分紅保單之實質存續期間

Abstract

既有文獻忽略了壽險保單的一個特質：淨現值在保單生命期中通常會變號。淨現值的變號會導致壽險保單的存續期間出現不尋常的值。第一，不同保單年度的保單其存續期間的正負號可能不同。在準備金大於0 的保單年度中，存續期間是正的；但在淨現值大於0 的年度中，存續期間會是負的。第二，壽險保單的存續期間可能很大。超大值會出現在淨現值接近0 的時候，因為淨現值是計算存續期間的分母。在本計畫中，我們以Cox, Ingersoll, and Ross (1985)的利率期間結構來模擬利率，計算不同年度的保單的實質存續期間。為了檢視分紅條款與利率的隨機性如何地影響保單的存續期間，我們還計算另外三個存續期間：不分紅保單的麥考利存續期間，分紅保單的麥考利存續期間，以及隨機利率下不分紅保單的存續期間。我們的結果和我們對保單有特殊存續期間的猜想一致。我們的結果屬於新發現，將對壽險公司的資產負債管理有實際的意涵。

We spot a feature of life insurance policies not recognized by the above papers: net present value (NPV) usually incurs sign changes during the policy life. The feature of sign-changing NPV would result in unusual duration figures for life insurance policies. First, the durations of life insurance policies in different policy years might have different signs. Policies in the policy years when reserves are positive have positive durations, but policies in the policy years when NPVs are positive would have negative durations. Second, life insurance policies could have enormous durations. These durations emerge at the times when NPV is close to zero, since NPV is a denominator in effective duration. In this project we calculate the effective durations of participating policies in different policy years, using a Cox, Ingersoll, Roll (1985) term structure (abbreviated as EDP) to simulate interest rate. We then analyze how participation and the randomness of interest rate affect policy duration by calculating three additional duration measures: the modified duration of a non-participating policy, the modified duration of a participating policy, and the effective duration of a non-participating policy. Our results confirm our speculations about the unusual effective durations for life insurance policies. They are new to the literature and would be useful in the asset-liability management of a life insurance company.