Analysis and implementation of provision for adverse deviation for payout annuities: A stochastic approach
Financial Accounting Standard Board Statement 60 (FASB 60) requires that reserves for payout annuities be determined by using realistic assumptions of mortality and interest, with a provision for adverse deviation (PAD). Until this research, the PAD has never been defined or quantified, but has been left to the judgement of the actuaries. This research provides a mathematical definition of PAD for mortality and interest. The simulation results show that the mortality PAD can be determined using a normal approximation, based on an analytical derivation of the standard deviation and the mean for a portfolio of payout contracts (single, J&S, C&C). The mortality PAD approaches zero as the portfolio size approaches infinity. A general rule for calculating the mortality PAD for a mixed portfolio is provided. The interest PAD is unaffected by the portfolio size and is determined by simulation. In order to recognize the long-term nature of payout contracts and the matching of assets and liabilities, an algorithm was developed to model the portfolio rate for a block of payout business. Finally, a combined mortality and interest PAD was quantified using Monte Carlo methods. Statistical tests were applied to study its relationship to the individual PADs. For variable annuities that pass the interest rate risk on to the contractholders, the only PAD to hold is the mortality PAD. Therefore, the general variance formula for the present value of variable annuity payments that was developed in this thesis will contribute to the study of variable annuities, products that are the most rapidly growing business in the life insurance industry.
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