二項式評價模型之實證研究 --以人壽保險增加保額選擇權為例

Abstract

現代人壽保險保險費之計算都是採用傳統的壽險精算方式，也就是利用生命表、預定利率、預定營業費用等三項要素去求算出每位投保人應繳的保險費，保險公司應提撥的責任準備金與保戶的保單價值準備金也都是根據這三項要素計算得之，而且一經計算完畢就固定不變。此外，保險公司於投保時，通常承諾免費給予客戶的權利也都是利用精算的概念，其中有兩項權利明顯具備選擇權的特質--轉換保單與增加保險金額，若依傳統精算方式計算，此兩種選擇權並不具備價值。 本研究為國內首篇以最基礎的保險商品—生死合險—為研究標的，針對保單給予投保人增加保險金額之權力為研究對象，利用利率變動會影響保單隱藏價值的特性，嘗試以二項式選擇權的評價模型為基礎，並以風險中立評價原理求得風險中立情況下的未來期望現金流量，再以無風險利率進行折現，求算出增加保險金額選擇權之價值。研究結果得到下列結論： 一、依選擇權評價模式，增加保險金額選擇權的確具有價值。 二、男性保戶擁有的增加保額選擇權價值高於女性保戶。 三、年紀較長之保戶擁有的增加保額選擇權價值高於年紀輕者。 四、隨著年齡的增加，男女間增加保額選擇權價值的差額越來越大。

The calculations of modern life insurance premiums are all relied on traditional actuarial approach by using three important elements of pricing, mortality tables, assumed interest rate, and expected operation expense rate to price the premiums of each covered person. In addition, the funded reserves of life insurance companies and the policy value reserves of insurers are also calculated by the same way, assuming the initial conditions are remain unchanged. During the insuring period, companies guarantee to provide a variety of rights to the insured free of charge according to the same actuarial concept, and two of very obvious options among them are conversion privilege and increase of sum assured. By traditionally actuarial calculations, they are of no value. The purpose of this research is the endowment of the most basic insurance product, focusing on increase of sum assured, via the feature of interest rate variable which effects the policy invisible value, based on the binomial options pricing model, trying to figure out the expected future cash flow under the condition and principle of risk neutral, and discounting upon the risk-free rate in order to calculate the value of increase of sum assured. The conclusions are as follows: 1. It is indeed with value in the options of increase of sum assured according to the options evaluation model. 2. The value of male's options in increase of sum assured is higher than the female's. 3. The value of the elder's options in increase of sum assured is higher than the younger's. 4. The difference of the value in increase of sum assured between male and female is larger and larger upon age increased.