Final Revision Flashcards
Describe the contribution method
Better interest
plus better mortality
plus better expenses and interest
Give the formula for contribution dividend
(V0+P)(i’-i)
+ (q-q’)(S-V1)
+ E(1+i) - E’(1+i’)
How is the contribution dividend paid, does it have a TB?
Dividend converted to paid up addition to benefit, not paid out in cash.
Yes.
Give the formula to reconcile data
Data(t-1)+NB-Run off Biz=Data(t)
What type of benefits can you have
Guaranteed (monetary/price index or similar)
Discretionary
Investment linked
What’s the formula for liability outgo?
Benefit payments + Expense outgo - Premium income
What is the words formula for appropriation price? Expropriation price?
NAV(offer basis)/#Units at valn date
NAV(bid basis)/#Units at valn date
In decided what goes into the NAV, what things are the same for both expropriation and appropriation?
What is different, how?
Same:
Current (Assets-Liabs)
+Accrued income
-Allowance for accrued tax
Different:
Market price of assets on offer basis+expenses incurred purchasing them (buying assets at high price)
MP of assets on bid basis-expenses incurred selling them (selling assets at low price)
Explain the bid offer spread? Which one is buying and selling, highest and lowest?
Offer = high price = price to buy Bid = low price = price to sell asset
Which is the lowest, bid or offer?
BID!
Is appropriation on offer or bid?
Offer
What basis are units prices if a net seller of units? What does that mean for the bid/offer price?
Bid basis
Find bid and offer using expropriation price
If company a net seller, what basis will it use, what’s the formula for offer price and bid price.
What about if it’s a net buyer?
Bid basis: Offer price: (buying) Expropriation price PLUS initial charge (bid-offer) Bid Price (selling) Expropriation price
Offer basis: Offer price: (buying) Appropriation price plus initial charge (bid-offer) Bid Price (selling) Appropriation price
Assets now = 10 Current assets = 2 Current Liabs = 4 #Units = 100 Selling cost of all assets = 3 Purchase cost of all assets = 1 Initial charge of 10% on bid and offer prices Net seller What is appropriation price? What is the bid price? (in words)
Net seller = exproprtiation basis for the bid price Appropriation price (buying) = (10+1+(2-4))/100 Bid price on expropriation basis = Expropriation price
Which price relates directly to whatever basis it’s on? Which price related to the basis including charges?
The bid price (appropriation or exp price)
The offer price (approp/exp price + init charge)
Explain what actuarial fund does?
Allows us to hold the present value of the unit fund
Explain the actuarial funding factor formula?
Unit fund at t * A(x+t:n-t)
ie. PV of current unit fund paid at death
T=0 normally
What formula shows the amount transferred to non-unit fund using actuarial funding
UF(0)*(1-A(x:n)) is transferred to the unit fund
ie. Difference between original unit fund and the PV of it
Give an alternative to actuarial funding factor that takes credit for future charges, what loan does it represent
Negative non-unit reserves
One from policyholders with positive non unit reserves repaid on future emerging profits
Give 3 constraints to negative non-unit reserves
Sum of all non-unit reserves >= 0
Sum of unit and non-unit reserve on policy >=guaranteed SV
Future profits must arise to repay loan
What risk is transferred BACK to company by guaranteed (maturity, surrender or annuity option), why?
Investment risk, attractive
What 2 guarantees are attractive on traditional policies?
GAO
Guaranteed minimum maturity value on EA
What’s the difference between risk of guarantees in a traditional policy or non-traditional policy
Company has no control over investment policy in non-traditional
How to value an option or guarantee (2 ways)
Option pricing technique
Stochastic simulated investment performance
Give 3 common mortality options
Additional benefit purchase without need for further health evidence Renewable policy (no further health evidence) Convertible policy - change part of SA from one contract to another
Why use T’s and C’s for mortality options, explain what it means for premium rates
Reduce anti-selection
ie. Those in poor health using option to get large amounts of life insurance at rates not reflecting their condition
Give some T’s and C’s examples for mortality options
Timing - fixed take up times
Birth child
Salary increase
SA(additional)<=SA(original)
Explain the cost of a mortality option
Difference between price should have charged given full underwriting information and price actually charged
What 2 assumptions over the normal pricing basis are needed to value a mortality option
P(option exercised)
qx of those who take-up option
How to get the EPV of cost of mortality option
EPV(ben) - EPV (prem)
Why is the conventional method the preferred choice in mortality option pricing?
NA requires double decrement tables
Difficult to obtain such data
NB won’t have it
What mortality assumptions are made in the North American method?
EPV(B) assumes lives not taking up option are Ult. Meaning average mortality is higher than Ult.
OR
Average mortality for all lives is Ult, change mortality of those who don’t take up to reflect
What assumptions underly the conventional method?
All lives eligible to take up option will do so
Mortality of those taking up option is Ult version of Select of those joiners
What data is needed in the conventional method?
Sel/Ult mortality tables
Give a problem with the conventional method?
How to get around it?
If multiple options/take up dates can’t be used
Choose worst option from a financial point of view is chosen with Probability 1.
Give the principle of surrender values
Simple PETS, DD CC ME
Take into account:
Simple
PRE
Equitable treatment of continuing and surrendering
TCF
SVmaturity, SV->Mat value
Discontinuities - don’t suffer by duration
Documented - clearly
Competitors - take account of them
Change - not too frequent
Minimal - Not exceed EAS in aggregate
Early - Not appear too low at early durations vs. premiums paid
Why don’t term assurance have SV?
Anti selection reduced
Cheaper premiums
Small reserve release anyway (reserves don’t tend to the sum assured)
What does A with a line on top of it mean?
An assurance of 1 payable at the exact moment of death
To calculate a proper retrospective reserve, not formula driven, what do you need?
Up to date EAS for reach policy