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Life Mortality Projection Year Contribution

Calculate the Discounted Capital at Risk Contribution instantly.

€
%
%

Capital at Risk

€90 000 000

×

Survival Factor

1.00

÷

Discount Factor

1.01

=

Discounted CAR Contribution

€89 332 500

1Step 1

Survival Factor

Survival Factork=(1−q)k−1\mathrm{Survival\ Factor}_k=(1-q)^{k-1}
2Step 2

Discount Factor

Discount Factork=(1+ik)k−0.5\mathrm{Discount\ Factor}_k=(1+i_k)^{k-0.5}
3Step 3

Discounted Capital at Risk Contribution

Contributionk=CARk×(1−q)k−1(1+ik)k−0.5\mathrm{Contribution}_k=\frac{CAR_k\times(1-q)^{k-1}}{(1+i_k)^{k-0.5}}

Understand the Life Mortality Projection Year Contribution

Overview

This calculator evaluates one yearly term in the Article 91 simplified mortality formula: the capital-at-risk amount for projection year k, weighted by expected survival to that year and discounted at the relevant spot rate.[1]

Input Terms

  • Projection Year (k): The future year whose Article 91 capital-at-risk contribution is being measured.[1]
  • Projection Year Capital at Risk (CAR<sub>k</sub>): The positive capital at risk in the selected projection year after recoverables from reinsurance contracts and special purpose vehicles. Life Mortality Year-k Capital at Risk calculates this Article 91 term from net death-payment and best-estimate amounts.[1]
  • Average Mortality Rate (q): The expected average mortality rate used for survival weighting.[1]
  • Projection Year Spot Rate (i<sub>k</sub>): The annualized spot rate for the projection maturity used to discount the yearly capital at risk.[1]

Technical Rationale

Article 91 scales the simplified mortality capital requirement by the prescribed mortality stress, the average mortality rate, and the sum of discounted capital-at-risk contributions across projection years.[1] This calculation focuses on one term of that sum so the survival weighting and discounting assumptions can be evidenced at the projection-year level.

Important Notes

  • Aggregation boundary: This value is one projection-year contribution. Article 91 requires the full sum across relevant projection years before applying the mortality stress and average mortality rate.[1]
  • Applicability: The simplification is only appropriate where the proportionality conditions for simplified standard-formula calculations are met.[2]
  • Gross vs. Net SCR: This calculator prepares an input for the standalone Life Mortality Risk simplification. Solvency II risk is only finalized as a net impact on Basic Own Funds after diversification in Life Risk, then within BSCR, and after the top-level LAC TP and LAC DT adjustments.

Sources

  1. Delegated Regulation (EU) 2015/35 - Art. 91 (Simplified calculation of the capital requirement for life mortality risk) - EIOPA
  2. Delegated Regulation (EU) 2015/35 - Art. 88 (Proportionality) - EIOPA

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.