Extras 9

Question 1

Why is the conventional method the preferred choice in mortality option pricing?

Answer 1

NA requires double decrement tables
Difficult to obtain such data
NB won’t have it

Question 2

What mortality assumptions are made in the North American method?

Answer 2

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

Question 3

What assumptions underly the conventional method?

Answer 3

All lives eligible to take up option will do so

Mortality of those taking up option is Ult version of Select of those joiners

Question 4

What data is needed in the conventional method?

Answer 4

Sel/Ult mortality tables

Question 5

Give a problem with the conventional method?

How to get around it?

Answer 5

If multiple options/take up dates can’t be used

Choose worst option from a financial point of view is chosen with Probability 1.

Question 6

Give the principle of surrender values

Answer 6

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

Question 7

Why don’t term assurance have SV?

Answer 7

Anti selection reduced
Cheaper premiums
Small reserve release anyway (reserves don’t tend to the sum assured)

Question 8

What does A with a line on top of it mean?

Answer 8

An assurance of 1 payable at the exact moment of death

Question 9

To calculate a proper retrospective reserve, not formula driven, what do you need?

Answer 9

Up to date EAS for reach policy

Question 10

Give a formula for retrospective SV

Answer 10

(1+i)^t  * 1/tPx * (Pax:t - SA(x:t)-I-Ra(x:t) - DA(x:t)) -  C
P = premiums annual
S = SA
I = Initial expenses
R=Renewal expense
D=Claims expense
C = Charge for surrendering (admin type)

Question 11

Give a formula for prospective SV

Answer 11

SA(x:t) + Ra(x:t) + DA(x:t) - Pa(x:t) - C

Value of Future sum assured plus expenses net of future premiums and charge

Question 12

What is the formula for Profit retained?

Answer 12

(EAS-SV(pricing assumps)) + (SV(pricing) - SV(actual assumps used))

Question 13

What does retrospective reserves represent, why is it not that good for companies?

Answer 13

The EAS at surrender, takes all the profits away so no loss, no gain. Profit = EAS-SV

Question 14

Give 2 disadvantages of retrospective

Answer 14

SV does not run into Mat Value

Not say anything about what profit would have been made, so equity between policyholders hard

Question 15

Give an advantage of retrospective

Answer 15

Not complex if EAS available

Question 16

What does prospective SV represent if done on realistic basis?

Answer 16

Value of the contract to company

Question 17

Why use prospective SV

Answer 17

Enables calculation of how much profit company wants to keep

So maintain equity

Question 18

Give disadvantages of propsepective SV

Answer 18

total SV’s might be > total EAS
Possible unreasonable SV’s early on
Small changes in interest rate, for long durations, have big SV effect

Question 19

Advantage of prospective SV

Answer 19

SV’s -> maturity value for without profits
Comparable to auction values
more likely comparable to competition
Easy to do, doesn’t require knowledge of past

Question 20

How does a company profit from SV’s?

Answer 20

Pay out less that EAS

ie. profit is EAS-SV