IFoA SP1 flashcards

33 cards. Read the term and the definition here. The deck at the top of this page is optional.

Prospective reserve

The reserve at time t equals the expected present value of future benefits minus the expected present value of future net premiums, calculated on the same valuation basis.

Recursive reserve formula

(V_t + P)(1+i) = q·S + p·V_{t+1}. It links successive reserves and lets you roll reserves forward or backward using mortality and interest assumptions.

Asset share

The accumulated value of premiums less charges and cost of cover, credited with actual investment returns. It drives with-profits payouts, smoothing and the distribution of the estate.

Risk discount rate

The rate used to discount projected profit-testing cash flows. It reflects the required return for the risks borne and determines NPV and the internal rate of return.

Guaranteed annuity option

A policyholder right to convert the fund at a guaranteed rate. It is valuable when rates fall, so it must be valued stochastically or with option-pricing methods.

Unit-linked non-unit reserve

A reserve held in addition to the unit fund to cover expected future expense and mortality strains, because the insurer cannot rely on future charges being sufficient.

Mortality improvement projection

An assumption about how future death rates decline over time, usually cohort-based. Annuity pricing is highly sensitive to it, so static tables are inadequate.

Gross premium

Expected present value of benefits plus expenses plus profit and risk margins, divided by the expected present value of an annuity of premiums, all on the pricing basis.

IBNR

Incurred but not reported claims: the estimated cost of claims that have occurred but have not yet reached the insurer, typically estimated by chain-ladder or Bornhuetter-Ferguson methods.

Chain-ladder factors

Development factor f_k = Σ C_{i,k+1} / Σ C_{i,k} across origin periods. Ultimate claims equal the latest cumulative claims multiplied by the product of remaining factors.

Bornhuetter-Ferguson method

Ultimate = reported claims + expected ultimate × proportion unreported. It blends an a-priori loss ratio with actual data, stabilising estimates for immature accident years.

Combined ratio

Losses divided by earned premium plus expenses divided by earned premium. A value above 100% indicates an underwriting loss; it is a key measure of general insurance performance.

Risk margin

An addition to the best-estimate liability representing the cost of holding the required capital. It is separate from the best estimate and reflects the transfer value of the liabilities.

Quota share reinsurance

The reinsurer takes a fixed percentage of every policy's premium and claims. It reduces both volatility and expected profit proportionally, and improves the solvency position.

Excess of loss reinsurance

The reinsurer pays claims above a retention up to a limit per risk or event. It protects against large individual losses and catastrophes rather than average claim frequency.

Unexpired risk reserve

A provision for claims arising after the valuation date on policies already written. It equals the expected cost of the unexpired period and is part of technical provisions.

Macaulay duration

The present-value-weighted average time of cash flows: Σ t·PV(CF_t)/Σ PV(CF_t). Modified duration equals Macaulay duration divided by (1 + yield).

Convexity adjustment

ΔP/P ≈ −D*·Δy + ½·C·(Δy)². Positive convexity means the price gain from a yield fall exceeds the loss from an equal rise.

Immunisation

Matching the present value and duration of assets to liabilities. It protects against small parallel yield shifts but not against large or non-parallel moves.

Put-call parity

For European options on a non-dividend stock: C − P = S − K·e^{−rT}. A deviation from this relation implies an arbitrage opportunity.

Capital Asset Pricing Model

E[R_i] = r_f + β_i(E[R_m] − r_f), with β = Cov(R_i,R_m)/Var(R_m). Only systematic risk earns a premium because idiosyncratic risk is diversifiable.

Value at Risk

The loss that will not be exceeded with a given probability over a given horizon. It is a quantile and ignores the size of losses beyond that point.

Expected shortfall

The average loss conditional on exceeding the VaR threshold. It is sub-additive and captures tail severity, unlike VaR, and is therefore a coherent risk measure.

Forward rate relationship

Spot and forward rates satisfy (1+s_n)^n = Π(1+f_k). The shape of the curve is explained by expectations, liquidity preference and market segmentation theories.

Risk-neutral pricing

The price of a derivative equals the expected discounted payoff under the risk-neutral measure, equivalent to the cost of a self-financing replicating portfolio.

DB funding contribution

Contribution = benefits paid + expenses − investment income + increase in deficit, where the deficit is the past-service liability minus scheme assets on the funding basis.

Final salary vs CARE

Final salary links benefit to pay at retirement; career average (CARE) accrues each year on that year's pay, revalued. CARE reduces salary-inflation and late-career pay risk.

Buy-in versus buy-out

A buy-in holds a bulk annuity as a scheme asset while the scheme retains the liability. A buy-out transfers both assets and liabilities to the insurer.

Longevity swap

A derivative in which the scheme pays fixed amounts and receives amounts linked to actual survivor experience, transferring longevity risk to the counterparty.

Pay-as-you-go state scheme

Current contributions fund current benefits, with no accumulated fund. The unfunded liability depends on demographic and economic assumptions and on future contribution rates.

Technical provisions

The funding-basis value of benefits accrued to date minus the value of future contributions, determined under the scheme funding regime with a recovery plan for deficits.

Income protection deferred period

The waiting period before benefit starts after a claim. A longer deferred period reduces claim cost and is often matched to employer sick-pay arrangements.

Critical illness survival period

The time a claimant must survive after diagnosis before the sum assured is paid. It reduces claim cost and must be consistent with the incidence assumptions used in pricing.