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Docs/Domain Glossary

Domain Glossary

Actuarial terms, formulas, and implementation notes used across the marketplace. Terms with a Python snippet show how the concept is implemented in code — click to expand.

21 / 21 terms
Mortality Modeling
qₓ
Annual mortality rate

Probability of death between exact age x and x+1. In the Gompertz model: qₓ = min(0.99, A × exp(B × x)) where A=0.00009 and B=0.091.

↓ implementation
S(x, t)
Survival function

Probability of surviving from age x to age x+t. Computed as the cumulative product of (1−qₓ₊ₛ) for s=0 to t−1.

↓ implementation
e̊ₓ
Curtate life expectancy

Expected remaining lifetime at current age. Sum of survival probabilities from t=1 onward: Σ S(x, t) for t=1 to max_age−x.

↓ implementation
lₓ
Life table survivors

Number of survivors to exact age x from a radix of 100,000. Derived from qₓ as lₓ₊₁ = lₓ × (1 − qₓ).

Mortality shock
Solvency II mortality stress

Stressed mortality rate under Solvency II SCR Life module: qₓ_stressed = qₓ × (1 + shock_rate/100). Tests whether reserves are adequate if actual mortality exceeds best estimate.

↓ implementation
Gompertz slope (B)
Makeham-Gompertz B parameter

Rate at which mortality increases with age. Value B=0.091 means mortality doubles roughly every 7.6 years (ln(2)/0.091). Calibrated to UK population data.

Portfolio Pricer
GBM
Geometric Brownian Motion

Stochastic process used to model asset prices: S(t) = S(0) × exp((μ − σ²/2)t + σW(t)). Ensures prices remain positive and exhibit log-normal returns.

μ (mu)
Expected annual return

Drift parameter of the GBM model. A value of 0.07 means 7% expected annual return before volatility correction. Applied as monthly drift: (mu − 0.5 × sigma²) × dt where dt=1/12.

↓ implementation
σ (sigma)
Annual volatility

Standard deviation of log-returns, annualized. A value of 0.20 means 20% annualized volatility. Monthly diffusion: sigma × sqrt(dt) × Z where Z~N(0,1).

↓ implementation
Equal weighting
Portfolio construction method

Each of the n_assets assets represents 1/n_assets of the portfolio. Portfolio value P(t) = (1/n_assets) × Σ Sᵢ(t). Starting value is the average of random initial prices, not normalized to 100.

Solvency II
SCR
Solvency Capital Requirement

Amount of capital required to withstand a 1-in-200 year shock (99.5th percentile VaR over one year). The key regulatory capital requirement under Solvency II.

BEL
Best Estimate Liability

Expected present value of future cash flows (premiums, claims, expenses) using best-estimate assumptions — no prudence margin. The central component of the technical provisions.

RM
Risk Margin

Cost of capital charge for non-hedgeable risks. Calculated as the cost of holding SCR for the runoff of the portfolio, at 6% cost of capital rate.

ORSA
Own Risk and Solvency Assessment

Annual self-assessment of capital needs, risk profile, and solvency position under own stress scenarios. Required by Solvency II Article 45. Not the same as the standard formula SCR.

MCR
Minimum Capital Requirement

Hard floor below which the regulator withdraws authorization. Calculated as a percentage of technical provisions and premiums, floored at 25% of SCR and capped at 45% of SCR.

QIS
Quantitative Impact Study

Calibration exercises run by EIOPA to assess the impact of proposed Solvency II parameters. QIS5 (2010) was the last major study before the Directive came into force in 2016.

IFRS 17
CSM
Contractual Service Margin

The unearned profit in an insurance contract at inception. Released to the P&L over the coverage period as insurance service is provided. Cannot be negative at initial recognition (day-1 loss recognized immediately).

GMM
General Measurement Model

The main IFRS 17 measurement model, also called the Building Block Approach (BBA). Liability = BEL + RM + CSM. Required for most long-term insurance contracts.

PAA
Premium Allocation Approach

Simplified model for short-duration contracts (coverage period ≤12 months, or where results approximate GMM). Similar to current IFRS 4 unearned premium reserve approach.

VFA
Variable Fee Approach

Modification of GMM for contracts where the entity participates in returns from underlying assets (e.g. unit-linked, with-profits). CSM adjusts for changes in the entity's share of fair value returns.

RA
Risk Adjustment

Compensation required for bearing uncertainty in the amount and timing of non-financial risk. IFRS 17 does not prescribe a calculation method — common approaches include CoC method (like Solvency II RM) and VaR/CTE.

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