April 2014 Q3

Hi Kiran

A surrender value would have a discontinuity by duration if it suddenly changed at some point in time. So for example a surrender value of 200 before time 5 and 1,300 from time 5 has a discontinuity as it jumps substantially at time 5. The surrender value in the question does not have a discontinuity as it increases smoothly over time, increasing by just the amount of the premium paid at each time.

You are right that the profit on a surrender is the asset share less the surrender value. So the basis used to calculate the surrender value determines the profit.

The profit made on alteration is a bit more complicated though. If we use the equating policy values method we need to think about the profit made in the past and the profit made in the future. The equating policy values method equates the value of the old policy with the value of the new policy. The profit made in the past is the asset share minus the value of the old policy, so yes this part of the profit is just like the surrender value calculation you mentioned. But we also need to think about the profit on the new policy - we think of this just like pricing a new contract, so that if the basis used to value the new policy contains margins, then those margins will be expected to lead to profits in the future, but if the basis is best estimate (without margins) then there will be no profit from the new policy. The total profit from the altered contract is obtained by adding together the profit from the old contract and the profit from the new contract.

For question 4, I'd want to consider matching the expenses of both contracts with index-linked bonds. I'd then consider whether to mismatch using equities for higher returns (and bonuses) for the with-profits contract. We wouldn't usually hold separate reserves for expenses - reserves would be calculated in aggregate as the present value of claims plus expenses less premiums.

I hope this helps.

Best wishes

Mark