How to calculate the SCR under the standard formula: modules, correlation matrix and a worked example

The Solvency Capital Requirement is the amount of own funds an EU or UK insurer must hold so that it can absorb a one in two hundred year loss and still meet its obligations. Under the standard formula the number comes out of a fixed sequence: calculate a capital charge for each risk module, aggregate the modules with a prescribed correlation matrix, add the operational risk charge, then subtract what deferred taxes and discretionary benefits would absorb. This article walks through that sequence with the actual coefficients and a worked example in round numbers, and ends with the row in template S.25.01 where each figure belongs. It is written for the actuary who has to produce or check the number, and for anyone evaluating SCR Tool, our SCR calculation software for the standard formula, who wants to see the mechanics first.

The SCR formula

Article 103 of Directive 2009/138/EC sets out the structure in one line. The SCR under the standard formula is the sum of three parts:

SCR = BSCR + SCR_op + Adj

BSCR is the Basic Solvency Capital Requirement, the aggregate of the risk modules. SCR_op is the capital requirement for operational risk. Adj is the adjustment for the loss-absorbing capacity of technical provisions and deferred taxes, which is zero or negative, so it reduces the total.

Articles 100 to 111 of the Directive carry the framework: Article 101 sets the calibration (Value-at-Risk of basic own funds at a 99.5 percent confidence level over one year), Article 102 the frequency, Articles 103 to 108 the structure, Article 109 the simplifications and Article 111 the mandate for the delegated acts. Those delegated acts are Title I, Chapter V of Delegated Regulation (EU) 2015/35, which supplies every shock and factor the Directive leaves open. The amendments in Directive (EU) 2025/2 touch several parts of the Directive; our explainer covers what changes for the standard formula.

The risk modules and their sub-modules

Article 104 of the Directive names the modules that make up the BSCR, and Article 105 lists the sub-modules each must contain at a minimum. The Delegated Regulation adds the detail in its own sections; the table gives the article where each starts.

Each module is itself an aggregation. Inside market risk the six sub-modules combine through their own correlation matrix; the counterparty default module combines its two exposure types with a fixed 1.5 cross term instead. This article stays at the module level.

The intangible asset risk module is the odd one out. The Directive’s Annex IV matrix covers five modules, and Article 87 of the Delegated Regulation adds the intangible charge outside the square root:

BSCR = sqrt( sum over i,j of Corr(i,j) x SCR_i x SCR_j ) + SCR_intangibles

The term is often zero, since few undertakings carry intangible assets on the Solvency II balance sheet, but it has its own row in S.25.01.

The correlation matrix from Annex IV

Point 1 of Annex IV to the Directive prescribes the coefficients. Corr(i,j) is the value in row i and column j:

The diagonal is 1, so each module contributes its full square. Most pairs sit at 0.25. Two pairs are zero, life against non-life and health against non-life, and one pair is 0.5, counterparty default against non-life, because a large non-life loss and a reinsurer failure tend to arrive together. The matrix is symmetric, which is why the worked example can list each pair once and double it.

A worked example: from five module charges to the BSCR

Take an undertaking whose module charges, in millions and already aggregated inside each module, are market 40, counterparty default 10, life 25, health 5, non-life 30 and intangible assets 0. The simple sum of the five modules is 110, the undiversified figure.

Step 1 is the squares on the diagonal, where the coefficient is 1:

40² + 10² + 25² + 5² + 30² = 1,600 + 100 + 625 + 25 + 900 = 3,250

Step 2 is the cross terms. Each pair appears twice in the double sum, so compute each pair once and double the total:

The pairs add up to 956.25. Doubled, that is 1,912.5.

Step 3 adds the two parts and takes the square root:

3,250 + 1,912.5 = 5,162.5

sqrt(5,162.5) = 71.85

Step 4 adds the intangible charge, zero here, so the BSCR is 71.85 million. The diversification benefit is 110 minus 71.85, or 38.15 million, reported as a negative number in its own row. With every off-diagonal coefficient at zero the result would have been sqrt(3,250), or 57.01; with every one at 1 it would have been the plain sum of 110.

The operational risk charge

Article 107 of the Directive says the operational risk charge reflects the operational risk not already captured in the modules, and caps it at 30 percent of the BSCR for business other than unit-linked. Article 204 of the Delegated Regulation turns that into a formula:

SCR_op = min(0.3 x BSCR; Op) + 0.25 x Exp_ul

Op is the larger of two volume measures. One is based on earned premiums: 4 percent of life premiums (excluding unit-linked) plus 3 percent of non-life premiums, with an extra term when premiums grew by more than 20 percent over the year. The other is based on technical provisions: 0.45 percent of life provisions (excluding unit-linked) plus 3 percent of non-life provisions, without risk margin and before reinsurance. Exp_ul is the expenses of the last twelve months on unit-linked business, and that part sits outside the cap.

Continuing the example, the cap is 0.3 x 71.85 = 21.56 million. Suppose the premium and provision measures give Op = 6 million and the undertaking writes no unit-linked business. Then SCR_op = min(21.56; 6) + 0 = 6 million. The cap only bites when premium or provision volumes are large relative to the diversified risk charges, for instance under heavy reinsurance.

The adjustment for loss-absorbing capacity

Article 108 of the Directive allows the SCR to be reduced where a loss would be partly absorbed by a cut in future discretionary benefits or by a movement in deferred taxes. Articles 205 to 207 of the Delegated Regulation define the two pieces.

The adjustment for technical provisions (Article 206) requires a second run of the BSCR in which the scenarios may change the value of future discretionary benefits. The result is the net BSCR, or nBSCR. The adjustment is the gap between gross and net, capped at the future discretionary benefits and floored at zero, with a minus sign in front:

Adj_TP = minus max( min(BSCR minus nBSCR; FDB); 0 )

The adjustment for deferred taxes (Article 207) is the change in deferred taxes that would follow an instantaneous loss equal to BSCR + Adj_TP + SCR_op. It is negative or zero. Paragraph 2 adds the condition: an increase in deferred tax assets counts only if the undertaking can demonstrate that future taxable profits will be available to use it, allowing for the loss just assumed. This is why S.25.01 now carries a block of rows on deferred taxes before and after the shock.

To close the example, suppose the net recalculation gives nBSCR = 68.85 million with future discretionary benefits comfortably above the 3 million difference, so Adj_TP = minus 3. Suppose the tax recalculation supports Adj_DT = minus 8. The SCR is then:

SCR = 71.85 + 6 minus 3 minus 8 = 66.85 million

With eligible own funds of 120 million the solvency ratio would be 120 / 66.85, or about 180 percent. The 3 and the 8 stand in for two undertaking specific recalculations; they are not factors to apply to someone else’s BSCR.

Where each number lands in S.25.01

Template S.25.01.21, Solvency Capital Requirement for undertakings on the standard formula, is the annual solo template that receives the figures above. With taxonomy 2.8.0 the layout has a gross column (C0040), a net column (C0030) for the module rows, and a single value column (C0100) for the totals below them. Using the example:

R0010 to R0050 carry the module charges gross in C0040 and net of future discretionary benefits in C0030; for a non-life undertaking the two columns are identical. R0060 is negative by construction and must reconcile to the modules and R0100. R0120 holds the adjustment for aggregating notional SCRs of ring-fenced funds and matching adjustment portfolios, which is zero for an undertaking without them; our post on ring-fenced funds under Solvency II explains where that figure comes from and why the template is repeated as SR.25.01 for each fund. Rows R0590 to R0640 document the deferred tax position behind R0150, and R0640 must equal R0150.

Where this lands in the software

SCR Tool follows the same sequence as this article. The Market-Risk-Constructor imports asset data and fund look-through information from QRT Tool, with the risk-free interest rate term structures and the symmetric adjustment of the equity shock already embedded, and produces a transparency list where the charge on each asset can be traced. The Underwriting-Risk-Constructor takes liability data from TP Tool for the underwriting modules. DataCollector pulls the remaining inputs from databases, Excel or CSV files through transformations defined once and reused every quarter. The overview shows each module, the diversification step, the operational risk charge and both adjustments, and you can drill into any component with its formula visible. The results appear in the QRT layout, so the S.25.01 rows above come out as reported. Groups manage every legal entity under one account, and UK undertakings can import the PRA versions of the term structures and the symmetric adjustment.