23+ 24. Reserves I - NPV and GPV

Question 1

What is the purpose of calculating reserves?

Answer 1

1. Demonstrate solvency
2. Know the true / realistic position of the company

Question 2

What are the two methods of calculating reserves?

Answer 2

1. Gross Premium Valuation
2. Net Premium Valuation

Question 3

What are the bases that can be used to calculate reserves?

Answer 3

1. Prudential
2. Best-estimate
3. Market consistent

Question 4

What is the GP reserve

Answer 4

EPV[Benefits] + EPV[Expenses] - EPV[Office Premiums]

Question 5

How is the GP reserve calculated?

Answer 5

1. Either use a cashflow model or formula

Question 6

Why is GP reserve usually negative at start of policy

Answer 6

• Premiums are usually more prudent
• If reserving basis is very prudent, gross premium reserve may be positive at start of policy

Question 7

What are the features of the GP reserve?

Answer 7

• Explicit allowance is made for expenses
• Explicit allowance for vested bonuses and future expected bonuses
• Future premiums are the actual office premiums
• The difference between the premium and valuation basis is immediately taken as profit.
• It may be negative at the outset due to initial expenses and capitalising future expected profit.
• Reserves are sensitive to changes in the basis.
• Ignores future withdrawals.

Question 8

What is the NP reserve?

Answer 8

EPV[Benefits] - EPV[Net Premiums]

Question 9

What are the features of the NP reserve?

Answer 9

• Simple
• Calculated only the basis of interest and mortality
• No explicit allowance for expenses
• No explicit allowance for future benefits
• Reserves are insensitive to changes in the basis

Question 10

Explain how reserves are calculated using a prudential basis

Answer 10

Aim: Have enough money required to pay claims and meet ongoing expenses without further financing.

Calculation:
Consider the yearly cashflows ro determine when a non-unit reserve is required
1. Start at the last projection period where there is a negative cashflow
2. Set up money at the start of the period to zeroise the cashflow allowing for investment return.
3. Deduct this money from the net cashflow at the end of the previous time period.
4. Work backwards until all the cashflows have been zeroised.
5. If adjusted cashflow is negative then the non-unit reserve will be set as the absolute value.

Question 11

Explain how reserves are calculated using a best estimate basis

Answer 11

• Similar to prudential cashflow zeroising, but all the cashflows are valued.
• The cashflows occuring in periods after last negative cashflow aren’t disregarded.
• Can have negative reserves

Question 12

Explain how reserves are calculated using a market consistent basis

Answer 12

• Assets are valued at market value
• Liabilities are valued at the price one wouldd charge fir taking over the liability
• The risk discount rate used is the risk free rate.
• RFR can be taken from govt bond yields or swap rates.
• Risk margin could be added.
• Illiquidity premium can be added if allowed by regulation

Question 13

What are the two approaches to calculating the risk margin for a best estimate basis

Answer 13

• Can calculate best estimate liabilities and add risk margin to the assumptions.
• Can use the cost of capital approach