Calculation of Technical Provisions

Hello,

I have a question on the calculation of Technical Provisions. I'm struggling to reconcile the definition given by the Core Reading about the inclusion of cashflows on a best estimate basis and the schematic on page 9 in this (possibly outdated) document: https://www.actuaries.org.uk/system/files/documents/pdf/sii-tp-wp-paper-giro40.pdf

Let's assume an extreme case where the insurer only writes one annual motor policy. The policy was written on Oct 1st, and the valuation date for the TP is Dec 31st. The premium is paid in monthly instalments of £100, with the first premium received on Oct 1st (i.e. when the policy was written). There has already been one claim for severe bodily injury, where the accident date is Nov 1st. The incurred claim is £10,000 but the estimated ultimate is £500,000 (on a BE basis). None of it has been paid yet.

The initial expected loss ratio for this policy is 50%, and that is what will be used to estimate the claims for the unexpired portion of the risk in the premium provision (I'm looking at the aforementioned schematic now).

Ignoring discounting, how are the claims provisions and premium provisions calculated in this case? In particular:

1. How to deal with the instalments payable? Following the cashflow approach, are only the future instalments included in the premium (or claims?) provision, or should there be an allowance somewhere else for the past instalments too?
2. Is only the ultimate claim amount (i.e. £500,000) included in the claims provision? Or is something else included too? Assume expenses are zero.
3. What goes in the premium provisions? Is it 50% (IELR) of the future premium instalments? What else should be included? Again, assume expenses are zero.

Finally, a slightly separate question: do the Technical Provisions have to be held in cash (as in, quite literally, money in the bank) or are other assets admissible?

Apologies for the long post - I wanted to be exhaustive for the avoidance of any doubt.

Thanks to anyone who will reply!

Enrico

 

Hi Enrico,

Fellow student here. These are my thoughts.

• Between Oct and Dec, you had three months - consider premium as paid and one major claim of 500k. Let us assume that this is paid in Dec of next year. This relates to the claims provision.
  
• The following 9 months have £100 being paid per month in premiums and £50 being paid out in expected claims per month. Let's assume these are paid at end of month (So last payment at end of Sept of following year). This relates to the premium provision. Let us also assume we add an ENID of £1 a month at end of each month.

I think this is answered above. Both claims and premium provision are prospective calculations of the expected cashflows - it depends on whether it is on the earned or unearned part.

Yes. The claims provision is the discounted value of 500k.

The premium provision is a series of cashflows: £100 at t=0, £100 (premium in) - £50 best estimate claim- £1 ENID = £49 at t=1 to 8 and, -£51 at t=9 where t is time in months.
In this case the premium provision is actually allowing for profit so is negative.

Just a note that it is very unlikely for insurers to use a monthly discount rate for their SII technical provisions. However given the current close to zero interest rate environment, it doesn't really matter - it will be about £441 and an asset.

 

Hi zuglubuglu,

That's really helpful, thank you!

As a final point - just to make sure that I understand this correctly - how would you modify this if all instalments were paid after the valuation date (i.e. Dec 31st?)

Let's say, for instance, that premium payments start on Jan 1st, and there's one final payment of £400 on Sep 1st (in the following year, of course, to "make up" for the first three £100 that were not paid). Would you still include all premium payments in the premium provision, in line with the cashflow approach?

My confusion here arises from the fact that, as at Dec 31st, even though no premium has been received yet, three months have already been earned. So which approach has "the last word", if you will? Proportion of earned/unearned or discounted cashflow?

 

Hi Enrico,
I doubt any insurer would in practice accept the cover those three months without having received anything. But let's assume that this is the case (maybe a captive?). There would be no change to the claims provision but the premium provision would increase by that £400 which is discounted by 9 months.