risk discount rate

[uktous]

Hi,

After reading the setting assumption chapter, I know that if a product is risky, the risk discount rate should be high.

However, if the discount rate is high in the pricing basis, the premium will be small.

Therefore, the conclusion is that
if a product is risky, then the premium will be low.


Anyone can explain a bit about it?

Thanks

 

[Mike Lewry]

RDR in pricing

When pricing a without-profits product, the aim is to find the premium that achieves the company's profit criterion.

Suppose we project all the cashflows (expenses, benefits, change in reserves etc) and find the premium that allows us to achieve the specified profit criterion.

If we then increase the RDR, the present value of the profits will be reduced and we'll no longer be meeting the profit criterion. So we'd need to increase the premium to get back up to meeting the profit criterion.

So you have the expected result: a riskier product will require a higher premium, all else being equal.

 

[Lynn Birchall]

Hi

You're correct that the riskier a product is, the higher the risk discount rate we should use to discount the future profits and see whether they meet our profit criteion.

Imagine a really simplified case, where the profit criterion is an NPV of $10 at t=0, and we're solving for what cash inflow is needed at t=1 to meet this.

The answer using an RDR=0% is a cash inflow of $10. The answer gets higher as we use a higher RDR.

So, the conclusion is that if a product is risky and we use a higher RDR, the calculated premium will be higher.

Hope this helps
Lynn

PS Note that "high discount rate gives prudence" is only correct when we're evaluating assets / positive cashflows. If we're valuing liabilities, a low discount rate is prudent. So, when we're doing supervisory reserving, for example, a low valuation rate of interest is prudent.