Hi Mark,
Thanks for the reply above. It is a bit clearer now.
However I am still not very clear as to how EAS - SV' is the accrued profit to date and how it gives the final profit at the end of the contract.
Is it possible to explain this in the form of the equations or perhaps a numerical example.
Also in the second point is it possible to explain this how the SV' compares with the EAS in terms of margins with the help of an example?
Hi Sayantani
We'll do a very simple calculation so we can focus on the principles.
Consider a 2 year single premium without-profits endowment. We'll ignore expenses, mortality and withdrawals. So we'll just focus on the investment assumption. The single premium is 100.
Let's assume that the best estimate of future returns is 10% and that reality turns out to be exactly the same as expected. Then the asset share AS_t at each future time t is:
AS_0 = 100
AS_1 = 110
AS_2 = 121
Now let's assume that pricing is performed using margins in the investment assumption, let's say 8%, and that there is no explicit profit margin (this is the assumption used in the formulae and graph in the notes too). On this basis the sum assured is SA = 100 x 1.08^2 = 116.64.
Calculating the reserve V_t using the same basis as the premium basis (which is the assumption used for SV') gives us
V_0 = 100
V_1 = 108
V_2 = 116.64
If we were to use the above numbers as the surrender values we would get the following profits:
AS_0 - V_0 =100 - 100 = 0 ie no profit - we haven't accrued any profit yet as the contract has just been sold
AS_1 - V_1 = 110 - 108 = 2 ie the profit accrued so far because we earned an extra 2% interest on the investment
AS_2 - V_2 = 121 - 116.4 = 4.6 ie the extra 2% of interest for the two years. This is the total profit. The insurer has assets of 121, but only needs to pay out 116.64.
I hope that helps to make it clearer.
Best wishes
Mark