Catastrophe IBNR and an Exhausted Reinstatement Cover
A commercial property carrier is reserving accident year 2025 at December 31, 2025. Non-catastrophe losses for AY2025 are $11.5M reported, of which $3.0M is case outstanding, and the selected 12-to-ultimate development factor for non-cat losses is 1.85. A single convective storm on May 14, 2025 is the only catastrophe in the year; gross reported losses on that event are $14.5M and no case reserves have been posted on about 400 late-reported claims. The company's historical reporting pattern for comparable storms shows 66% of ultimate gross loss reported at 7.5 months. The catastrophe treaty is $15.0M excess of $3.0M per occurrence, with one reinstatement at 100% additional premium, pro rata as to amount, and no ceding commission. Annual catastrophe premium is $4.0M and no other event has eroded the cover. The CFO wants the gross and net AY2025 ultimate, the ceded loss and the reinstatement premium, and has heard that the actuary should just apply 1.85 to the cat since it is an AY2025 loss.
1. Estimate the gross catastrophe ultimate and the non-catastrophe ultimate, and explain why the cat is not developed with the 1.85 factor.
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Catastrophe. Use the reporting pattern rather than a development factor: 14.5 / 0.66 = $21.97M, round to $22.0M gross. Cat IBNR is $7.5M, which is essentially the 400 late-reported claims.
Non-catastrophe. 11.5 x 1.85 = $21.28M; non-cat IBNR = 21.28 - 11.5 = $9.78M.
Gross AY2025 ultimate = 22.0 + 21.28 = $43.3M.
Why not develop the cat.
- A catastrophe is a single event, not a cohort of claims at a common maturity. Its reporting profile is driven by the event's footprint, the share of small claims, and the local litigation and assignment-of-benefits environment, not by the age of an accident year.
- The 1.85 factor is a volume-weighted average across all non-cat years and is dominated by attritional claims that report quickly and close slowly. Applying 1.85 to the cat would give 14.5 x 1.85 = $26.8M, which nothing in the reporting evidence supports.
- The cat already has an IBNR estimate embedded in the reporting pattern; developing it again would double count the unreported portion.
- Cat claims can develop upward later through litigation, but that is a separate provision, not a development factor on a 7.5-month-old event.
2. Compute the ceded loss, the net ultimate and the reinstatement premium.
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Ceded. Treaty is $15.0M excess of $3.0M per occurrence.
- Gross less retention: 22.0 - 3.0 = 19.0
- Ceded = min(19.0, 15.0) = $15.0M, so the limit is fully exhausted
- Net cat = 22.0 - 15.0 = $7.0M
Net ultimate. Gross 43.28 less ceded 15.0 = $28.28M net loss and LAE.
Reinstatement premium. 100% additional premium, pro rata as to amount used: (15.0 / 15.0) x $4.0M = $4.0M
Because the limit is fully eroded, the full reinstatement premium is incurred; if only part of the limit had been used, the premium would be proportional to the amount used. Conventional presentation is as additional ceded premium (an underwriting expense) rather than as loss, so the net loss and LAE is $28.28M while the combined ratio also bears $4.0M of reinstatement cost. If the CFO wants net IBNR specifically: gross IBNR 7.5 + 9.78 = 17.28, less ceded IBNR of 15.0 (assuming nothing on the cat has been ceded or paid yet) = $2.28M net IBNR.
Because the layer is exhausted, every additional dollar of gross cat development falls entirely to net. That is the single most important fact in this reserve review.
3. Assess the uncertainty in the cat estimate, quantify the effect of getting it wrong, and respond to the suggestion to apply 1.85 to the cat.
Read the worked answer
Sensitivity. The 66% reporting assumption drives the answer. If reporting is 60%, gross ultimate is 14.5 / 0.60 = $24.2M; if 72%, it is $20.1M. Because the ceded loss is capped at $15.0M once gross reaches $18.0M, the net result moves dollar for dollar with the gross estimate in that whole range:
- Gross $20.1M: ceded $15.0M, net $5.1M
- Gross $22.0M: ceded $15.0M, net $7.0M
- Gross $24.2M: ceded $15.0M, net $9.2M
So a $2M gross error is a $2M net error. A point estimate of $22.0M with a disclosed range of roughly $20M to $24M gross, $5M to $9M net is the right presentation, and the $4.0M reinstatement premium is fixed regardless of where inside the range the event settles.
Response to the 1.85 suggestion. Reject it. It would produce $26.8M gross, above the top of any supportable range, it double counts the reporting-lag IBNR already embedded in the estimate, and it applies an attritional-claim development pattern to a concentration of small property claims that report on a different clock. It would also push the net result to $11.8M, almost $5M above the point estimate, with no evidentiary basis.
Monitoring. Compare the late-reported claim count monthly against the 66% pattern. If counts are running ahead, raise the estimate. Also confirm the cover really is exhausted so that no second-event protection remains for the rest of the treaty period, and check whether the $4.0M reinstatement premium has been accrued, since it is easy to omit from a loss-only view.