Reinsurance Tower Methodology

1. Executive Summary

A reinsurance tower is the stack of layers a (re)insurer places to cap its net retained exposure. The Reinsurance Tower Designer lets the underwriter assemble the entire stack — quota share, working layer XoL, cat XoL, and aggregate stop-loss — and run a single Monte Carlo simulation that produces gross, ceded, and net loss distributions, per-layer expected cession, premium economics, and 1-in-N return-period exceedance curves.

Unlike traditional spreadsheets that handle one layer at a time, the engine applies layers in their inuring order — a 30% quota share placed first will reduce the gross loss seen by every subsequent layer, completely changing the economics of a downstream cat XoL.

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2. Tower Architecture

A tower is an ordered list of layers. Each layer has:

• Type — QS, WORKING_XOL, CAT_XOL, or AGG_STOP
• Inuring order — integer; lower numbers apply first
• Type-specific parameters — cession %, attachment, limit, reinstatements, RoL, etc.
• Premium economics — rate-on-line for excess layers, ceding commission for QS

3. Layer Types

3.1 Quota Share (QS)

A quota share cedes a fixed percentage of every loss, regardless of size. The reinsurer receives the same percentage of premium minus a ceding commission that compensates the cedent for acquisition + admin costs.

3.2 Working Layer Excess of Loss (WORKING_XOL)

A per-risk excess of loss layer pays the portion of any single risk's loss between an attachment point and an attachment + limit ceiling. Reinstatements determine how many full limits are available per year.

3.3 Catastrophe XoL (CAT_XOL)

A per-event excess of loss layer that responds to aggregated event losses (one ransomware wave, one supply chain incident) rather than individual risks. Same math as working XoL but applied to event losses with reinstatement provisions.

3.4 Aggregate Stop-Loss (AGG_STOP)

Caps the cedent's annual aggregate net retained loss. Once total losses in the year exceed the aggregate attachment, the reinsurer pays everything up to the aggregate limit.

4. Inuring Waterfall

Each layer is applied to the net retained loss after all preceding layers have been applied. The order matters enormously:

• If the QS is applied first, the cat XoL sees a 70% reduced loss universe → its expected cession drops, its rate-on-line should be lower.
• If the cat XoL is applied first, it absorbs the largest events at full size; the QS then cedes 30% of what's left.

The engine applies layers in ascending inuring_order per simulated year. The frontend lets you reorder layers with up/down arrows to test alternative tower constructions instantly.

5. Monte Carlo Engine

The engine simulates 1,500 to 10,000 years of gross losses using a Poisson-lognormal model calibrated per insured. Each insured contributes:

For each simulated year, each insured's losses are drawn, capped by the per-policy coverage limit, summed to a year total, and the year is added to a vector. The engine returns the per-year total loss vector and a per-insured per-year matrix.

6. Premium Economics

For each layer the engine reports:

• Premium — derived from rate-on-line × limit (XoL) or cession × gross premium (QS)
• Expected cession — mean per-year ceded loss across the simulation
• Loss ratio — expected cession ÷ premium. Above 1.0 = the reinsurer is losing money in expectation.
• Margin — premium − expected cession. The reinsurer's expected profit before expenses.

7. Cession Optimizer

The cession optimizer sweeps the QS percentage from 0% to 70% in 10% steps, holding all other layers fixed, and reports the net AAL, net VaR99, ceded premium, and a "$ saved per $ ceded" efficiency ratio at each point. This identifies the capital-efficient cession point.

8. Data Sources

9. Glossary