IFoA CM1 key terms

The factor by which a unit investment grows over a period, equal to one plus the effective rate of interest for that period; used to move cashflows forward in time.

The present value of one unit payable at a future date, equal to the reciprocal of the accumulation factor; used to move cashflows backward in time.

The actual rate earned over a unit time period after compounding within that period; differs from nominal rates when compounding frequency is greater than once per period.

A rate quoted per unit time but convertible more frequently, such as convertible monthly; it must be divided by the conversion frequency before being applied to each sub-period.

The instantaneous rate of growth of a fund, defined as the derivative of the log of the accumulation function; constant force corresponds to continuous compounding.

The amount that must be invested now, at a given rate of interest, to meet a specified future cashflow or stream of cashflows.

The amount to which an initial investment or series of payments has grown by a specified later date, allowing for interest earned over the intervening period.

A series of payments made at specified times over a fixed term, where payment does not depend on survival; valued using interest functions only.

An equation equating the present or accumulated value of assets and liabilities at a chosen comparison date, used to solve for unknown rates, amounts or timing.

The annual effective yield on a zero-coupon bond maturing at a given future date, representing the rate for a single payment at that term.

The interest rate agreed now for lending or borrowing over a future period; implied by the ratio of spot discount factors at the start and end of that period.

The relationship between spot or redemption yields and term to maturity at a point in time; may be upward sloping, flat or inverted.

A stochastic process in which successive changes are independent and identically distributed; the discrete-time building block for simple models of log asset prices.

A continuous-time process in which the logarithm of the asset price follows Brownian motion with drift, giving strictly positive prices and lognormal returns over any horizon.

The distribution of a variable whose logarithm is normal; used for asset prices under geometric Brownian motion, so returns over a period are normally distributed.

A representation of a contract as a set of payments at specified times, each contingent on defined events such as survival, death or surrender.

A probability model for the future lifetime of a life, specified by a survival function or force of mortality, from which payment probabilities are derived.

The random present value of the benefits payable under a contract, where randomness arises from the time of payment and possibly from interest rates.

The premium basis under which the expected present value of future premiums equals the expected present value of future benefits plus expenses at outset.

The probability that a life aged zero survives to at least age x; a non-increasing function starting at one and tending to zero.

The instantaneous rate of mortality at a given age, equal to minus the derivative of the log of the survival function; the continuous-age analogue of the mortality rate.

A mortality law in which the force of mortality increases exponentially with age, producing a straight line when its logarithm is plotted against age.

A mortality law adding a constant to the Gompertz form, so the force of mortality has an age-independent component plus an exponentially increasing component.

A tabulation by age of survivors, deaths and derived probabilities from a radix, used to compute assurance and annuity values.

Mortality that depends on duration since underwriting as well as attained age, typically lower in early durations; shown by select and ultimate columns in a table.

A model in which lives are exposed to two or more mutually exclusive causes of exit, such as death and withdrawal, with dependent probabilities derived from independent rates.

A model in which a life moves between states such as healthy, sick and dead, with transition intensities governing movement; includes permanent disability and income protection.

A payment contingent on death or another insured event, such as whole life, term or endowment assurance, valued as an expected present value.

A series of payments contingent on the survival of a named life, payable for life or a fixed term; valued using survival probabilities and interest.

The premium determined by the equivalence principle ignoring expenses, so that expected benefit outgo equals expected premium income at issue.

The premium actually charged, equal to the net premium plus a loading to cover expenses, profit and margins for risk and adverse experience.

The retrospective or prospective value of future benefits less future net premiums at a given duration, computed on the premium basis.

A reserve allowing for future expenses and the actual gross premium, typically lower than the net premium reserve in early durations.

The set of assumptions, including interest, mortality, expenses and persistency, used to value liabilities; usually more prudent than the premium basis.

A projection of premiums, benefits, expenses and reserves by duration to derive emerging profit, its present value and a profit signature.

A comparison of actual and expected experience by source, such as interest, mortality, expenses and persistency, to explain the change in surplus over a period.

The capital a life insurer must hold so that assets cover liabilities with a prescribed high probability over a specified horizon, as under risk-based capital regimes.

A pension arrangement promising benefits based on salary and service, with the sponsor bearing investment and longevity risk.

A pension arrangement where contributions are invested and benefits depend on the accumulated fund at retirement, so the member bears investment risk.

A pension funding method spreading the cost of benefits over service, with the contribution rate set so assets meet liabilities by a chosen target date.