Duration/timing for capital cost in commutation calculation

xuchaofan

Hi,

Does someone know why in the commutation calculation, the capital cost discounted from 1, 2, 3,... but the claim to pay discounted from 0.5, 1.5, 2.5,...? That means we suppose that the claim will be paid evenly during the year but the capital requirement for the unpaid claim will be released annually at the end of the year? Also, why not just use the present value of claim cash-flow X capital cost % X required capital ratio? the capital requirement calculation uses the discounted unpaid claim without PfAD right?

Any reason for that or it's just an assumption? According to the exam report, it seems like the exam adjusters just accept the method in the reading, because they mentioned 3 samples in 2019 spring 17, but all of them use the same approach. And in the common errors, they mentioned "Using the wrong capital duration for the calculation of the risk margin"...

Thanks,

cfx

graham

Question 1: "That means we suppose that the claim will be paid evenly during the year but the capital requirement for the unpaid claim will be released annually at the end of the year?"

• Yes, that's correct. We assume the claims are paid on average in the middle of the year, but the margin is kept for the whole year, I assume just to be safe.

Question 2: "Why not just use the present value of claim cash-flow X capital cost % X required capital ratio?"

• If I understand correctly, you're basically asking why the PV of claims and the margin are not calculated together instead of doing a separate discount calculation for each? Each year, we discount what we expect to be paid in that year to get PV(claims). But the margin is based on what is yet to be paid so it's a different number, and since it's discounted differently the calculation must be separate.

Question 3: "The capital requirement calculation uses the discounted undiscounted unpaid claim without PfAD right?"

• That's the method given in the source text but there is no explanation to justify it. The method does incorporate a margin but it's calculated a little differently from the normal claims PfAD and interest rate PfAD. (The reinsurance PfAD is gone because of the commutation.)

I hope that helps. If anyone else has any comments on this, please post.

xuchaofan

Thanks @graham

bkmlocks

In question 3 above, what is Capital requirement referring to? Are we talking about Required Margin * Undiscounted Future Payments ? (highlighted Yellow below) If that's the case, then we would be using the Undiscounted **Unpaid Claim and **not the Discounted Unpaid Claim right?

Thank you!

graham

Yes, my mistake. For the required margin, the input is the undiscounted unpaid. Then there are 2 steps to get the final value of the required margin:

• apply the TMF factor to get the dollar-value of the cost of capital
• discount the cost of capital to PV (but using integer exponents)

Thanks