Assignment X5 Que 2 part (iii)

[Rajat gupta]

Hi All,

Can somebody please explain working of solution to the above question? I am finding it difficult to understand

Thanks in advance

 

[Mark Willder]

Hi All,

Can somebody please explain working of solution to the above question? I am finding it difficult to understand

Thanks in advance

Hi Rajat

Pricing a mortality option is the same as pricing any other contract. We project the cashflows each year and then discount them. In this simplified example we ignore the effect of expenses and reserves, so we just have premiums and claims.

Each year we split the policyholders into those that have exercised the option and those that have not. Those that exercise the option will have a higher sum assured, they will also have paid a premium for the extra sum assured (using standard premium rates as that is what the option offers them). However, those exercising the option suffer from higher mortality, so we need to charge an extra premium to cover the fact that expected claims will exceed the standard premium rates.

I hope that gives you enough to get started on the question. If there is a specific part of the question that doesn't make sense then please let me know.

Best wishes

Mark

 

[Rajat gupta]

Hi Mark,

Thanks for your reply on it!
Here what I understand is solution is divided into three parts: cash flows for year 1, for year 2 and for year 3
My question is on year 1:-
Here in the solution cash flows in year 1 is :-
P-386.47
Similarly for year 2 and year 3 are -787.56 & -959 respectively
then to what value is the last equation equated to arrive at the premium P? Is their some error or omission in the solution?

 

[Mark Willder]

Hi Mark,

Thanks for your reply on it!
Here what I understand is solution is divided into three parts: cash flows for year 1, for year 2 and for year 3
My question is on year 1:-
Here in the solution cash flows in year 1 is :-
P-386.47
Similarly for year 2 and year 3 are -787.56 & -959 respectively
then to what value is the last equation equated to arrive at the premium P? Is their some error or omission in the solution?

Hi Rajat

We want the expected present value to be zero. So using the expected present values of the cashflows from each year we get:

P-386.47-787.56-959=0

Best wishes

Mark

 

[Rajat gupta]

Hi Mark

Now it make sense! Thanks Mark

 

[Rajat gupta]

Hi Mark

Is the above question part of syllabus objective on Mortality option?

 

[Mark Willder]

Hi Mark

Is the above question part of syllabus objective on Mortality option?

Hi Rajat
Yes, this question is suitable for the current syllabus. All our Q&A and assignment questions are modified each year for the latest syllabus.
The old syllabus looked at methods of pricing mortality options using a formula approach, ie using the big "A" and little "a" functions in the yellow tables.
The new syllabus describes a cashflow approach to valuing mortality options. This question demonstrates how these cashflows could be calculated each year.
Best wishes
Mark