifies the number of years for which historical data are available.
If the annual loss frequency is () distributed and the true underlying
severity distribution is , and if the experts are of oracle quality in the sense of
actually knowing and , then the assessments provided should be
1
= −1 (1 − ). (1)

To see this, let denote the number of loss events experienced in years

and let denote the number of these that are actually greater than . Then

~() and the conditional distribution of given is binomial with

parameters and 1 − = P(X ≥ ) = 1 − ( ) with ~ and =

( ). Therefore = [( | )] = [ (1 − )] = (1 − ( )) .

1
Requiring that =1, yields (1) and = 1 − .

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