Analysis and Valuation of Surrender Option in Life Insurance Policy

[[abstract]]近年來，投資型保險商品或分紅保單漸成主流，然而，全球金融風暴後，傳 統壽險保單又開始受到市場重視，不同的是，現行保單之預定利率已不若以往水 準。這樣的金融環境與保戶投保態度的改變，亦衍生出另一值得深思議題—若市 場利率再度走高，是否加劇解約案件而對保險公司形成重大衝擊？所以，本計劃 將著眼於保單解約選擇權之分析與評價。 保單解約選擇權之本質屬美式選擇權型態，其價值隨市場利率或被保險人死 亡率波動之加劇而增高。因此，保單解約權價值之審慎計算，將是壽險公司評估 發單成本不得不重視之課題。解約選擇權收益因市場利率或被保險人死亡率之變 化而改變；而保戶是否解約之決擇，除了考量解約收益外，尚掺雜保戶對保單之 忠誠度因素。因此，本計劃擬同時考量利率波動、被保險人死亡率變化以及保單 忠誠度情況，透過利率與死亡率隨機過程之模擬，以有限差分法來評價傳統壽險 保單的解約選擇權。相較於先前研究之差異，本計劃主要強調有二，一為著重於 以精算方法解析解約選擇權之收益型態，另一為評價過程中加入保單忠誠度之考 量。[[abstract]]In the recent, investment-linked insurance are gradually becoming mainstream. After the start of the global financial crisis, traditional life insurance policies have once again begun to receive market attention. What is different is that the scheduled interest rates of current policies are inferior to past levels. This sort of financial environment, along with changes in the attitudes of those purchasing insurance, results in another question worthy of deep consideration –if market interest rates climb once again, what sort of impact will this have on insurance companies? This research will focus on the analysis and valuation of surrender option in life insurance policy. The essence of this right pertains to American option types. Its value dramatically increases following the fluctuations of interest rate and insured’s mortality. Therefore, careful calculation of the value of the surrender option for the insured is a problem that life insurance companies must emphasize in reaction to policy costs. The payoff of surrender options changes with the variability of interest rate and insured’s mortality heterogeneity. In addition to considering the payoff of the surrender option, the decision of clients to surrender is also entangled with their loyalty toward the insurer. Thus, this study simultaneously considers interest volatility, individual insured mortality variability and the loyalty of insurance customers using random model and the finite difference method, to evaluate the surrender option in traditional life insurance. This paper has two points of emphasis which differ from those of earlier research. One is a focus on using the actuarial method to analyze the payoff types of the surrender option. The other is adding considerations of the loyalty of the insured into the valuation process.[[note]]NSC101-2410-H327-02