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Non-Life Standard Deviation

Calculate the Total Non-Life Standard Deviation instantly.

SegmentPremium VolumeReserve VolumeTotal Segment VolumeSegment Sigma
Motor Vehicle Liability
€
€
€
8.59%
Other Motor
€
€
€
0.00%
Marine, Aviation and Transport
€
€
€
0.00%
Fire and Property
€
€
€
0.00%
General Liability
€
€
€
0.00%
Credit and Suretyship
€
€
€
0.00%
Legal Expenses
€
€
€
0.00%
Assistance
€
€
€
0.00%
Miscellaneous Financial Loss
€
€
€
0.00%
Non-Proportional Casualty
€
€
€
0.00%
Non-Proportional MAT
€
€
€
0.00%
Non-Proportional Property
€
€
€
0.00%

Total Non-Life Standard Deviation

8.59%

=

Square-Root Portfolio Variance

€10 175 603

÷

Total Volume Measure

€118 518 929

Non-life standard deviation correlation build-up

Waterfall chart showing standalone component charges, correlation adjustment, and diversified result.
StepDeltaRunning
Motor Vehicle Liability10175603.07686957210175603.076869572
Segment Sigma-Volume Sum10175603.07686957210175603.076869572
Square-Root Portfolio Variance10175603.07686957210175603.076869572
Segment sigma-volume shares
Segment sigma-volume sharesShare of each segment in the total.Motor VehicleLiability100.0% · €10M
ModuleShareAmount
Motor Vehicle Liability100.0%€10M

Annex IV correlation matrix

1.000.250.50
Annex IV correlation matrix
01Motor Vehicle Liability02Other Motor03Marine, Aviation and Transport04Fire and Property05General Liability06Credit and Suretyship07Legal Expenses08Assistance09Miscellaneous Financial Loss10Non-Proportional Casualty11Non-Proportional MAT12Non-Proportional Property
01Motor Vehicle Liability
1.00
0.50
0.50
0.25
0.50
0.25
0.50
0.25
0.50
0.25
0.25
0.25
02Other Motor
0.50
1.00
0.25
0.25
0.25
0.25
0.50
0.50
0.50
0.25
0.25
0.25
03Marine, Aviation and Transport
0.50
0.25
1.00
0.25
0.25
0.25
0.25
0.50
0.50
0.25
0.50
0.25
04Fire and Property
0.25
0.25
0.25
1.00
0.25
0.25
0.25
0.50
0.50
0.25
0.50
0.50
05General Liability
0.50
0.25
0.25
0.25
1.00
0.50
0.50
0.25
0.50
0.50
0.25
0.25
06Credit and Suretyship
0.25
0.25
0.25
0.25
0.50
1.00
0.50
0.25
0.50
0.50
0.25
0.25
07Legal Expenses
0.50
0.50
0.25
0.25
0.50
0.50
1.00
0.25
0.50
0.50
0.25
0.25
08Assistance
0.25
0.50
0.50
0.50
0.25
0.25
0.25
1.00
0.50
0.25
0.25
0.50
09Miscellaneous Financial Loss
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
1.00
0.25
0.50
0.25
10Non-Proportional Casualty
0.25
0.25
0.25
0.25
0.50
0.50
0.50
0.25
0.25
1.00
0.25
0.25
11Non-Proportional MAT
0.25
0.25
0.50
0.50
0.25
0.25
0.25
0.25
0.50
0.25
1.00
0.25
12Non-Proportional Property
0.25
0.25
0.25
0.50
0.25
0.25
0.25
0.50
0.25
0.25
0.25
1.00
1Step 1

Calculate each Annex II segment standard deviation from premium and reserve volumes

σs=f(Vprem,s,Vres,s,NGRs)\sigma_s = f(V_{prem,s},V_{res,s},NGR_s)
2Step 2

Aggregate segment standard deviations using the Annex IV correlation matrix

σNL=∑i∑jCorrijσiViσjVj∑iVi\sigma_{NL}=\frac{\sqrt{\sum_i\sum_j Corr_{ij}\sigma_iV_i\sigma_jV_j}}{\sum_i V_i}

Understand the Non-Life Standard Deviation

Overview

This calculator implements the Non-Life Standard Deviation calculation within the Solvency II standard formula.[1] The standard deviation is defined as the measure of volatility associated with the undertaking's non-life insurance and reinsurance obligations. It is calibrated to reflect the expected fluctuations in claims frequency and severity over a one-year horizon.

Input Terms

  • Prescribed Market Volatility: The volatility factors provided by EIOPA for each line of business (LoB).[1]
  • Undertaking-Specific Parameters (USP): The internal volatility estimates used if the undertaking has supervisory approval for custom factors.
  • Combined Standard Deviation: The volatility measure after aggregating the premium and reserve risk components.

Technical Rationale

The Non-Life Standard Deviation is the primary volatility driver for the Premium & Reserve Risk requirement. It ensures that the capital requirement is representative of the undertaking's specific risk profile and the diversification between LoBs.

The calculation aggregates the standard deviations for each LoB using the prescribed correlation matrix. This ensures the undertaking holds enough capital to absorb the risk of simultaneous large losses across multiple segments. The result is then multiplied by the Non-Life Volume Measure to determine the total capital requirement for Premium & Reserve risk.[2][3]

Important Notes

  • Regulatory deviation: Material deviation from standard-formula assumptions at this layer may support a capital add-on or a move toward an internal model where justified.[4]
  • Reporting: The displayed result is intended to support the corresponding standard-formula component feeding the S.25.01.01 standard-formula reporting view.[5]

Sources

  1. Delegated Regulation (EU) 2015/35 - Art. 117 (Standard deviation for non-life premium and reserve risk) - EIOPA
  2. Delegated Regulation (EU) 2015/35 - Art. 115 (Non-life premium and reserve risk sub-module) - EIOPA
  3. Delegated Regulation (EU) 2015/35 - Art. 116 (Volume measure for non-life premium and reserve risk) - EIOPA
  4. Directive 2009/138/EC - Art. 37 (Capital add-on) - EIOPA
  5. Commission Implementing Regulation (EU) 2023/894 - QRT S.25.01.01 (SCR standard formula) - EUR-Lex

Default values are illustrative sample inputs for navigation, training, and QA. Replace them with controlled data before using the result in capital analysis, governance, or reporting decisions.