9.5 Risk margins and solvency capital requirements

Definition of risk margins

Risk margins are an additional amount held on top of the best estimate of liabilities, designed to buffer against uncertainty in the valuation of insurance liabilities. They ensure an insurer can meet its obligations with a high degree of confidence, even when actual experience deviates from assumptions.

Risk margins are closely tied to technical provisions, which represent the total amount an insurer sets aside to cover future claims and expenses.

Role in solvency assessment

Risk margins help ensure an insurer holds sufficient financial resources to withstand adverse events and fulfill obligations to policyholders. By including them in the valuation of liabilities, insurers demonstrate their capacity to absorb potential losses and maintain financial stability.

Solvency frameworks like Solvency II (the EU regulatory regime) require insurers to calculate and hold adequate risk margins as part of their overall capital requirements.

Relationship to technical provisions

Technical provisions have two components:

• Best estimate of liabilities: the expected present value of future cash flows related to insurance obligations, based on realistic assumptions about mortality, morbidity, expenses, and other factors.
• Risk margin: an addition to the best estimate that accounts for the uncertainty in those assumptions and provides extra protection against adverse deviations.

Together, these form a key element of an insurer's balance sheet and solvency assessment.

Calculation of risk margins

Calculating risk margins means quantifying the additional capital needed to cover uncertainty in liability valuations. The choice of method and parameters depends on the insurer's specific business profile and risk characteristics.

Cost-of-capital approach

The cost-of-capital (CoC) approach is the primary method under Solvency II. The underlying principle: an insurer should hold enough capital to cover the cost of transferring its liabilities to a willing third-party insurer if it can no longer meet its obligations.

The risk margin under this approach is calculated as:

$RM = CoC \cdot \sum_{t \geq 0} \frac{SCR(t)}{(1 + r_{t+1})^{t+1}}$

where:

• $CoC$ is the cost-of-capital rate (set at 6% under Solvency II)
• $SCR(t)$ is the projected Solvency Capital Requirement at time $t$
• $r_{t+1}$ is the risk-free discount rate for maturity $t+1$

In words, you're discounting the cost of holding the required capital at each future time point back to the present.

Assumptions and parameters

Several assumptions drive the result:

• Risk-free rate: used to discount future capital costs
• Cost-of-capital rate: the return investors would require to take on the insurer's liabilities (fixed at 6% under Solvency II)
• Projection period: the time horizon over which future cash flows are considered
• Granularity: whether risk margins are calculated by line of business, by product, or at a more aggregate level
• Diversification effects: how offsetting between different risk sources is treated

Small changes in these parameters can significantly affect the final risk margin, so careful calibration matters.

Projection of future SCRs

To apply the cost-of-capital approach, insurers must project their future SCRs over the full lifetime of their liabilities. This involves:

1. Estimating the capital required to cover risks at each future time point
2. Accounting for expected business growth, changes in risk profile, and the runoff of existing liabilities
3. Aggregating across risk modules while reflecting diversification

This projection is computationally demanding and often requires simplification techniques (such as proportional methods or driver-based approximations) alongside expert judgment.

Solvency capital requirements (SCR)

The Solvency Capital Requirement (SCR) is the cornerstone of modern solvency frameworks like Solvency II. It represents the capital an insurer must hold to ensure it can meet obligations to policyholders over the next 12 months with a 99.5% confidence level.

Definition and purpose

Formally, the SCR is defined as the Value-at-Risk (VaR) of an insurer's basic own funds at the 99.5% confidence level over a one-year time horizon:

$SCR = VaR_{0.995}(\Delta BOF)$

where $\Delta BOF$ represents the change in basic own funds over one year.

This means the insurer holds enough capital to survive a 1-in-200-year adverse event without defaulting. The purpose is to ensure financial resilience and protect policyholders even under severe stress.

Regulatory framework

SCR calculations are governed by regulatory frameworks. Under Solvency II:

• The European Insurance and Occupational Pensions Authority (EIOPA) oversees implementation and enforcement
• Detailed rules cover calculation principles, reporting obligations, and disclosure requirements
• Insurers must demonstrate compliance on an ongoing basis, not just at a single point in time

Standard formula vs. internal models

Solvency II gives insurers two options for calculating the SCR:

Internal models offer greater accuracy but require substantial investment and regulatory approval. Most smaller insurers use the standard formula.

SCR calculation

The SCR is calculated using a modular approach that breaks overall risk into sub-components, each targeting a specific risk category. Individual charges are then aggregated using correlation matrices.

Structure of standard formula

The standard formula follows a tree-like structure:

1. Calculate capital charges for each sub-module (e.g., interest rate risk, equity risk, mortality risk)
2. Aggregate sub-modules into risk modules using correlation matrices
3. Aggregate risk modules into the Basic SCR (BSCR) using a higher-level correlation matrix
4. Add the operational risk charge separately
5. Adjust for the loss-absorbing capacity of technical provisions and deferred taxes

$SCR = BSCR + SCR_{op} - Adj$

where $Adj$ represents the loss-absorbing capacity adjustments.

Risk modules and sub-modules

The main risk modules are:

• Market risk: losses from fluctuations in financial markets (interest rates, equity prices, property values, exchange rates, credit spreads)
• Counterparty default risk: losses from default or credit deterioration of counterparties such as reinsurers, derivatives counterparties, and intermediaries
• Life underwriting risk: risks from life insurance contracts, including mortality, longevity, disability, lapse, and expense risks
• Non-life underwriting risk: risks from non-life policies, including premium and reserve risk, lapse risk, and catastrophe risk
• Health underwriting risk: risks from health insurance obligations, split into those similar to life techniques (SLT) and those that are not (non-SLT)
• Operational risk: losses from inadequate or failed internal processes, people, systems, or external events

Correlation matrices

Correlation matrices aggregate capital charges across modules and sub-modules. They reflect the dependencies between risk factors and allow for diversification benefits, since not all risks will materialize at the same time.

The aggregation formula for two risk modules follows:

$SCR_{agg} = \sqrt{\sum_i \sum_j \rho_{ij} \cdot SCR_i \cdot SCR_j}$

where $\rho_{ij}$ is the prescribed correlation coefficient between modules $i$ and $j$.

The correlation coefficients are set by the regulator based on industry research and consultation.

Diversification benefits

Because risks are not perfectly correlated, a diversified portfolio of risks can reduce overall capital requirements. Losses in one area may be partially offset by stability or gains in another.

The standard formula explicitly captures this through the correlation matrices. However, there are limits: regulators ensure insurers don't rely too heavily on diversification and maintain a prudent capital level. The aggregated SCR will always be less than the simple sum of individual module charges, but greater than the largest single module charge.

Market risk module

The market risk module captures potential losses from adverse movements in financial markets. Capital requirements are calculated using standardized stress scenarios applied to the insurer's assets and liabilities.

Interest rate risk

Interest rate risk reflects the sensitivity of assets and liabilities to changes in interest rates. The standard formula applies both upward and downward shocks to the yield curve using prescribed stress factors.

The capital requirement equals the larger loss from the two scenarios:

$SCR_{int} = \max(SCR_{int}^{up}, SCR_{int}^{down})$

Assets affected include bonds and other fixed-income instruments. On the liability side, insurance contracts with guaranteed returns are particularly sensitive.

Equity risk

Equity risk covers losses from changes in equity prices. The standard formula distinguishes two exposure types:

• Type 1: listed equities in developed markets, subject to a 39% downward shock
• Type 2: unlisted equities, private equity, hedge funds, and other alternatives, subject to a 49% downward shock

A symmetric adjustment mechanism can modify these shocks based on recent equity market performance, dampening procyclical effects.

Property risk

Property risk captures losses from declining real estate values. The standard formula applies a 25% downward shock to the value of all property investments. Insurers calculate the resulting impact on their property portfolio to determine the capital charge.

Spread risk

Spread risk arises from changes in credit spreads over the risk-free rate. The standard formula applies risk factors to the market value of fixed-income investments, calibrated by:

• Credit quality (rating)
• Duration of the instrument

Higher-duration and lower-rated bonds attract larger capital charges.

Currency risk

Currency risk covers losses from exchange rate movements. The standard formula applies a 25% upward or downward shock to the insurer's net foreign currency exposures. The capital charge is the larger loss from the two directional scenarios.

Concentration risk

Concentration risk addresses the additional danger from insufficient diversification or large single-name exposures. The standard formula:

1. Compares each counterparty exposure against prescribed threshold values (which vary by credit quality)
2. Applies capital charges to the excess above those thresholds
3. Aggregates charges across all exposures

The charges increase as concentration levels rise, penalizing portfolios that are heavily tilted toward a few counterparties.

Life underwriting risk module

This module addresses risks specific to life insurance contracts, where actual experience may deviate from the assumptions used in pricing and reserving. Capital requirements are based on standardized stress scenarios applied to each sub-risk.

Mortality risk

Mortality risk arises when actual death rates exceed those assumed. The standard formula applies a permanent 15% increase to best estimate mortality rates. The capital charge equals the resulting increase in life insurance liabilities.

Longevity risk

Longevity risk is the opposite concern: policyholders (particularly annuitants) living longer than expected, leading to higher annuity payments. The stress is a permanent 20% decrease in best estimate mortality rates for annuity contracts.

Disability-morbidity risk

This sub-module captures losses from higher-than-expected disability or morbidity rates. The standard formula applies combined stresses to:

• Best estimate disability and morbidity inception rates
• Recovery rates
• Termination rates

Lapse risk

Lapse risk reflects uncertainty about whether policyholders will surrender, lapse, or continue their contracts. The standard formula tests three scenarios:

1. Permanent increase in lapse rates
2. Permanent decrease in lapse rates
3. Mass lapse event (a large proportion of policies lapsing simultaneously)

The capital requirement is the maximum loss across these three scenarios.

Expense risk

Expense risk covers the possibility that administration and servicing costs exceed assumptions. The standard formula applies:

• A 10% permanent increase to best estimate expense assumptions
• A 1 percentage point increase to the expense inflation rate

Revision risk

Revision risk applies to annuities subject to revision (e.g., workers' compensation annuities where benefits can be revised upward). The stress is a permanent 3% increase in revision rates.

Catastrophe risk

Life catastrophe risk covers extreme events not captured by the other sub-modules, such as pandemics or large-scale terrorist attacks. The standard formula uses prescribed stress scenarios that vary by geography and contract type. The capital charge is the maximum loss across the relevant scenarios.

Non-life underwriting risk module

This module addresses risks from non-life insurance contracts, where claims frequency, severity, and expenses may deviate from pricing and reserving assumptions.

Premium and reserve risk

These are the two core non-life risks:

• Premium risk: the risk that premiums charged are insufficient to cover actual claims and expenses for future exposure periods
• Reserve risk: the risk that reserves for outstanding claims prove inadequate

The standard formula applies prescribed volume-based factors that vary by line of business and geographical segment. The capital charge is aggregated across all segments, accounting for diversification.

Lapse risk

Non-life lapse risk captures losses from policyholders discontinuing or surrendering contracts. The standard formula applies a stress combining a permanent increase in lapse rates with a mass lapse event. This is most relevant for multi-year non-life contracts where future profitable premiums would be lost.

Catastrophe risk

Non-life catastrophe risk covers extreme events beyond what premium and reserve risk captures. The standard formula uses standardized scenarios for:

• Natural catastrophes: windstorms, earthquakes, floods, hail
• Man-made catastrophes: industrial accidents, large fires, aviation disasters, marine losses
• Other catastrophes: pandemic-type health events affecting non-life lines

Insurers calculate capital charges for each relevant scenario and aggregate them to determine the total non-life catastrophe risk charge. Reinsurance and other risk mitigation can be reflected in the calculation.

Health underwriting risk module

The health underwriting risk module captures risks from health insurance contracts. It is split into two categories based on how the business is modeled:

• SLT health (similar to life techniques): health insurance that resembles life insurance in its long-term nature, such as disability income or long-term care. The sub-modules mirror the life underwriting risk structure (mortality, longevity, disability-morbidity, lapse, expense, and revision risk).
• Non-SLT health: health insurance modeled using non-life techniques, typically short-term contracts. The sub-modules mirror non-life underwriting risk (premium and reserve risk, lapse risk).
• Health catastrophe risk: covers mass accident events, pandemic scenarios, and concentration risks specific to health portfolios.

The capital charges from these three components are aggregated using a correlation matrix to produce the total health underwriting risk charge.