Solvency evaluation of the guaranty fund at a large financial cooperative 301two policies for premiums were simulated: the current policy which is expressed as
1/14 of 1% of the risky assets of the insured credit union and a hypothetical relaxed
policy of 1/17 of 1% of the risky assets. The latter policy was simulated because it
was anticipated that given the excellent capital of the fund it could maintain a good
solvency level while easing its burden on its insured members.
In total four combinations of scenarios were simulated according to whether the
parameters had base-case or stressed values and to whether the policy for premiums
was modelled as base-case or relaxed. Table 4 below shows the results for each of
the four cases. The probabilities estimated over the 15-year horizon were converted
to a one-year horizon as it is this latter horizon that is used for reference by rating
agencies such as S&P and Moody’s.
It is striking that under the two base case scenarios, the level of insolvency is
much lower than one basis point, thus allowing an implied credit rating of AAA to
be granted to the fund. Under the two stressed cases, the level of solvency is close to
the threshold needed to get a triple A rating. Overall, the simulation model leads to
the belief that the solvency of the fund is indeed excellent.
Ta b le 4 .Solvency estimates of the guaranty fund by Monte Carlo simulationParameters Base case Stressed case
Policy for premiums 1/14 % 1/17 % 1/14 % 1/17 %
Nb of cases of insolvency 6 10 74 101
Nb of cases of solvency 49994 49990 49926 49899
Total number of cases 50000 50000 50000 50000
Solvency over 15 years 99.9880 % 99.9800 % 99.8520 % 99.7980 %
Solvency over 1 year 99.9992 % 99.9987 % 99.9901 % 99.9865 %
Insolvency over 15 years 0.0120 % 0.0200 % 0.1480 % 0.2020 %
Insolvency over 1 year 0.0008 % 0.0013 % 0.0099 % 0.0135 %
Implied rating AAA AAA AAA AAA6 Comparison of the two approaches
It is now interesting to compare the results obtained under the aggregated and dis-
aggregated approaches. Table 5 summarises these results. Overall, Table 5 provides
a sensitivity analysis of the solvency estimates while varying methods and hypothe-
ses about distributions, parameters and premium policies. Obviously, there is a wide
margin between the best and the worst estimates. However, apart from the log-normal
distribution, all other results are basically in the same range. One clear advantage of
the simulation model is that it allows the analysis of hypothetical cases, as was done
in the last three scenarios considered. So, to make a fair comparison between the
statistical distribution approach and the simulation approach one must use the first