Standard formula add-on calculations

Some data of the standard formula are themselves the result of a calculation: reinsurance recoverables of a catastrophe scenario, volumes net of reinsurance, exposure rows on reinsurers. An add-on calculation, called P, calculates them from more detailed inputs, closer to your contracts. The standard formula is not changed: the P only fills some of its data.

To open a P:

• the “detailed entry Pn” badge appears at the top of the columns it can fill, in the Data block of the working page;
• it opens a panel: your inputs, the standard formula values the P reads (read-only) and a preview of the data it would provide, recalculated at each input;
• “Confirm” links these data to the P: the badge becomes “detailed entry Pn ✓”, the cells are locked and marked Pn, and the P is recalculated before the standard formula at each “Run the calculation”;
• “Enter by hand” breaks the link: the data take the last calculated value and become ordinary inputs again; “Cancel” restores the inputs as they were before opening.

The tables of a P have no predefined rows: you create each treaty, reinsurer or placement by typing its name in the last row of the table. These names are free; they only serve to link rows together, for example a placement to the reinsurer that accepts it. A greyed-out cell does not apply to the type of the row; an empty required cell is shown in orange and listed under “To be completed”, each line of which leads to the cell.

For each data item provided, the Detail block shows the expression of the P, its value at the last calculation and what it reads. Each P states what it does not calculate and in which direction its simplifications may mislead the result.

Fills the net reinsurance recoverables of the natural catastrophe scenarios of the Annex XIII regions: windstorm and hail (scenarios A and B), flood (A and B), earthquake, subsidence. Badge at the top of the recoverables columns of the table “Natural catastrophe — Annex XIII regions”.

Table of treaties, one row per treaty:

• rank: order of application, 1 for the first; each treaty applies to the loss net of lower-ranked treaties;
• type: quota share, or per-event excess of loss;
• windstorm, hail, flood, earthquake, subsidence: “covered” for each peril the treaty covers, at least one;
• regions: codes of the Annex XIII regions separated by commas (FR, BE…), as shown in the setup; empty: all the regions selected;
• quota share: ceded share as a decimal (0.30 for 30%) and, if the treaty provides one, a per-event limit in euros;
• excess of loss: per-event retention and layer limit in euros, placed share as a decimal, number of reinstatements, reinstatement rate (1 for 100% of the premium) and initial premium in euros.

For each scenario, the P applies the treaties event by event (the event shares of the standard formula table), uses up the layer and its reinstatements from one event to the next and deducts the reinstatement premiums. The result is capped at the gross loss of the scenario.

What it does not do: per-risk excess of loss, stop-loss, global covers and non-indemnity contracts; their recoverables are entered by hand, with P1 detached. Reinsurer default falls under the default module (see P3).

Simplifications: the retention applies region by region and the layer of a treaty covering several regions is shared between them: your recoverables tend to be understated, your SCR overstated.

Texts: Delegated Regulation (EU) 2015/35, consolidated version, Articles 119 to 125 (natural catastrophe); EIOPA-BoS-14/173 guidelines on the treatment of reinsurance in the catastrophe sub-modules.

Fills, by non-life and NSLT health segment, the premium and reserve volumes net of reinsurance (premiums to be earned, earned and future, claims provisions), the indicator of non-proportional reinsurance in place, as well as the net written premiums and provisions of the MCR. Badges at the top of the corresponding columns.

Table of segments, sixteen fixed rows: N1 to N12 for the non-life segments of Annex II, S1 to S4 for the NSLT health segments of Annex XIV. You enter the volumes gross of reinsurance in euros: written and earned premiums of the last 12 months, premiums to be earned over the next 12 months, future premiums beyond, gross best estimates of the claims and premium provisions, and the amounts recoverable from your excess of loss treaties on the claims provisions, already adjusted for expected losses due to reinsurer default.

Table of treaties, one row per treaty:

• type: quota share or excess of loss;
• segments: codes N1 to N12 and S1 to S4 separated by commas;
• quota share: ceded share as a decimal, the same on all its segments;
• excess of loss: premium of the last 12 months and of the next 12 months in euros, and “in place” if it is non-proportional reinsurance in place on these segments.

The P first deducts the quota shares, then the premium of each excess of loss, spread between its segments in proportion to retained premiums, and the recoverables entered. Net volumes do not go below 0. The MCR segment follows from a correspondence table shown in the panel.

Non-proportional reinsurance factor: until 29/01/2027, the 80% factor of segments N1, N4 and N5 applies in all cases; from 30/01/2027, only where non-proportional reinsurance is in place on the segment (EIOPA, Q&A 3578: non-proportional reinsurance factor after Delegated Regulation 2026/269).

What it does not do: stop-loss, global covers not broken down by segment, finite reinsurance, securitisation; their net volumes are entered by hand, with P2 detached.

Simplifications: the premium of an excess of loss covering several segments is spread in proportion to retained premiums: no effect on the total, the error between segments goes either way; future premiums beyond 12 months are not reduced by excess of loss premiums: your SCR tends to be overstated; recoverables entered without adjustment for default understate your SCR.

Texts: Delegated Regulation (EU) 2015/35, consolidated version, Articles 116, 117, 147 and 250; Directive 2009/138/EC (Solvency II), consolidated version, Article 81 (adjustment of recoverables).

Adds to the type 1 exposures of the counterparty default module one row per reinsurer, calculated from your placements. The rows you enter by hand (banks, derivatives, repos, co-reinsurance) stay in the table and remain editable; the rows of P3 are shown below them, locked and marked P3. Badges at the top of the columns of the table “Default — type 1 exposures”.

Table of reinsurers, one row per reinsurer, under the name you choose:

• group: name you give to the group the reinsurer belongs to. There is no list of groups: you make it up, and two reinsurers bearing exactly the same group name are treated as a single debtor, a “single name exposure” (Article 190). Empty: the reinsurer forms its own single name, under its name;
• credit quality: the step corresponding to the reinsurer's rating, or its situation if unrated; it is your declaration, under your responsibility;
• solvency ratio, in %: only for an unrated reinsurer covering its MCR (last ratio published in its solvency report); the cell is greyed out otherwise;
• encumbered assets: “encumbered” if the reinsurer is an undertaking whose assets are encumbered in your favour;
• collateral: risk-adjusted value of the collateral received from this reinsurer, in euros, all treaties together.

Table of placements, one row per share of a treaty placed with a reinsurer:

• reinsurer: chosen from the list of rows of the table of reinsurers;
• treaty: free name; placements bearing the same treaty name form one treaty, whose shares do not exceed 100%;
• placed share as a decimal; recoverables and risk-mitigating effect of the treaty at 100%, in euros; the risk-mitigating effect of the treaties of P1 and P2 can be calculated by P4: cell locked and marked P4.

For each reinsurer, the P adds up placed share × recoverables, and placed share × risk-mitigating effect, over its placements. The loss-given-default, the probability of default and the grouping by single name remain those of the standard formula: the rows of a same group are added up and their probability of default averaged, which concentrates the risk and increases the default SCR.

Direction of error: two reinsurers of a same group left without a common group are treated as independent: default SCR understated; a risk-mitigating effect not entered counts as 0: default SCR understated.

Texts: Delegated Regulation (EU) 2015/35, consolidated version, Articles 189 and 190 (exposures, single name), 192 (loss-given-default), 196 and 197 (risk-mitigating effect, collateral), 199 and 200 (probability of default).

The risk-mitigating effect of a reinsurance treaty is the reduction in capital requirement it provides: without it, your SCR would be higher. The counterparty default module takes it into account in the loss-given-default of the reinsurer (Article 192): the larger the effect, the more the default of the reinsurer would cost. P4 calculates this effect for the treaties you entered in P1 or P2, and carries it over to the “risk mitigation” column of the placements of P3. Badge at the top of this column, in the panel of P3.

Calculation:

• underwriting requirement: life, health and non-life modules aggregated with the BSCR correlation matrix, as stated in EIOPA Q&A 1862;
• full method: for each treaty, the session is recalculated without the row of the treaty in P1 and P2; effect = requirement without the treaty − requirement with it, at least 0 (Article 196);
• simplified method: a single calculation without any treaty of P1 and P2; the total effect is allocated between treaties in proportion to their recoverables at 100% read in P3 (Article 107). It requires the proportionality attestation (Article 88) in the settings.

Matching: a placement of P3 receives the effect of the treaty whose exact name it bears; a treaty bearing the same name in P1 and in P2 is removed from both. Placements whose treaty is neither in P1 nor in P2 keep the effect you enter. P4 has an effect only if P3 is linked, together with P1 or P2.

Direction of error: the effect on market risk is not calculated: effect understated, default SCR understated if it is positive; life and health SLT recoveries are not removed in the calculations without the treaty (P5): effect of life treaties understated, default SCR understated.

Texts: Delegated Regulation (EU) 2015/35, consolidated version, Articles 88 (proportionality), 107 (simplified calculation), 192 (loss-given-default), 196 (risk-mitigating effect); EIOPA, Q&A 1862: hypothetical underwriting capital requirement for the risk-mitigating effect.