Chapter 23

Question 1

What are the benefits of using the Gross Premium Valuation (GPV) method over the Net Premium Valuation (NPV) method, and vice versa?

Answer 1

Benefits of GPV over NPV
* Explicit Allowance for Expenses
* Explicit Allowance for Bonuses: GPV can include vested and expected future bonuses, whereas NPV includes only declared bonuses.
* Use of Actual Premiums: GPV uses actual gross (office) premiums; NPV uses a notional net premium.
* Realistic Profit Capitalization: On a realistic basis, GPV capitalizes all future expected profits.
* Prudence Management: On a prudent basis, GPV capitalizes less profit upfront, giving protection if experience worsens.

Benefits of NPV over GPV
* Simplicity: Easier formulas and data requirements compared to GPV.
* Insensitivity to Basis Changes: NPV reserves for regular premium contracts are less sensitive to changes in assumptions.
* Non-Capitalization of Profit Margins: Avoids realizing all future profits upfront, which is safer for supervisory reserves (esp. with-profits).
* Regulatory Acceptance: Sometimes prescribed (e.g., certain African countries).
* Focus on Core Costs: NPV isolates interest and mortality costs, excluding expenses and profit assumptions.
* Suitability for Regular Premiums: Works well for regular premium business; less suited for single premiums.

Question 2

Describe the two primary reserving methods

Answer 2

1. Gross premium valuation method
   * cashflow approach or formula approach
2. Net premium valuation approach
   * here the difference between this net premium and office premium implicitly covers the profit margins and the expenses

Question 3

Another term for gross premium valuation method

Answer 3

Bonus reserve valuation

Question 4

Describe the Gross Premium Valuation (GPV) method and state the general structure for calculating reserves.

Answer 4

• Description: The GPV method places a value on a life insurance company’s liabilities by explicitly valuing the future office premiums payable, expenses, and claims, with claims possibly including future discretionary benefits.
  Structure for calculation is formula approach or cashflow approach
• Reserve Calculation Structure:
  ◦ {Present value of expected future benefit outgo}
  ◦ $+$ {Present value of expected future expenses}
  ◦ $-$ {Present value of expected future premiums}
• Alternative Approach: Reserves can be calculated using a cashflow approach where net cashflows are calculated for each future point in time and then discounted back, as an alternative to the formulae approac

Question 5

What are the salient features of the Gross Premium Valuation method?

Answer 5

• An explicit allowance is made for expenses.
• An explicit allowance can be made for vested and expected future bonuses (often called a bonus reserve valuation).
• The future premiums valued are the actual (“office”) premiums expected.
• Any differences between the pricing and valuation bases will immediately be taken as profit or loss.
• Reserves may initially be negative for non-linked business, partly due to heavy initial expenses and partly due to capitalising the expected future profit.
• The reserves tend to be quite sensitive to changes in basis.

Question 6

What is the purpose of holding negative non-unit reserves, and when are they most likely to arise?

Answer 6

• Meaning: A negative reserve occurs when the value of future positive cashflows outweighs the value of the negative cashflows. It treats the contract as an asset because future charges are expected to exceed future expenses and costs
• Benefit: They reduce the total reserve (unit plus non-unit), thus improving the capital efficiency of the product and reducing new business strain.

Question 7

What typical regulatory constraints may be imposed on the use of negative non-unit reserves in a prudential valuation? (4)

Answer 7

• The sum of the unit and non-unit reserve for a policy should not be less than any guaranteed surrender value.
• The future profits arising on the policy with the negative non-unit reserve need to emerge in time to repay the “loan”.
• After taking account of the future non-unit reserves, there should be no future negative cashflows for the policy (i.e., no future valuation strain).
• In aggregate, the sum of all non-unit reserves should not be negative. (Note: The positive reserves for offset can come from anywhere in the company’s business, though regulations may restrict offsetting against unit reserves

Question 8

When calculating negative non-unit reserves for a prudential valuation, how should the assumptions be adjusted to ensure prudence?

Answer 8

• Prudence requires ensuring that the negative non-unit reserves are not too large in absolute value, because if future cashflows are smaller than expected, the company could incur a future loss.
• A prudent approach could be calculated by assuming that:
  ◦ Future positive cashflows are lower than best estimates.
  ◦ The rate of interest used to discount them should be higher than best estimate.
  ◦ Survival rates are lower than best estimates.
• Note: This adjustment differs from calculating prudent positive non-unit reserves, for which a lower than best-estimate discount rate would typically be use