excess inflation vs ground up inflation
Hello,
If there is a deductible and no limit, then the excess trend will be greater or equal to ground up trend. However, if there is a limit, it is not certain. If tau_s = 8% and ground up inflation = 10%, and the exam asked why is tau_s lower than ground up inflation, how would I answer this?
Thank you!
Comments
In the case where there's a deductible and no limit then inflation will inflate claims already above the deductible by more than the ground up inflation rate.
Example: $100 claim, $20 deductible, 10% ground up inflation -> after inflation $110 claim, insurer pays $110 - $20 = $90 instead of $100 - $20 = $80. tau_s is then $90 / $80 -1 = 12.5%.
We'll also get claims that were in the deductible layer now requiring some payout by the insurer. All this means the layer above the deductible experiences greater inflation than the ground-up inflation.
When there is also a policy limit the outcome depends heavily on the distribution of claims relative to both the policy limit and deductible. Claims which are already at the policy limit aren't impacted by inflation at all because the payout is the same. Claims which were at the deductible and now trend fully into the layer receive the full excess inflation impact. The overall impact of inflation is then a weighted average of a bunch of impacts for various claim sizes, some of these impacts will be greater than the ground up inflation while others will be lower than the ground up inflation. The net result depends on where the distribution of claims lies.
To answer your question, I would say the distribution of claims likely lies closer to the policy limit which reduces the impact of inflation as the insurer is not responsible for losses in excess of the policy limit.