Effective Duration Analyses on the Policy Reserves of Life Insurance

壽險保單準備金之有效存續期間分析

10.6545/JFS.2012.20(1).2

詹芳書(Linus Fang-Shu Chan)；蔡政憲(Cheng-Hsien Tsai)

有效存續期間 ； 保單準備金 ； 總準備金 ； effective duration ； policy reserve ； aggregate reserves

財務金融學刊

20卷1期（2012 / 03 / 31）

33 - 62

英文

鑑於解約率會受到利率的影響，壽險保單責任準備金的利率風險應使用有效存續期間來衡量。本研究採用一般化的反正切利差解約率模型與CIR模型，並根據保單儲蓄成分的不同來設定解約率對利差的敏感度。我們分析死亡險、生存險與生死合險，計算三者在不同保單年度下之一張保單準備金與其總準備金的有效存續期間，並分析在不同業務銷售比重下，其總準備金之有效存續期間。分析發現保單準備金與其有效存續期間並未維持同號，且三種保單準備金之有效存續期間與保單到期期限的類雙曲線關係並非完全一致。最後，包含三個險種的一籃子保單總準備金之有效存續期間缺口會隨利率下降而擴大。

Life insurers need to employ effective duration to measure the interest rate risk of policy reserves because the surrender rate depends on interest rates, which makes cash flows interest-rate-sensitive. This study uses a general surrender rate model and CIR interest rate model, besides assuming different interest rate sensitivities according to product characteristics. Products analyzed include term life insurance, endowment and pure endowment. We first calculate the effective durations of these products’ reserves by policy years. Then we calculate effective durations of reserves aggregated by products, and across products. Our results identify a new pattern of effective durations of policy reserves with time to maturity on three types of policies not reported by Tsai (2009). Furthermore, the gap between duration of using Treasury bonds to match policy reserves broadens as the interest rate falls.

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