在Hull-White隨機利率及動態生存率下評價保證最低提領給附保險附約

Abstract

保證最低提領給付保險附約(Guaranteed Minimum Withdrawal Benefit; GMWB)為一投資型保單，發行公司會以投保人的躉繳保費做為資金，拿去市場上進行投資配置，在此期間的損益將會反應在投保人的帳戶價值中，並保證投保人在每一年都可以從帳戶中提領固定金額的年金，直到保單存續期間結束為止，因此此商品也是變額年金保險(Variable annuities; VA)的另一種新型態，但在保單結束的當下若帳戶價值仍有剩餘，則可全數歸還給保戶，因此可以讓保戶獲得額外的報酬。且本身是保險契約，為保單的一種，在稅賦上也可獲得優惠，適合長期的退休/生涯規劃。 本文旨在找出GMWB保單的公平保費費率，以期能做為此商品買賣雙方可以參考的依據。在過去文獻中，早期GMWB的評價多假設商品為固定利率和連續提領且無遞延期的存在。但GMWB為一長期的投資型商品，除了利率的影響外，投保人在保單存續期間的存亡與否，也會大幅影響商品評價的正確性。一旦投保人在投保期間不幸過世，則此GMWB保單隨即會解約，投保人將無法再獲得未來保證提領的權益。此外，投保人也能在投保期間自行提前解約，將帳戶價值全數領出，以規避未來可能的景氣下滑風險，但超額提領的部份需承擔提前解約的賠償費，而且也會取消未來的保證提領權益。 因此本文除考慮商品在隨機利率和離散提領的狀況外，另外加上動態生存率模型，以計算投保人生存和死亡下的獲益；以及提前解約機制，讓投保人能獲取帳戶現值，以期能更貼近實務上的保單設計，評價出合適的公平保費費率。最後我們也會分析各個因素對GMWB價值的影響，做為未來制定此類商品的參考。

The Guaranteed Minimum Withdrawal Benefit (GMWB) is a unit-linked insurance plan. The policy holder save a single premium to personal account at the beginning, then the insurance company will invest this account in financial markets, and gains and losses will be reflected to the personal account value. The GMWB promises that the policy holder cans regularly withdrawal a predetermined amount from personal account. So the GMWB can be seen as a variable annuity. At the maturity, if there is a surplus value of personal account after withdrawing, all of the surplus value will be returned to the policy holder, it can be seen as an investment premium. In addition, the GMWB has tax concession because of it is classified as a policy; therefore the GMWB is a good investment decision for long-term retirement and career planning. In this paper, we aim to evaluate the fair insurance fee. Most of past literature assume interest rate, continuous withdrawal and don’t consider the existence of deferred period, which will affect GMWB value and insurance fee. Furthermore, death rate of policy holder also affects the accuracy of pricing value of GMWB. This is because the GMWB contact is terminated, the account value is returned to policy holders, and the future annuity is cancelled, when the policy holder dies. In addition, policy holder can surrender the GMWB early and take away the personal account value to avoid the risk of future economic downturn, but the over withdrawal part of annuity will be deducted by a penalty amount. Our study will consider the stochastic interest rate, discrete withdrawal, dynamical survival model and early surrender mechanism to make our pricing model close to the real-world situation and find an appropriate fair insurance rate. Finally, we also analysis the influences of fair insurance rate between different scenarios to provide a reference basis of future design of GMWB.