Reinsurance in depth

In RiskAtoms Insurance SE's worst property year in 200, the account loses €1,774m before reinsurance. After it, the loss is €565m. The programme costs about €139m a year of expected profit. Is that a good deal? Answering it means knowing what each treaty does, how it is priced, and what it does to capital.

L2.6.07: Insurance and reinsurance introduced quota share and excess of loss on single losses; L3.8.05: Catastrophe risk built the cat event set. An insurer combines several treatiesA reinsurance contract that covers a whole class of business automatically for a year, as opposed to facultative cover bought risk by risk., each aimed at a different problem. RiskAtoms ceded €900m of its €9,000m non-life premium in 2025:

Proportional: the surplus treaty

A quota share cedes the same share of every policy. A surplus treatyA proportional treaty in which the insurer keeps a fixed amount of each risk (the line) and cedes the share of the sum insured above it, up to a number of lines. cedes more of the big risks and none of the small ones. RiskAtoms keeps a lineIn a surplus treaty, the amount of sum insured the insurer keeps on any one risk. Capacity is counted in lines: nine lines on a €10m line means up to €90m ceded. of €10m on each commercial risk and cedes the rest, up to 9 lines (€90m). The reinsurer takes that share of the premium and of every loss on the risk, and pays a 40% cedingThe insurer that buys reinsurance and passes (cedes) risk to a reinsurer. commission. What is above €100m needs facultativeFacultative reinsurance: cover negotiated for one risk at a time, used for what is too large or unusual for the treaties. cover: 1 of the 40 largest risks.

The insurer keeps the same €10m of every large risk, so its exposure per risk is level however big the building. A €40m fire at the €92m factory: the surplus pays 89.1%, €35.7m. The €4.35m kept then meets the per-risk XLExcess of loss on any one risk: it pays the part of a single risk's loss above the retention, up to a limit. of €8m xs €2m, which pays €2.35m. Net cost: €2m. A total loss of the €160m shopping centre splits €90m surplus, €60m facultative, €8m per-risk XL and €2m kept. Together the two treaties cap any single fire at €2m.

Non-proportional: the cat XL and its reinstatements

A cat XLExcess of loss on the total of all claims from one event, such as a windstorm, above a retention, up to a limit. pays on the total of one event. RiskAtoms buys 1,500 xs 500 in two layers: 500 xs 500 at a 5% rate on lineRate on line: the layer's premium divided by its limit. A 5% rate on line on a €500m layer is €25m. (€25m) and 1,000 xs 1,000 at 2.5% (€25m). Each has one reinstatementA refill of an excess of loss layer's limit after a loss uses it up, so it can pay again later in the year. It is usually paid for with a reinstatement premium. at 100%: once a storm uses the limit, it is refilled for the rest of the year in return for the layer's premium, pro rata to the amount used. In the book's event set:

Between 1-in-50 and 1-in-100 the net cost barely moves: the programme holds the loss at €500m plus a reinstatement premium. Above €2,000m it runs out, and the 1-in-250 storm costs €1,210m, 1.7 times the 1-in-200's €703m. A second storm in the same year meets a layer that has already used part of its annual limit. Take storms of €1,600m, €1,200m and €900m: the layers recover €1,100m and €700m on the first two, layer 1's annual limit is then gone, and the third storm is kept in full. The year costs €1,945m including €45m of reinstatement premium. Try your own season:

Pricing a layer

The fair price of a layer starts from its expected annual loss: each event's rate times the part of it inside the layer, summed over the event set (M-C02: Expectation). Divide by the limit for the loss on lineLoss on line: the layer's expected annual loss divided by its limit. Premium ÷ expected loss is the multiple.. The premium is a multiple of it, to pay for capital, uncertainty in the model and the reinsurer's costs.

The higher the layer, the rarer the loss and the higher the multiple: 2.5× for layer 1, 3.0× for layer 2 and 3.4× for the optional third. A reinsurer must hold capital against a layer that is rarely hit but loses its whole limit when it is, and the cat model is least certain far out in the tail.

Stop loss

A stop lossCover on a whole account's result: it pays when the loss ratio for the year goes above an attachment point, up to a limit. protects the year's result rather than a risk or an event. The book's option pays the property net loss ratio above 80%, up to 20 points, priced at 1.5 times its expected recovery: €3.8m a year. It catches what the other treaties leave, such as a bad attritional year on top of a storm that exhausted the cat XL, and takes the 1-in-200 net year from −€565m to −€448m. Because a stop loss also pays for the insurer's own underpricing, it is hard to find, expensive and seldom unlimited.

Gross and net, 50,000 years

The book simulates the property account for 50,000 years: attritional and large losses, plus the cat events of L3.8.05: Catastrophe risk, through the whole programme. Property earned €3,359m gross in 2025 and €2,647m net.

Reinsurance costs €138.9m of expected result a year (gross mean less net mean) and improves the worst year in 200 by €1,210m: about €8.7 of tail for each euro of margin. The expected cost is real money every year; the protection is used rarely. That trade is the point.

Capital relief, and its price

Solvency II measures non-life risk net of reinsurance, so reinsurance lowers the SCR. The book prices three ways to release capital:

The quota share gives away 20% of the non-life profit, and its commission is below the expense ratio: €112m a year for €282m of relief. The cat layer costs its premium less its expected recovery. The longevity swap (L3.8.07: Longevity risk) is by far the cheapest relief per euro because longevity is the largest life risk and the fee is small. Set any of them against the cost of the capital it frees: the risk margin assumes 6% a year. Only the swap clears that on capital alone; the others are bought for what they do to bad years, earnings and growth.

Relief also shrinks on its way up. The third layer cuts the cat sub-module by €151m, the non-life module by €69m, the BSCR by €44m and the SCR by €36m: each aggregation step with imperfect correlation dilutes a cut in one part (L3.8.12: Insurer investment risk and the ORSA).

What reinsurance adds: counterparty risk

Reinsurance swaps insurance risk for credit risk. RiskAtoms already counts recoverablesAmounts the reinsurers are expected to pay the insurer on claims already incurred: an asset on the insurer's balance sheet, and a credit exposure. of €544m on its modelled non-life reserves, and after the 1-in-200 storm its cat reinsurers would owe €1,500m, just when they are paying everyone else's storm claims too. Insurers manage this with panels of several highly rated reinsurers, limits per reinsurer, collateral from unrated ones, and watching the reinsurers' ratings. The standard formula charges it in the counterparty default module (stated here as €150m); the book's quota share option ignores the extra counterparty risk it would add, which flatters it.

The reinsurance cycle

Reinsurance has its own cycle, like the primary market's (L3.8.04: Premium risk and the underwriting cycle). After a large loss, capital is scarce and prices rise; high prices then draw in new capital and prices soften. Hurricane Andrew in 1992 is the textbook case: the market hardened sharply and new reinsurers were founded in Bermuda to supply catastrophe capacity (Spark Atoms below). For a buyer, that means the cost of the same protection changes from year to year, and the programme should be judged over the cycle, not at one renewal.

The spread of what is kept. With gross annual cat loss $G$ and recoveries $R$, the variance of the net loss $G − R$ follows from the rules for combining random variables (M-C11: Combining random variables). On the book's 50,000 cat years, in €m², with sample variances (divisor n − 1):

The covariance term does the work: recoveries come in the years with large gross losses (correlation 0.87), so subtracting them removes far more variance than their own variance adds. A cover that paid at random would add variance. In 96.9% of years the cat XL pays nothing at all.

The 1-in-200 year. Sort the 50,000 simulated years and take the value at position $\lceil 0.995\,n \rceil$, the 251st largest loss (M-C09: Quantiles): gross annual cat loss €2,507m, net €1,093m before reinstatement premium. The annual figure is above the 1-in-200 single storm (€2,153m gross, €653m net) because bad years often have several events, and the second and third meet layers that are partly used.

Expected layer loss. With event rates $\lambda_j$ and event losses $x_j$, the expected annual loss to a layer $L$ xs $D$, counting every event in full, and its multiple are

Today's programme is the starting point. Add a quota share, a third cat layer or a stop loss and watch the mean, the spread and the 1-in-200 year. Which choice buys the most tail per euro? Which barely moves it?

All figures from the book, € millions.

Solvency II recognises reinsurance in the SCR: premium and reserve risk are measured on net premiums and net reserves (Delegated Regulation (EU) 2015/35, Art 116), the premium risk standard deviation of the motor vehicle liability, fire and other damage to property, and general liability segments is multiplied by an 80% adjustment factor for non-proportional reinsurance (Art 117(3)), and the cat charge is net of the programme. In return, recoverables enter the counterparty default module. The UK's Prudential Regulation Authority published SS5/24 on funded reinsuranceFunded reinsurance: a life insurer passes both the longevity risk and the investment risk of annuities to a reinsurer, often overseas, backed by collateral. If the reinsurer fails, the insurer takes the business back (recapture). on 26 July 2024, expecting annuity writers to set limits on it, measure what an immediate recapture would cost, keep collateral policies and stress the exposures in their ORSA where material. How reinsurance, risk mitigation and the counterparty module work in detail is in M4.6: Solvency II and insurance regulation; IFRS 17's treatment of reinsurance held is in M4.8: Insurance accounting: IFRS 17 (overview).

• A programme layers treaties: the surplus levels large risks to a €10m line, the per-risk XL caps any fire at €2m, the cat XL caps an event at €500m up to €2,000m, and a stop loss protects the year.
• An XL layer pays min(max(X − D, 0), L) per event and at most (1 + m)L a year; each reinstatement is paid pro rata to the limit used.
• Layer prices are multiples of expected loss, and the multiple rises with height: 2.5×, 3.0×, 3.4× here.
• On 50,000 years, reinsurance improves the 1-in-200 property year from −€1,774m to −€565m for €139m a year of expected margin.
• As capital relief, the quota share costs €0.40 a year per euro of SCR, the cat layer €0.30 and the longevity swap €0.05; diversification dilutes relief on the way up.
• Reinsurance creates counterparty risk exactly when it pays, and its price follows a cycle driven by losses and capital.

Treaty

A reinsurance contract that covers a whole class of business automatically for a year, as opposed to facultative cover bought risk by risk.

Surplus treaty

A proportional treaty in which the insurer keeps a fixed amount of each risk (the line) and cedes the share of the sum insured above it, up to a number of lines.

Line (retention line)

In a surplus treaty, the amount of sum insured the insurer keeps on any one risk. Capacity is counted in lines: nine lines on a €10m line means up to €90m ceded.

Facultative reinsurance

Facultative reinsurance: cover negotiated for one risk at a time, used for what is too large or unusual for the treaties.

Per-risk excess of loss

Excess of loss on any one risk: it pays the part of a single risk's loss above the retention, up to a limit.

Catastrophe excess of loss (cat XL)

Excess of loss on the total of all claims from one event, such as a windstorm, above a retention, up to a limit.

Reinstatement

A refill of an excess of loss layer's limit after a loss uses it up, so it can pay again later in the year. It is usually paid for with a reinstatement premium.

Rate on line

Rate on line: the layer's premium divided by its limit. A 5% rate on line on a €500m layer is €25m.

Loss on line and multiple

Loss on line: the layer's expected annual loss divided by its limit. Premium ÷ expected loss is the multiple.

Stop loss

Cover on a whole account's result: it pays when the loss ratio for the year goes above an attachment point, up to a limit.

Reinsurance recoverables

Amounts the reinsurers are expected to pay the insurer on claims already incurred: an asset on the insurer's balance sheet, and a credit exposure.

Capital relief

The fall in required capital (here the SCR) that a reinsurance or hedge brings.

Funded reinsurance

Funded reinsurance: a life insurer passes both the longevity risk and the investment risk of annuities to a reinsurer, often overseas, backed by collateral. If the reinsurer fails, the insurer takes the business back (recapture).