Hi Mark,
I am aware that the assurance function needs a "1" above the age, as mentioned in my post
I just don't know how to type it out in the textbox here.
After seeing the solution again, I realise I confused between the "cost" and "premium":
The "cost" should be based on ultimate mortality because this is what we will realistically expect the experience to be.
Whereas the "premium" should be based on select mortality, because this is the intention of the guaranteed renewability option without underwriting.
Therefore the cost of the benefits is supposed to be : Pa
x+10:10= SA
x'
+10:10
(where x' represents the little "1" above x)
and the premium basis will be: Pa
[x+10]:10= SA
[x'
+10]:10.
The difference between these 2 makes the (additional) cost of the option.
Relooking at the formula again, I think I now know where does the " *a
x+10:10 " comes from:
The parts not highlighted, P= S*A
[x'
+10]:10/a
[x+10]:10 represents the annual premium we are charging.
We want to evaluate the PV
cost (instead of regular premium) as at the option exercise date, therefore, the LHS and RHS of the equation multiplies by a
x+10:10 (highlighted yellow) as this is the best estimate basis.
And then the next line after this:
S* [ A
x'
+10:10 - A
[x'
+10]:10/a
[x+10]:10 ]
is to get the premium difference the option makes
And this difference gets discounted back to the inception date, allowing for survivorship to arrive to the final premium.
Is this the correct explanation?
Click to expand...