Difference between revisions of "ERD Example"
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| − | + | Formula: | |
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| + | :{| class="wikitable" | ||
| + | |- | ||
| + | | ERD <span style="color: red;">'''='''</span> prob(of NPV reinsurer loss) <span style="color: red;">'''x'''</span> NPV(reinsurer loss) <span style="color: red;">'''/'''</span> (reinsurance premium) | ||
| + | |} | ||
| + | |||
| + | Some simple examples for the ERD (Expected Reinsurer Deficit) test for risk transfer: | ||
:{| class="wikitable" | :{| class="wikitable" | ||
|- | |- | ||
| − | ! 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 |
|} | |} | ||
| − | <span style="color: red;">'''<sup>1</sup>'''</span> | + | <span style="color: red;">'''<sup>1</sup>'''</span> The NPV is ''net of reinsurance premium''. For example, if the ceded loss amount were $100 and the reinsurance premium were $20, the ''NPV(reinsurer loss) 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 <u>frequency distribution</u>. The examples in the above table were simplified | + | '''Note''': In general you would calculate the ERD from a <u>frequency distribution</u>. The examples in the above table were simplified where there is probability ''p'' of a specified loss and probability ''(1-p)'' of no loss. |
Latest revision as of 17:16, 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 The NPV is net of reinsurance premium. For example, if the ceded loss amount were $100 and the reinsurance premium were $20, the NPV(reinsurer loss) 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 where there is probability p of a specified loss and probability (1-p) of no loss.
