在Hull-White隨機利率及隨機死亡率下評價保證終身提領給付保險附約

Abstract

GLWB(guaranteed lifelong withdrawal benefit)為一個普及的長天期商品。現今已被視為退休金規劃或是家庭收支規劃的一項重要選擇，同時滿足對投資及保險的需求。然而，由於GLWB的價值會根據利率、市場價格風險、死亡率風險與長壽風險而改變，因此難以對其進行評價與避險。在過去的文獻中，大多假設商品為固定利率和動態死亡率，而這會大幅影響商品評價的準確性。本研究旨在隨機死亡率及隨機利率下找出GLWB商品之公平保費費率。為了貼近實務，本研究亦探討分期繳費機制對保費的影響。 從研究結果中，我們發現GLWB價值與提領比率成正比。當帳戶價值與利率呈現正相關時，公平保費隨著利率波動度而增加，反之亦然。GLWB價值隨著投保人年齡增加而遞減，但當投保者年齡過大時此現象將產生反轉。在繳費現值固定下，年繳費次數越少的保單，公平保費較低；年提領次數越高，公平保費越高。

The Guaranteed Life Withdrawal Benefit, abbreviated as GLWB, is a popular long-term policy. Nowadays, it is considered as the most important choice for pension and household income-expenditure plan to satisfy customers’ need on investment and insurance. However, it is hard to price and hedge GLWB since the value of this GLWB varies due to the interest risk, the market price risk, the mortality risk, and the longevity risk. Most of literature evaluates GLWB under fixed interest rate and mortality risk assumptions, which affect the accuracy of valuation. This thesis evaluates the GLWB and the fair charge under the stochastic mortality and the interest model. In order to approximate reality, we also investigate the influence of installment payments on the fair charge. In our sensitive analysis, we can find that the withdrawal rate is proportional to the value of GLWB. When the correlation between the account value and the interest rate is positive, the fair charge increases with the volatility of the interest rate, and vice versa. As the age of policy holder increases, the value of GLWB decreases, but this phenomena inverse when the policy holder is too old. Under the fixed present value of total payments, the number of installment payments is positive related with fair charge of policy.