F_Short q's 8

Question 1

• Profitability: cross subsidies

Answer 1

 The premium should cover benefit payments, expenses and a profit margin.
 If there are cross-subsidies, the additional risk may mean that the product needs to be priced with a bigger profit margin requirement to compensate for the additional risk.
 The sensitivity of profits to changes in business mix may inform the decision on the size of the required margin.

Question 2

• Financing Requirements: cross subsidies

Answer 2

 Cross-subsidies introduce additional risk, which may affect the solvency reserves required on the product, increasing capital required.
 This in turn affects the profit margin requirements for this product.

Question 3

iii. The company also offers guaranteed annuity options at maturity for its with-profit endowment assurances.

Outline how the company can make use of:
a. a put option strategy; and

to reserve for the cost of its guaranteed annuity options. You may assume that the guaranteed annuity options apply only to level annuities. [4]

Answer 3

A portfolio of fixed interest stock/bonds would match the annuity
Put option
Or use a put on an interest rate
So if interest rates reduce below the implied guaranteed rate, the increased cost to the company of providing the guarantee is offset by an increase in the value of the put option.
This is a market-consistent approach to liability valuation and hence market values of assets would need to be adopted.

Question 4

iii. The company also offers guaranteed annuity options at maturity for its with-profit endowment assurances.

Outline how the company can make use of:

b. a call option strategy,

to reserve for the cost of its guaranteed annuity options. You may assume that the guaranteed annuity options apply only to level annuities. [4]

Answer 4

A portfolio of fixed interest stock/bonds would match the annuity
Call option
The current cost of call options on such a bond portfolio could be used
Strike date is the policy maturity date
So if interest rates reduce below the implied guaranteed rate, the increased cost to the company of providing the guarantee is offset by an increase in the value of the call option
Hence the value of the call option represents the expected cost of the annuity guarantee provided by the company

Question 5

The multinational life company for which you work has just released its financial year-end results. The analysis of change in the embedded value shows a substantial increase in the value of in-force business from the previous year.
Discuss possible reasons for this increase. [4]

Answer 5

Possible reasons:
• Experience may have been better than expected (i.e. a positive experience variance).
• Substantially more new business sold in the year. This will add to the value of in force provided the business is profitably priced.
• A change in valuation basis. Changes in basis assumption may result in an increase in the value. For example, higher assumed investment return may result in higher future margins and hence a higher value of in force.
• Reduction in the discount rate used. The lower the discount rate used to calculate the value of in force, the higher the value will be.
• Exchange rate movements. A weakening of the local currency will result in a higher value of in force of off shore business.

Question 6

Principles for surrenders:

• Practical Issues:

Answer 6

o the method should be well-documented
o it should be simple to apply and easy to explain
o the scale should not change too frequently owing to the administrative work involved
o anti-selection should be avoided, e.g. selective withdrawals or financial anti-
o selection, and surrender values should take account of financial conditions
o surrender values, in conjunction with new business premiums, should not encourage lapse and re-entry
o surrender values should be stable, i.e. small differences in policies should produce small differences in surrender values
o whether any “blending” is required between an old and a new surrender value scale
o surrender values should be consistent with any other alterations offered

Question 7

The following are principles that apply to all alterations

• Small change in benefit

Answer 7

 However, a small reduction in sum assured could possibly lead to a relatively large change in premium rates, depending on how the current premium basis compares to the original premium basis.
 This could lead to a smaller premium on the altered policy (compared to the current premium), for approximately the same sum assured, encouraging alterations.
 There could even be an increase in premium for a reduction in sum assured.

Question 8

How to set mortality assumption (e.g. for prospective GPV) for surrenders

Answer 8

Mortality
The mortality basis chosen should reflect the future expected mortality of those policyholders who are surrendering
(May be lighter than for policyholder who do not surrender)

Could track mortality experience of previously surrendered policies, but difficult since lapsed policies not tracked
But for most assurance contracts that have surrender values the mortality assumption will not have a large effect upon the resulting value)

It is unlikely that any margins would be included in the assumption as these will increase the surrender value