In my presentation, Simply Unlocking, at the 2015 Valuation Actuary Symposium I started the development of an unlocking toolkit with a formula introduced by Bruce R. Darling in a 1992 issue of the Financial Reporter. Neither the article nor my presentation showed how to derive this “Cumulative Effect” formula. In Simply Unlocking, I introduced a corresponding formula to measure the total cumulative effect for DAC and related liabilities (URL and SOP reserves).
In an article, also titled Simply Unlocking, I introduced formulas to estimate amounts of amortization and cumulative effect (unlocking) directly from specific sources of profit and variances therefrom.
In this document, I show a derivation of the general Cumulative Effect formula, followed by a derivation of Darling’s formula as a special case. I also show derivations of the formulas for source-specific cumulative effect and net amortization rates.
Read the rest of it by downloading the pdf Simply Unlocking – Formula Development.