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.
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.
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.
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.
Number of survivors to exact age x from a radix of 100,000. Derived from qₓ as lₓ₊₁ = lₓ × (1 − qₓ).
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.
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.
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.
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.
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).
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.
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.
Expected present value of future cash flows (premiums, claims, expenses) using best-estimate assumptions — no prudence margin. The central component of the technical provisions.
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.
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.
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.
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.
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).
The main IFRS 17 measurement model, also called the Building Block Approach (BBA). Liability = BEL + RM + CSM. Required for most long-term insurance contracts.
Simplified model for short-duration contracts (coverage period ≤12 months, or where results approximate GMM). Similar to current IFRS 4 unearned premium reserve 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.
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.