以樹狀模型評價保證最低提領給付保險附約

Abstract

保證最低提領給付保險附約(guaranteed minimum withdrawal benefits; GMWB)為變額年金保險(variable annuities; VA)之新型態附約，因其提供最低給付保證，兼具投資功能與報酬保障，為近年來新興之投資型保險商品。文獻上評價GMWB之方法大體上可歸類為蒙地卡羅模擬法和以數值方法求解PDE方程式兩種，本文將運用樹狀結構法更直觀且更貼近實務的對GMWB進行評價。我們以Milevsky與Salisbury (2006)的靜態模型為基礎，提出GMWB可拆解為一離散型單一向下失效障礙選擇權(discrete down-and-out single barrier option)加上一定期確定年金(generic term-certain annuity)，沿用Dai與Lyuu (2004)和Dai (2009)設計的階梯樹狀模型(stair tree)股價會因配發現金股利而呈階梯狀下降之想法，運用Dai與Lyuu (2008)提出的bino-trinomial tree (BTT)評價GMWB內含選擇權。我們發現運用此法計算出的公平費用率與蒙地卡羅模擬法的數值結果完全相同，且運算速度更快。

Guaranteed minimum withdrawal benefits (GMWB) is an innovative rider of variable annuity (VA) policies. In recent years GMWB has gained popularity due to it being an investment-linked insurance while guaranteeing minimum return. The pricing method of GMWB can be generally classified in two ways: Monte Carlo simulation and numerical PDE techniques. In this research, the tree model is used to price GMWB rider in a more realistic and intuitive fashion than existing methods. We extend the static model in Milevsky and Salisbury (2006), showing that the product can be decomposed into a discrete down-and-out single barrier option plus a generic term-certain annuity. We follow the idea of stair tree in Dai and Lyuu (2004) and Dai (2009), using bino-trinomial tree (BTT) in Dai and Lyuu (2008) to price the GMWB’s embedded exotic option. Numerical experiments show this method to be more accurate and efficient.