Reinsurance Structures and Pricing

Reinsurance transfers risk from a ceding insurer to a reinsurer in exchange for premium. The structure chosen determines both how risk is shared and how it must be priced; this article surveys the standard structures and the two workhorse pricing techniques — experience rating and exposure rating.

Proportional structures

Under quota share (QS), the reinsurer takes a fixed percentage $c$ of every risk's premium and losses: if the cession rate is 40%, the reinsurer receives 40% of premium and pays 40% of losses, typically returning a ceding commission to the cedent to cover acquisition and overhead expense and a margin. Net premium retained by the reinsurer is $P(1-\text{commission rate})$. QS is simple, provides pro-rata capacity relief, but transfers little tail risk relative to premium ceded.

Surplus share treaties cede a variable percentage per risk based on how far each risk's sum insured exceeds the cedent's retained "line," giving the cedent more control over the portfolio's net retention on large risks while ceding proportionally more of large risks than small ones.

Non-proportional structures

Excess of loss (XoL) reinsurance pays losses in a defined layer above an attachment point. Layers are written "limit xs attachment," e.g., a 4,000,000 xs 1,000,000 layer pays losses between 1,000,000 and 5,000,000.

• Per-risk XoL applies the layer separately to each individual risk's loss.
• Per-occurrence XoL (also "per-event" or "catastrophe" for cat perils) applies the layer to the sum of all losses from a single occurrence, aggregating across risks — essential when a single event (e.g., a hurricane) can generate correlated losses across many policies.
• Clash covers respond when a single occurrence produces losses to two or more policies/lines that in aggregate pierce a high retention, protecting against unmodeled accumulation.
• Aggregate stop-loss covers use annual aggregate losses (across the whole book, or a defined layer's aggregate) as the trigger, e.g., paying losses once the annual loss ratio exceeds 80% up to 120%.

Ceding commissions and reinstatements

Proportional treaties use a ceding commission as the primary pricing lever, often on a sliding scale tied to the treaty's loss ratio, so that the cedent shares favorably in good years and the reinsurer is protected in bad ones. XoL treaties instead price via a rate and typically require reinstatement premiums: after a layer limit is exhausted by a loss, coverage is "reinstated" for a fee proportional to the fraction of the limit used, $RP = P \times (\text{loss}/\text{limit}) \times c$, where $c$ is the reinstatement premium factor (often 100%, i.e., pro-rata, but can be loaded).

Experience rating vs. exposure rating

Experience rating prices a treaty (or layer) from the cedent's own historical loss experience: losses are trended and developed to the layer's prospective period, capped at the layer limit, and divided by trended subject premium — the burning cost. This is the empirical loss cost of the layer.

Exposure rating instead uses a curve of expected loss by size (an increased limits factor curve, or for property, exposure/PML curves) applied to the cedent's exposure profile, without relying on the cedent's own loss history — essential when losses in the layer are rare or the cedent's history is thin/volatile. For general liability, exposure rating commonly uses ISO/NCCI increased limit factor (ILF) tables; for workers' compensation excess layers, NCCI's Excess Loss and Loss Adjustment Expense Factors (ELPPF), more commonly written ELF, give the expected loss ratio in an excess layer per unit of expected losses, reflecting the heavy-tailed severity distribution of WC claims (particularly permanent total and fatal claims).

$\text{ELF}(L) = \frac{E[\max(X-L,0)]}{E[X]}$

so that expected excess losses = expected ground-up losses × ELF(L), a direct application of a limited expected value function to the severity curve.

Worked layer-pricing example: burning cost and rate on line

A cedent seeks pricing for a property per-occurrence XoL layer of 4,000,000 xs 1,000,000. Five years of occurrence losses, trended and developed to the prospective period, and capped at the layer, are:

Total losses to layer = 0 + 1,800,000 + 0 + 3,500,000 + 900,000 = 6,200,000.

Total subject premium = 20,000,000 + 21,000,000 + 22,000,000 + 23,000,000 + 24,000,000 = 110,000,000.

Burning cost rate = 6,200,000 / 110,000,000 = 5.636% of subject premium.

Applying a loading for parameter/model risk and expenses of 1.30× gives a technical rate of 5.636% × 1.30 = 7.33% of a prospective subject premium of, say, 25,000,000, giving layer premium of 25,000,000 × 7.33% = 1,832,500.

Rate on line expresses the premium as a fraction of the limit purchased:

$ROL = \frac{\text{Layer premium}}{\text{Layer limit}} = \frac{1,832,500}{4,000,000} = 45.8\%.$

ROL is a convenient market-quoted metric for comparing layers of different sizes and is inversely related to attachment probability for well-behaved severity curves — higher layers (further from the loss distribution's mass) trade at lower ROL.

Pitfalls

• Using burning cost alone for high, thinly-populated layers — five years of zeros tells you little about a 1-in-100 layer; exposure rating or a blended credibility-weighted approach is more defensible.
• Forgetting to trend AND develop losses to the layer before capping — capping before development understates losses that would have pierced the layer once fully developed.
• Ignoring reinstatement premium income when comparing ROL across treaties — a treaty with cheap reinstatements is effectively cheaper than its stated rate suggests.
• Applying ILF/ELF curves calibrated to one jurisdiction or era without on-leveling for benefit-level or judicial trend changes (particularly relevant for WC ELFs after benefit reform).

Exam relevance

Reinsurance pricing structures, burning cost, exposure rating, and ELPPF are core CAS Exam 8 topics.

Further reading

• Clark, Basics of Reinsurance Pricing, CAS Study Note
• Bear & Nemlick, Pricing Excess of Loss Reinsurance
• NCCI, Retrospective Rating and Excess Loss Factor documentation