Question: A proprietary life insurance company sells conventional with-profits endowment policies as well as without-profits business. The with-profits business is written in a separate ring-fenced fund in the company so that it does not share in the profits arising from the without-profits business. The with-profits policies have been sold for many years but recent new business volumes have been steadily declining. The company operates in a territory where the regulatory regime is similar to Solvency II. The company sets the BELs for its with-profits business to be the asset shares plus the cost of guarantees. (ii) Explain why this is a reasonable approach for the BELs. 1) my understanding for BEL = PV(future c/f) = PV(future liabs) - PV(future prem) the answer mentioned "The main future cashflow is the claim payment" --> where is the future premium component? Do we ignore future prem component because the NB volumes steadily declining? 2) If i understand correctly, the future liabilities where guaranteed component = COG, discretionary component = AS So, if the question did not mention WP NB declining ie normal WP business does the BEL = AS + COG - future premium?
Hi - I can appreciate your confusion here, but you need to disregard the point about changes in new business volumes (remember that the supervisory balance sheet only reflects in-force business, not future new business). Broadly speaking, a WP BEL can be approximated as current asset share + cost of guarantees (possibly also + cost of smoothing). We know that (for regular premium business) the BEL = PV {Future benefits + future expenses - future premiums} You are confused about why 'future premiums' seems to have disappeared from this statement. That's because 'future benefits' will be based on the asset share at the point of claim, ie a future asset share. This 'future asset share' will include future premiums, and will also have future expenses deducted from it. Simplistically, 'future asset share' = current asset share + future premiums - future expenses + future investment returns. (This ignores various other items that might be included in an asset share development, but what we are talking about here is a pragmatic approximation.) So the future expenses and future premiums items cancel out within the BEL formula. And the 'future investment returns' item (which would be accumulated at the risk-free rate) is 'cancelled out' by the discounting back from the claim date to the valuation date (since we also discount at the risk-free rate). So we get back to just the current asset share. And because the benefit would be higher than asset share if the guarantee bites, we also need to add on that cost of guarantee (ie the market-consistent valuation of guaranteed benefits in excess of asset share).
