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Non-Life Standard Deviation

Non-Life

Calculate the Total Non-Life Standard Deviation instantly.

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Total Non-Life Standard Deviation

0.09

1Step 1

nonlife_segment_01_net_to_gross_premium_ratio

nonlife_segment_01_net_to_gross_premium_ratio=1\textit{nonlife\_segment\_01\_net\_to\_gross\_premium\_ratio} = 1
2Step 2

nonlife_segment_02_net_to_gross_premium_ratio

nonlife_segment_02_net_to_gross_premium_ratio=1\textit{nonlife\_segment\_02\_net\_to\_gross\_premium\_ratio} = 1
3Step 3

nonlife_segment_03_net_to_gross_premium_ratio

nonlife_segment_03_net_to_gross_premium_ratio=1\textit{nonlife\_segment\_03\_net\_to\_gross\_premium\_ratio} = 1
4Step 4

nonlife_segment_04_net_to_gross_premium_ratio

nonlife_segment_04_net_to_gross_premium_ratio=1\textit{nonlife\_segment\_04\_net\_to\_gross\_premium\_ratio} = 1
5Step 5

nonlife_segment_05_net_to_gross_premium_ratio

nonlife_segment_05_net_to_gross_premium_ratio=1\textit{nonlife\_segment\_05\_net\_to\_gross\_premium\_ratio} = 1
6Step 6

nonlife_segment_06_net_to_gross_premium_ratio

nonlife_segment_06_net_to_gross_premium_ratio=1\textit{nonlife\_segment\_06\_net\_to\_gross\_premium\_ratio} = 1
7Step 7

nonlife_segment_07_net_to_gross_premium_ratio

nonlife_segment_07_net_to_gross_premium_ratio=1\textit{nonlife\_segment\_07\_net\_to\_gross\_premium\_ratio} = 1
8Step 8

nonlife_segment_08_net_to_gross_premium_ratio

nonlife_segment_08_net_to_gross_premium_ratio=1\textit{nonlife\_segment\_08\_net\_to\_gross\_premium\_ratio} = 1
9Step 9

nonlife_segment_09_net_to_gross_premium_ratio

nonlife_segment_09_net_to_gross_premium_ratio=1\textit{nonlife\_segment\_09\_net\_to\_gross\_premium\_ratio} = 1
10Step 10

nonlife_segment_10_net_to_gross_premium_ratio

nonlife_segment_10_net_to_gross_premium_ratio=1\textit{nonlife\_segment\_10\_net\_to\_gross\_premium\_ratio} = 1
11Step 11

nonlife_segment_11_net_to_gross_premium_ratio

nonlife_segment_11_net_to_gross_premium_ratio=1\textit{nonlife\_segment\_11\_net\_to\_gross\_premium\_ratio} = 1
12Step 12

nonlife_segment_12_net_to_gross_premium_ratio

nonlife_segment_12_net_to_gross_premium_ratio=1\textit{nonlife\_segment\_12\_net\_to\_gross\_premium\_ratio} = 1
13Step 13

Motor Vehicle Liability Segment Standard Deviation

Motor Vehicle Liability Segment Standard Deviation=nonlife_segment_standard_deviation⁡(1,Motor Vehicle Liability Premium Volume Measure,Motor Vehicle Liability Reserve Volume Measure,nonlife_segment_01_net_to_gross_premium_ratio)\textit{Motor Vehicle Liability Segment Standard Deviation} = \operatorname{nonlife\_segment\_standard\_deviation}\left(1, \textit{Motor Vehicle Liability Premium Volume Measure}, \textit{Motor Vehicle Liability Reserve Volume Measure}, \textit{nonlife\_segment\_01\_net\_to\_gross\_premium\_ratio}\right)
14Step 14

Other Motor Segment Standard Deviation

Other Motor Segment Standard Deviation=nonlife_segment_standard_deviation⁡(2,Other Motor Premium Volume Measure,Other Motor Reserve Volume Measure,nonlife_segment_02_net_to_gross_premium_ratio)\textit{Other Motor Segment Standard Deviation} = \operatorname{nonlife\_segment\_standard\_deviation}\left(2, \textit{Other Motor Premium Volume Measure}, \textit{Other Motor Reserve Volume Measure}, \textit{nonlife\_segment\_02\_net\_to\_gross\_premium\_ratio}\right)
15Step 15

Marine, Aviation and Transport Segment Standard Deviation

Marine, Aviation and Transport Segment Standard Deviation=nonlife_segment_standard_deviation⁡(3,Marine, Aviation and Transport Premium Volume Measure,Marine, Aviation and Transport Reserve Volume Measure,nonlife_segment_03_net_to_gross_premium_ratio)\textit{Marine, Aviation and Transport Segment Standard Deviation} = \operatorname{nonlife\_segment\_standard\_deviation}\left(3, \textit{Marine, Aviation and Transport Premium Volume Measure}, \textit{Marine, Aviation and Transport Reserve Volume Measure}, \textit{nonlife\_segment\_03\_net\_to\_gross\_premium\_ratio}\right)
16Step 16

Fire and Property Segment Standard Deviation

Fire and Property Segment Standard Deviation=nonlife_segment_standard_deviation⁡(4,Fire and Property Premium Volume Measure,Fire and Property Reserve Volume Measure,nonlife_segment_04_net_to_gross_premium_ratio)\textit{Fire and Property Segment Standard Deviation} = \operatorname{nonlife\_segment\_standard\_deviation}\left(4, \textit{Fire and Property Premium Volume Measure}, \textit{Fire and Property Reserve Volume Measure}, \textit{nonlife\_segment\_04\_net\_to\_gross\_premium\_ratio}\right)
17Step 17

General Liability Segment Standard Deviation

General Liability Segment Standard Deviation=nonlife_segment_standard_deviation⁡(5,General Liability Premium Volume Measure,General Liability Reserve Volume Measure,nonlife_segment_05_net_to_gross_premium_ratio)\textit{General Liability Segment Standard Deviation} = \operatorname{nonlife\_segment\_standard\_deviation}\left(5, \textit{General Liability Premium Volume Measure}, \textit{General Liability Reserve Volume Measure}, \textit{nonlife\_segment\_05\_net\_to\_gross\_premium\_ratio}\right)
18Step 18

Credit and Suretyship Segment Standard Deviation

Credit and Suretyship Segment Standard Deviation=nonlife_segment_standard_deviation⁡(6,Credit and Suretyship Premium Volume Measure,Credit and Suretyship Reserve Volume Measure,nonlife_segment_06_net_to_gross_premium_ratio)\textit{Credit and Suretyship Segment Standard Deviation} = \operatorname{nonlife\_segment\_standard\_deviation}\left(6, \textit{Credit and Suretyship Premium Volume Measure}, \textit{Credit and Suretyship Reserve Volume Measure}, \textit{nonlife\_segment\_06\_net\_to\_gross\_premium\_ratio}\right)
19Step 19

Legal Expenses Segment Standard Deviation

Legal Expenses Segment Standard Deviation=nonlife_segment_standard_deviation⁡(7,Legal Expenses Premium Volume Measure,Legal Expenses Reserve Volume Measure,nonlife_segment_07_net_to_gross_premium_ratio)\textit{Legal Expenses Segment Standard Deviation} = \operatorname{nonlife\_segment\_standard\_deviation}\left(7, \textit{Legal Expenses Premium Volume Measure}, \textit{Legal Expenses Reserve Volume Measure}, \textit{nonlife\_segment\_07\_net\_to\_gross\_premium\_ratio}\right)
20Step 20

Assistance Segment Standard Deviation

Assistance Segment Standard Deviation=nonlife_segment_standard_deviation⁡(8,Assistance Premium Volume Measure,Assistance Reserve Volume Measure,nonlife_segment_08_net_to_gross_premium_ratio)\textit{Assistance Segment Standard Deviation} = \operatorname{nonlife\_segment\_standard\_deviation}\left(8, \textit{Assistance Premium Volume Measure}, \textit{Assistance Reserve Volume Measure}, \textit{nonlife\_segment\_08\_net\_to\_gross\_premium\_ratio}\right)
21Step 21

Miscellaneous Financial Loss Segment Standard Deviation

Miscellaneous Financial Loss Segment Standard Deviation=nonlife_segment_standard_deviation⁡(9,Miscellaneous Financial Loss Premium Volume Measure,Miscellaneous Financial Loss Reserve Volume Measure,nonlife_segment_09_net_to_gross_premium_ratio)\textit{Miscellaneous Financial Loss Segment Standard Deviation} = \operatorname{nonlife\_segment\_standard\_deviation}\left(9, \textit{Miscellaneous Financial Loss Premium Volume Measure}, \textit{Miscellaneous Financial Loss Reserve Volume Measure}, \textit{nonlife\_segment\_09\_net\_to\_gross\_premium\_ratio}\right)
22Step 22

Non-Proportional Casualty Segment Standard Deviation

Non-Proportional Casualty Segment Standard Deviation=nonlife_segment_standard_deviation⁡(10,Non-Proportional Casualty Premium Volume Measure,Non-Proportional Casualty Reserve Volume Measure,nonlife_segment_10_net_to_gross_premium_ratio)\textit{Non-Proportional Casualty Segment Standard Deviation} = \operatorname{nonlife\_segment\_standard\_deviation}\left(10, \textit{Non-Proportional Casualty Premium Volume Measure}, \textit{Non-Proportional Casualty Reserve Volume Measure}, \textit{nonlife\_segment\_10\_net\_to\_gross\_premium\_ratio}\right)
23Step 23

Non-Proportional MAT Segment Standard Deviation

Non-Proportional MAT Segment Standard Deviation=nonlife_segment_standard_deviation⁡(11,Non-Proportional MAT Premium Volume Measure,Non-Proportional MAT Reserve Volume Measure,nonlife_segment_11_net_to_gross_premium_ratio)\textit{Non-Proportional MAT Segment Standard Deviation} = \operatorname{nonlife\_segment\_standard\_deviation}\left(11, \textit{Non-Proportional MAT Premium Volume Measure}, \textit{Non-Proportional MAT Reserve Volume Measure}, \textit{nonlife\_segment\_11\_net\_to\_gross\_premium\_ratio}\right)
24Step 24

Non-Proportional Property Segment Standard Deviation

Non-Proportional Property Segment Standard Deviation=nonlife_segment_standard_deviation⁡(12,Non-Proportional Property Premium Volume Measure,Non-Proportional Property Reserve Volume Measure,nonlife_segment_12_net_to_gross_premium_ratio)\textit{Non-Proportional Property Segment Standard Deviation} = \operatorname{nonlife\_segment\_standard\_deviation}\left(12, \textit{Non-Proportional Property Premium Volume Measure}, \textit{Non-Proportional Property Reserve Volume Measure}, \textit{nonlife\_segment\_12\_net\_to\_gross\_premium\_ratio}\right)
25Step 25

Total Non-Life Standard Deviation

Total Non-Life Standard Deviation=nonlife_portfolio_standard_deviation⁡(Motor Vehicle Liability Segment Volume Measure,Motor Vehicle Liability Segment Standard Deviation,Other Motor Segment Volume Measure,Other Motor Segment Standard Deviation,Marine, Aviation and Transport Segment Volume Measure,Marine, Aviation and Transport Segment Standard Deviation,Fire and Property Segment Volume Measure,Fire and Property Segment Standard Deviation,General Liability Segment Volume Measure,General Liability Segment Standard Deviation,Credit and Suretyship Segment Volume Measure,Credit and Suretyship Segment Standard Deviation,Legal Expenses Segment Volume Measure,Legal Expenses Segment Standard Deviation,Assistance Segment Volume Measure,Assistance Segment Standard Deviation,Miscellaneous Financial Loss Segment Volume Measure,Miscellaneous Financial Loss Segment Standard Deviation,Non-Proportional Casualty Segment Volume Measure,Non-Proportional Casualty Segment Standard Deviation,Non-Proportional MAT Segment Volume Measure,Non-Proportional MAT Segment Standard Deviation,Non-Proportional Property Segment Volume Measure,Non-Proportional Property Segment Standard Deviation)\textit{Total Non-Life Standard Deviation} = \operatorname{nonlife\_portfolio\_standard\_deviation}\left(\textit{Motor Vehicle Liability Segment Volume Measure}, \textit{Motor Vehicle Liability Segment Standard Deviation}, \textit{Other Motor Segment Volume Measure}, \textit{Other Motor Segment Standard Deviation}, \textit{Marine, Aviation and Transport Segment Volume Measure}, \textit{Marine, Aviation and Transport Segment Standard Deviation}, \textit{Fire and Property Segment Volume Measure}, \textit{Fire and Property Segment Standard Deviation}, \textit{General Liability Segment Volume Measure}, \textit{General Liability Segment Standard Deviation}, \textit{Credit and Suretyship Segment Volume Measure}, \textit{Credit and Suretyship Segment Standard Deviation}, \textit{Legal Expenses Segment Volume Measure}, \textit{Legal Expenses Segment Standard Deviation}, \textit{Assistance Segment Volume Measure}, \textit{Assistance Segment Standard Deviation}, \textit{Miscellaneous Financial Loss Segment Volume Measure}, \textit{Miscellaneous Financial Loss Segment Standard Deviation}, \textit{Non-Proportional Casualty Segment Volume Measure}, \textit{Non-Proportional Casualty Segment Standard Deviation}, \textit{Non-Proportional MAT Segment Volume Measure}, \textit{Non-Proportional MAT Segment Standard Deviation}, \textit{Non-Proportional Property Segment Volume Measure}, \textit{Non-Proportional Property Segment Standard Deviation}\right)

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]

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.[3]
  • Reporting: The displayed result is intended to support the corresponding standard-formula component feeding the S.25.01 standard-formula reporting view.[4]

Sources

  1. Delegated Regulation (EU) 2015/35 - Art. 117 (Standard deviation) - EUR-Lex
  2. Delegated Regulation (EU) 2015/35 - Art. 115 (Non-life premium and reserve risk sub-module) - EIOPA
  3. Directive 2009/138/EC - Art. 37 (Capital add-on) - EIOPA
  4. Commission Implementing Regulation (EU) 2015/2450 - QRT S.25.01 - 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.