This exam problem had a typo that made the answer in the examiner's report confusing. The examiner's report says near the bottom that:
Regrettably, there was a typographical error in this part of the question; the calculation year was misstated as 2018 when it was intended to be 2019. Given this error, multiple interpretations of discounting and payment patterns were accepted.
What they really wanted was for you to calculate the MCT on Dec 31, 2019 (not 2018). Now, the cat occurred on Jan 1, 2019 and the insurer's retention was 55,000. If you apply the payment pattern, where 60% is paid in the first 12 months, and 40% in the second 12 months, we would have 60% paid on Dec 31, 2019. That leaves 40% to be paid in 2020, which is why they multiplied by 0.4.
I'm not too sure I understand your other question:
Could you explain a bit more on why for claims we have a division term in the discounting.
Which calculation line of the solution are you referring to here?
When we calculate claim liabilities, we seem to divide the incremental change in paid amount by 1- what is paid within the first 12 months. Here we did not have to do that, is there a reason why?
Ok, I see what you're asking now. This problem is slightly different because normally when you calculate the APV for claims liabilities, you're given the nominal amount at age 12 months. Then you distribute that amount to the intervals 12-24, 24-36, and so on (however far out the payment pattern goes.) To do that correctly however, you have to rebase the payment pattern as if it starts at 12 months, and that's why everything is divided by (1-x) where x is the percentage at 12 months.
But here, you're told the cat occurred on Jan 1, 2019, which is basically age 0 months. So you don't have to rebase the payment pattern. You just apply it as given, which means a flat 60% for age 0-12, and then the remaining 40% for age 12-24. At that point, the cat is fully paid.
Comments
This exam problem had a typo that made the answer in the examiner's report confusing. The examiner's report says near the bottom that:
What they really wanted was for you to calculate the MCT on Dec 31, 2019 (not 2018). Now, the cat occurred on Jan 1, 2019 and the insurer's retention was 55,000. If you apply the payment pattern, where 60% is paid in the first 12 months, and 40% in the second 12 months, we would have 60% paid on Dec 31, 2019. That leaves 40% to be paid in 2020, which is why they multiplied by 0.4.
I'm not too sure I understand your other question:
Which calculation line of the solution are you referring to here?
When we calculate claim liabilities, we seem to divide the incremental change in paid amount by 1- what is paid within the first 12 months. Here we did not have to do that, is there a reason why?
Ok, I see what you're asking now. This problem is slightly different because normally when you calculate the APV for claims liabilities, you're given the nominal amount at age 12 months. Then you distribute that amount to the intervals 12-24, 24-36, and so on (however far out the payment pattern goes.) To do that correctly however, you have to rebase the payment pattern as if it starts at 12 months, and that's why everything is divided by (1-x) where x is the percentage at 12 months.
But here, you're told the cat occurred on Jan 1, 2019, which is basically age 0 months. So you don't have to rebase the payment pattern. You just apply it as given, which means a flat 60% for age 0-12, and then the remaining 40% for age 12-24. At that point, the cat is fully paid.