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Actuably

Life Risk

Calculate the Life Risk Solvency Capital Requirement instantly.

€
€
€
€
€
€
€

Standalone Component Total

€48 000 000

Before correlation diversification

−

Diversification Benefit

€22 990 002

−47.9% of standalone

Capital relief

=

Life Risk SCR

€25 009 998

After diversification

Life Risk

Waterfall chart showing the Life Risk SCR build-up.
StepImpactRunning
Mortality Risk1200000012000000
Longevity Risk900000021000000
Disability-Morbidity Risk700000028000000
Life Expense Risk500000033000000
Revision Risk400000037000000
Lapse Risk800000045000000
Life Catastrophe Risk300000048000000
Standalone Component Total4800000048000000
Diversification Benefit-22990001.999200425009998.0007996
Life Risk SCR25009998.000799625009998.0007996
Life sub-module shares
Life sub-module sharesShare of each segment in the total.Mortality25.0% · €12MLongevity18.8% · €9.0MLapse16.7% · €8.0MDisability-Morbidity14.6% · €7.0MLife Expense10.4% · €5.0MRevision8.3% · €4.0MLife Catastrophe6.3% · €3.0M
ModuleShareAmount
Mortality Risk25.0%€12M
Longevity Risk18.8%€9.0M
Lapse Risk16.7%€8.0M
Disability-Morbidity Risk14.6%€7.0M
Life Expense Risk10.4%€5.0M
Revision Risk8.3%€4.0M
Life Catastrophe Risk6.3%€3.0M

Life risk correlation matrix

1.00-0.250.000.250.50
Life risk correlation matrix
MORTMortalityLONGLongevityDISDisabilityEXPExpenseREVRevisionLAPLapseCATLife Catastrophe
MORTMortality
1.00
-0.25
0.25
0.25
0.00
0.00
0.25
LONGLongevity
-0.25
1.00
0.00
0.25
0.25
0.25
0.00
DISDisability
0.25
0.00
1.00
0.50
0.00
0.00
0.25
EXPExpense
0.25
0.25
0.50
1.00
0.50
0.50
0.25
REVRevision
0.00
0.25
0.00
0.50
1.00
0.00
0.00
LAPLapse
0.00
0.25
0.00
0.50
0.00
1.00
0.25
CATLife Catastrophe
0.25
0.00
0.25
0.25
0.00
0.25
1.00
1Step 1

Life Risk SCR

Life Risk SCR=∑i,jCorri,j×SCRi×SCRj\textit{Life Risk SCR} = \sqrt{\sum_{i,j} Corr_{i,j} \times SCR_i \times SCR_j}
2Step 2

Diversification Benefit

Diversification Benefit=max⁡(0,Mortality Risk+Longevity Risk+Disability-Morbidity Risk+Life Expense Risk+Revision Risk+Lapse Risk+Life Catastrophe Risk−Life Risk SCR)\textit{Diversification Benefit} = \max(0, \textit{Mortality Risk} + \textit{Longevity Risk} + \textit{Disability-Morbidity Risk} + \textit{Life Expense Risk} + \textit{Revision Risk} + \textit{Lapse Risk} + \textit{Life Catastrophe Risk} - \textit{Life Risk SCR})

Understand the Life Risk

Overview

This calculator implements the diversified capital requirement for the Life Underwriting Risk module within the Solvency II standard formula.[1] The Life Risk requirement is defined as the economic capital necessary to cover the loss in basic own funds resulting from a 1-in-200 year stress event affecting underwriting risk factors including mortality, longevity, lapse, and catastrophes.[2]

Input Terms

  • Mortality Risk: The capital requirement for the permanent increase in mortality rates affecting life-insurance obligations.[3]
  • Longevity Risk: The capital requirement for the permanent decrease in mortality rates affecting annuity and longevity-sensitive obligations.[4]
  • Disability-Morbidity Risk: The capital requirement for the adverse change in disability, sickness, and morbidity rates.[5]
  • Life Expense Risk: The capital requirement for the unexpected increase in the level of expenses or the rate of expense inflation.[6]
  • Revision Risk: The capital requirement for the adverse change in revision rates affecting annuity benefits.[7]
  • Lapse Risk: The capital requirement for the adverse change in the rate of policy lapses, encompassing lapse-up, lapse-down, and mass-lapse scenarios.[8]
  • Life Catastrophe Risk: The capital requirement for extreme, mass-casualty events or pandemics leading to a spike in short-term mortality.[9]

Technical Rationale

The Life Underwriting Risk module follows a 99.5% confidence level over a one-year horizon. Each sub-module measures the instantaneous change in net asset value following the application of the regulatory stress. The standard formula then aggregates these sub-module requirements using the correlation matrix defined in Article 136 of the Delegated Regulation.[1]

Article 136 aggregates life underwriting risks through prescribed correlations because biometric and policyholder-behavior stresses do not move as a simple sum.[1] Most notably, the correlation matrix recognizes the partial hedge between mortality and longevity exposures, where a single shock to mortality rates would affect the two portfolios in opposite directions.

Important Notes

  • Article 113 Scope: The Life underwriting module applies to life insurance and reinsurance obligations other than health obligations. Health obligations belong in the Health underwriting module, while non-life obligations other than health belong in the Non-Life underwriting module.[10]
  • Lapse Binding Scenario: Lapse risk is calculated as the maximum loss across three distinct scenarios (up, down, and mass-lapse). The binding scenario is policy-specific and depends on whether the contract represents an asset or a liability to the undertaking in a lapse situation.[8]
  • Hedging Recognition: While the correlation matrix allows for diversification, each sub-module capital requirement is floored at zero to ensure that profit-making scenarios do not offset other losses within the module aggregation.[1]
  • 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.[11]
  • Reporting: The displayed result is intended to support the corresponding standard-formula component for the S.25.01.01 standard-formula reporting view.[12]

Sources

  1. Delegated Regulation (EU) 2015/35 - Art. 136 (Life underwriting risk correlation coefficients) - EIOPA
  2. Directive 2009/138/EC - Art. 101 (99.5% VaR / 1-in-200 calibration) - EIOPA
  3. Delegated Regulation (EU) 2015/35 - Art. 137 (Life mortality risk sub-module) - EIOPA
  4. Delegated Regulation (EU) 2015/35 - Art. 138 (Life longevity risk sub-module) - EIOPA
  5. Delegated Regulation (EU) 2015/35 - Art. 139 (Life disability-morbidity risk sub-module) - EIOPA
  6. Delegated Regulation (EU) 2015/35 - Art. 140 (Life-expense risk sub-module) - EIOPA
  7. Delegated Regulation (EU) 2015/35 - Art. 141 (Revision risk sub-module) - EIOPA
  8. Delegated Regulation (EU) 2015/35 - Art. 142 (Lapse risk sub-module) - EIOPA
  9. Delegated Regulation (EU) 2015/35 - Art. 143 (Life-catastrophe risk sub-module) - EIOPA
  10. Delegated Regulation (EU) 2015/35 - Art. 113 (Scope of the underwriting risk modules) - EIOPA
  11. Directive 2009/138/EC - Art. 37 (Capital add-on) - EIOPA
  12. 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.