分析死亡率模型在評價GLWB公平保費的風險

Abstract

醫療系統的改善使得死亡率減少，也造成人口高齡化的現象，為了確保退休後的生活水平，各種退休基金與相關生存年金商品的發行在金融保險市場扮演了十分重要的角色。為了更精確的替這些商品訂價，可以透過更複雜的死亡率模型得到死亡率與長壽風險，本文研究不同的Lee-Carter模型與CBD模型，並分析這些死亡率模型的變化對評價保證終身提領保險附約（Guaranteed Lifelong Withdrawal Benefit；GLWB）的公平保費有何影響。本文使用JP-Morgan提供的參數校正程式來估計1950~2004年的美國死亡率資料，並使用時間序列分析來預測年代效應（period-effect）與世代效應（cohort-effect）的序列參數，透過Bayesian Information Criterion（BIC）去檢測這些模型的配適程度，再將這些資料去預測2005~2010年的死亡率，且使用Mean Absolute Percentage Error（MAPE）衡量預測結果是否精確。在真實世界下測量的死亡率透過Wang Transform轉換在風險中立測度下，再與張國培（2012）提出的GLWB定價程式結合，以得到GLWB的公平保費率。本文也分析這些死亡率模型或其他市場變數如何影響公平保費率。

Population aging phenomenon becomes more significant due to decrements of mortality rates caused by the improvements of healthcare systems. To ensure the living standard of retiree, various pension funds and related survival annuity products are issued and these products are playing more significant roles in financial and insurance markets. Complex mortality models are developed to capture the mortality and longevity risks in order to accurate price these products. This thesis studies the variations of Lee-Carter mortality model and the CBD model and analyzes how variations of mortality models influence the evaluation of the fair insurance fees of Guaranteed Lifelong Withdrawal Benefits（GLWB）. We use the parameter-calibration program provided by JP Morgen to make these mortality models fit 1950~2004 mortality data of USA. Time series analyses are used to predict the series for modeling period-effects and cohort-effects. We use Bayesian Information Criterion（BIC） to measure how these models fit real mortality data. Then we use these models to predict 2005~2010 mortality rates and measure their performance by mean absolute percentage error （MAPE）. The mortality rates under the real-world measure are transferred in the rates under the risk-neutral measure. These transferred rates are incorporated into Chang (2012) GLWB pricing model in order to price the fair insurance fees. Sensitivity analyses are given to analyze how mortality models or other market variables influence fair insurance fees.