Al Burns said:
On 4/30/2009 11:35:19 AM
For an ordinary life plan, the Commissioner's Reserve Valuation Method (CRVM) is equivalent to the Full Preliminary Term Method (FPT) by definition. For FPT valuation, Beta(x) equals NLP(x+1). It follows that any derivation of Beta(x) for an ordinary life plan must produce Beta(x) equal to NLP(x+1). If it doesn't produce NLP(x=1), the formula must be incorrect.
If one attempts to calculate Beta as the NLP plus the amortized expense allowance, and multiplies the expense allowance by Dbar(x)/Dcurt(x), a Beta(x) equal to NLP(x+1) is obtained. This proves the necessity of the procedure.
However, if one attempts to calculate Beta as the NLP plus the amortized expense allowance, but without multiplying the expense allowance by Dbar(x)/Dcurt(x), a Beta(x) larger than NLP(x+1) is obtained. This results in a negative first year reserve, which cannot be correct. If the Beta so obtained is then used to calculate Alpha, the Alpha so obtained is less than the Alpha defined by the FTP method, again proving that the formula cannot be correct without using Dbar(x)/Dcurt(x).
General reasoning can be used to explain why the Dbar(x)/Dcurt(x) adjustment is needed. Expense allowances are defined in terms of the present value at issue of the excess of the renewal net premium (Beta) over the first year net premium (alpha). At issue, the difference must be multiplied by an annuity factor for 1 year. When premiums are assumed to be paid annually, the annuity factor is equal to 1, and needn't be shown in any formula. However, when premiums are paid continuously, the annuity factor is Dbar(x)/Dcurt(x), and so must be included.