Life Risk

Inputs

Mortality RiskSolvency capital required for mortality risk within the life underwriting module.

€

Longevity RiskSolvency capital required for longevity risk within the life underwriting module.

€

Disability-Morbidity RiskSolvency capital required for disability-morbidity risk within the life underwriting module.

€

Life Expense RiskSolvency capital required for expense risk within the life underwriting module.

€

Revision RiskSolvency capital required for revision risk within the life underwriting module.

€

Lapse RiskSolvency capital required for lapse risk within the life underwriting module.

€

Life Catastrophe RiskSolvency capital required for life catastrophe risk within the life underwriting module.

€

Standalone Life Sum

€370

Before diversification

−

Diversification Benefit

€176

−47.7% of standalone

Capital relief

=

Life Risk SCR

€194

After diversification

Step	Delta	Running
Mortality Risk	90	90
Longevity Risk	70	160
Disability-Morbidity Risk	55	215
Life Expense Risk	40	255
Revision Risk	30	285
Lapse Risk	65	350
Life Catastrophe Risk	20	370
Standalone Life Sum	370	370
Diversification Benefit	-176.35083268962916	193.64916731037084
Life Risk SCR	193.64916731037084	193.64916731037084

Life sub-module shares

Module	Share	Amount
Mortality Risk	24.3%	€90
Longevity Risk	18.9%	€70
Lapse Risk	17.6%	€65
Disability-Morbidity Risk	14.9%	€55
Life Expense Risk	10.8%	€40
Revision Risk	8.1%	€30
Life Catastrophe Risk	5.4%	€20

Life risk correlation matrix

1.00-0.250.000.250.50

Life risk correlation matrix
	MORTMortality	LONGLongevity	DISDisability	EXPExpense	REVRevision	LAPLapse	CATLife 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

\textit{Life Risk SCR} = \sqrt{\sum_{i,j} Corr_{i,j} \times SCR_i \times SCR_j}

2Step 2

Diversification Benefit

\textit{Diversification Benefit} = \max\left(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}\right)

\textit{Diversification Benefit} = \max\left(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}\right)

Understand the Life Risk

What this calculator does

This calculator implements the Life Underwriting Risk module within the standard formula. It aggregates the main life underwriting stresses into the diversified life-risk term that feeds into BSCR^[1]^[2].

Input terms

Mortality Risk: The change in net asset value from the prescribed permanent increase in mortality rates^[3].
Longevity Risk: The change in net asset value from the prescribed decrease in mortality rates for annuity-like exposures^[4].
Disability-Morbidity Risk: The combined disability-incidence and recovery stress used for relevant life-health exposures^[5].
Life Expense Risk: The combined expense-level and expense-inflation stress^[6].
Revision Risk: The stress for annuities whose payment level may be revised upward^[7].
Lapse Risk: The worst result across lapse-up, lapse-down, and mass-lapse scenarios, depending on which direction is adverse for the contract set^[8].
Life Catastrophe Risk: The short-term mortality catastrophe stress for mass-casualty or pandemic-style events^[9].

Calculation

Each sub-module is calculated independently as a change in net asset value under the prescribed actuarial stress, and the resulting standalone charges are then combined through the standard-formula life correlation matrix^[1]. The structure recognizes that demographic risks can share some common drivers while still behaving differently enough to justify diversification, most notably between mortality and longevity books^[1].

Important notes

Mortality and longevity are not simply additive.: The life matrix recognizes a natural hedge between mortality-heavy and longevity-heavy portfolios, although each sub-module charge is still floored at zero^[1].
Lapse stresses are adverse-direction stresses.: The relevant scenario depends on the economics of the policy, so lapse-up is not automatically the binding shock for every product^[8].
Reinsurance reduces the net underwriting charge,: but the residual reinsurer non-payment exposure still needs to be captured separately in counterparty default risk^[10]^[11].
Simplifications exist: for undertakings that qualify to use the prescribed simplification routes rather than a full change-in-net-asset-value approach^[11].
Reporting: The life-risk result is intended to reconcile to the life-underwriting part of the Solvency II QRT package, including the S.26 family of views^[12].

Sources