Ch 32: Valuation of liabilities - Options and guarantees

[JL24]

Hi there, on page 14 of Chapter 32, there is a core reading text that says "When using deterministic and closed form (eg Black-Scholes) methods to value guaranteed options, the traditional approach has been to assume that the take-up rate reflects the financial value of the option only - in other words a high take-up rate is used."

1. Why does 'reflecting only the financial value of the option' mean a high take-up rate is used?
- Is it because we are omitting the fact that some people would not exercise an option even if it is in-the-money (and hence actual take-up would be lower)?
- However, we could equally say that some people would exercise an option even if it is out-of-the-money, wouldn't that result in an even higher take-up?

2. Would assuming a high take-up for options always result in higher provisions (more prudent)? From what I understand, the option to surrender a life insurance policy is also an 'option', but if a high take-up were to be assumed for surrenders towards the middle/end of the policy term (when initial expenses have already been recouped), wouldn't a high take-up (i.e. high surrender) assumption be too optimistic?

Thank you in advance!

 

[Lindsay Smitherman]

Hi - let me take each of your questions in turn.

Hi there, on page 14 of Chapter 32, there is a core reading text that says "When using deterministic and closed form (eg Black-Scholes) methods to value guaranteed options, the traditional approach has been to assume that the take-up rate reflects the financial value of the option only - in other words a high take-up rate is used."

1. Why does 'reflecting only the financial value of the option' mean a high take-up rate is used?
- Is it because we are omitting the fact that some people would not exercise an option even if it is in-the-money (and hence actual take-up would be lower)?
- However, we could equally say that some people would exercise an option even if it is out-of-the-money, wouldn't that result in an even higher take-up?

This paragraph is talking about 'guaranteed options', ie offering the individual an option to take some form of (alternative) benefit, such as converting the normal lump sum benefit into an income stream at a guaranteed conversion rate.

The sentence that you quote is referring to a 'traditional approach' which means a conservative or cautious approach. [The rest of the paragraph goes on to talk about what would be done if using a best estimate approach.]

Remember that we are valuing just the extra cost of the guaranteed option here. If using the Black-Scholes formula, an option has zero value at the exercise date if it is out-of-the-money at that point, and a positive value at the exercise date if in-the-money at that point. If we combine that outcome with a high assumed take-up rate when it is in-the-money, that is a cautious approach. [It doesn't matter what proportion 'take up the option' when out-of-the-money under this method as the B-S formula gives a zero outcome in that situation.]

Assuming 100% take-up when in-the-money would be the most prudent approach - but it might be too prudent if, as you say, in practice some individuals wouldn't (fully) take it up, eg for tax reasons, or due to the utility value of cash-in-hand, or due to poor health etc.

This approach effectively ignores the fact that some individuals might, in theory, exercise a guaranteed option in an insurance policy even if it is out-of-the-money at the time, eg because they don't realise that to be the case. For example, they might convert their lump sum to an income at the guaranteed rate without realising that they could have obtained a better rate by purchasing an annuity in the open market. That could be beneficial to the insurer (ie if the PV of the income is lower than the lump sum that otherwise would have been paid) and therefore would lower the provisions if allowed for. So it is cautious / prudent to assume that this doesn't happen. In any case, it might well only happen when the difference is pretty small (ie the option isn't very far out-of-the-money so they might decide not worth shopping around, therefore doesn't actually make much difference to the insurer's provisions) and the insurer would no doubt include warnings to the customer that they might obtain better rates elsewhere.

 

[Lindsay Smitherman]

2. Would assuming a high take-up for options always result in higher provisions (more prudent)? From what I understand, the option to surrender a life insurance policy is also an 'option', but if a high take-up were to be assumed for surrenders towards the middle/end of the policy term (when initial expenses have already been recouped), wouldn't a high take-up (i.e. high surrender) assumption be too optimistic?

Yes, surrendering a life insurance policy could also be considered to be an 'option', but it isn't (normally) a 'guaranteed option' as such - the insurer typically has discretion as to the amount paid. [Also, we don't tend to think about it in terms of 'take-up rates', but just as 'surrender rates' or 'withdrawal rates'.]

As described in Chapter 22, the benefits payable on surrender (the 'surrender value'), if any, would need to be such to be fair to the insurer, those leaving and those staying. Broadly speaking, if the amount paid on withdrawal exceeds the underlying value that the insurer holds for that policy (eg the 'asset share' or reserve), it is more prudent to assume a high surrender rate, and vice versa.

So, as you indicate, early on in a policy even paying no surrender value at all could incur a loss for the insurer - so higher surrender rates are prudent at such durations.

At later durations, it depends on the type of policy, eg:

• For a term assurance, no surrender value is paid (the policy lapses without value) - but the insurer is likely to have accumulated a small positive reserve / asset share for that policy once initial expenses have been recouped; so in this case, yes - it could well be more prudent to assume a lower surrender rate at medium to later durations.
• For a conventional endowment assurance, a surrender value will be paid - so whether surrender generate profits or losses depends entirely on the surrender value scale that the insurer has decided to use.
• For any unit-linked policy, the insurer makes profits from the charges that are taken from the unit fund and any ongoing premiums - so surrenders are generally not good for the insurer whenever they occur (ie even after initial expenses have been recouped) and so a higher assumption would be prudent.

Hope that helps - but don't worry if it all sounds a bit too complicated as we are definitely encroaching into Specialist level material here!

 

[JL24]

Yes, surrendering a life insurance policy could also be considered to be an 'option', but it isn't (normally) a 'guaranteed option' as such - the insurer typically has discretion as to the amount paid. [Also, we don't tend to think about it in terms of 'take-up rates', but just as 'surrender rates' or 'withdrawal rates'.]

As described in Chapter 22, the benefits payable on surrender (the 'surrender value'), if any, would need to be such to be fair to the insurer, those leaving and those staying. Broadly speaking, if the amount paid on withdrawal exceeds the underlying value that the insurer holds for that policy (eg the 'asset share' or reserve), it is more prudent to assume a high surrender rate, and vice versa.

So, as you indicate, early on in a policy even paying no surrender value at all could incur a loss for the insurer - so higher surrender rates are prudent at such durations.

At later durations, it depends on the type of policy, eg:

• For a term assurance, no surrender value is paid (the policy lapses without value) - but the insurer is likely to have accumulated a small positive reserve / asset share for that policy once initial expenses have been recouped; so in this case, yes - it could well be more prudent to assume a lower surrender rate at medium to later durations.
• For a conventional endowment assurance, a surrender value will be paid - so whether surrender generate profits or losses depends entirely on the surrender value scale that the insurer has decided to use.
• For any unit-linked policy, the insurer makes profits from the charges that are taken from the unit fund and any ongoing premiums - so surrenders are generally not good for the insurer whenever they occur (ie even after initial expenses have been recouped) and so a higher assumption would be prudent.

Hope that helps - but don't worry if it all sounds a bit too complicated as we are definitely encroaching into Specialist level material here!

Hi Lindsay, yes, both explanations help a lot, I understand now. Thank you so much for your help!