Difference between revisions of "ERD Example"
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| − | ! prob(of NPV reinsurer loss) !! | + | ! prob(of NPV reinsurer loss) !! NPV <br> of reinsured loss !! reinsurance <br> premium !! NPV(reinsurer loss) <span style="color: red;">'''<sup>1</sup>'''</span> !! ERD !! risk transfer |
|- style="text-align: center;" | |- style="text-align: center;" | ||
| − | | 10% || 3m || 1m || 2m || style="text-align: left;" | ERD = 10% x 2m/1m = 20% <span style="color: green;">'''> 1%'''</span> || yes | + | | 10% || 3m || 1m || 2m = 3m - 1m|| style="text-align: left;" | ERD = 10% x 2m/1m = 20% <span style="color: green;">'''> 1%'''</span> || yes |
|- style="text-align: center;" | |- style="text-align: center;" | ||
| − | | 10% || 2m || 1m || 1m || style="text-align: left;" | ERD = 10% x 1m/1m = 10% <span style="color: green;">'''> 1%'''</span> || yes | + | | 10% || 2m || 1m || 1m = 2m - 1m || style="text-align: left;" | ERD = 10% x 1m/1m = 10% <span style="color: green;">'''> 1%'''</span> || yes |
|- style="text-align: center;" | |- style="text-align: center;" | ||
| − | | 10% || 1m || 1m || 0m || style="text-align: left;" | ERD = 10% x 0m/1m = 0% <span style="color: red;">'''< 1%'''</span> || no | + | | 10% || 1m || 1m || 0m = 1m - 1m || style="text-align: left;" | ERD = 10% x 0m/1m = 0% <span style="color: red;">'''< 1%'''</span> || no |
|- style="text-align: center;" | |- style="text-align: center;" | ||
| − | | 25% || | + | | 25% || 150 || 100 || 50 = 150 - 100 || style="text-align: left;" | ERD = 25% x 50/100 = 12.5% <span style="color: green;">'''> 1%'''</span> || yes |
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Revision as of 17:14, 15 December 2018
Formula:
ERD = prob(of NPV reinsurer loss) x NPV(reinsurer loss) / (reinsurance premium)
Some simple examples for the ERD (Expected Reinsurer Deficit) test for risk transfer:
prob(of NPV reinsurer loss) NPV
of reinsured lossreinsurance
premiumNPV(reinsurer loss) 1 ERD risk transfer 10% 3m 1m 2m = 3m - 1m ERD = 10% x 2m/1m = 20% > 1% yes 10% 2m 1m 1m = 2m - 1m ERD = 10% x 1m/1m = 10% > 1% yes 10% 1m 1m 0m = 1m - 1m ERD = 10% x 0m/1m = 0% < 1% no 25% 150 100 50 = 150 - 100 ERD = 25% x 50/100 = 12.5% > 1% yes
1 This severity amount is net of reinsurance premium. For example, if the ceded loss amount were $100 and the reinsurance premium were $20, the severity net of premium would be $80, and it's this $80 value that would be used in the ERD forumla.
Note: In general you would calculate the ERD from a frequency distribution. The examples in the above table were simplified: There is probability p of a specified loss and probability (1-p) of no loss.
