解約率因素下附保證給付投資型保險的風險價差

• Main Author: 潘冠宇
• Language: 中文
• Published: 國立政治大學
• Subjects: 風險價差; 滿期給付投資型保險; 經濟因子脫退率; risk spreads; GMMB; lapse rates
• Online Access: http://thesis.lib.nccu.edu.tw/cgi-bin/cdrfb3/gsweb.cgi?o=dstdcdr&i=sid=%22G0099358023%22.

近年來因市場波動劇烈, 保險公司紛紛推出的「附保證投資型保單」, 給 予保戶在投資上的保證。然而, 附最低給付保證條件卻使得保險公司必須面 對更大的核保與財務風險。所以計算出附有最低保證條件商品的保費就顯 得格外地重要。 傳統附保證保單在訂價時,都是假設固定己知的脫退率,因為他們認為 脫退率的變化不會是影響保單價值的主因。但在Mary hardy 所著的《Investment Guarantees》一書中page 96 特別提到脫退風險: Withdrawals are more problematic. Withdrawals are, to some extent, related to the investment experience, and the withdrawal risk is, therefore, not fully diversifiable. 因此, 本文希望透過建立受經濟因子影響的解約率模型,來得到附保證保險 的風險價差。 本文考慮附保證滿期給付投資型商品(GMMB),並且使用 Heston (1993) 提出的財務市場模型以及參考Mercurio (1996,2001) 評價投資型保險之風 險承擔價差方法, 使用效用函數來描述保險契約雙方之風險趨避程度。同 時根據Kolkiewicz & Tan (2006) 假設受經濟因子的危險比率模型(hazard rate model), 來反映出資產的平均波動程度會影響保戶的脫退率。最後以 情境方式分別模擬5、10及15年到期的附保證最低滿期投資型保險之風險 價差。本研究推導之模型主要得出下列結果: (1) 保單期間愈長, 價差愈大。 (2) 價外賣權的價差高於價內。(3) 風險規避程度越高買賣價差越大。(4) 脫 退率受經濟影響愈深, 保單的買賣價差愈大。(5) 當保險公司所保證的價格 愈高時, 價差的影響愈大。 === With the fluctuation in the financial market in 2008, insurance company provided the consumers with equity-linked life insurances embedded guarantees. On the other hand, there are more risk in the financial literacy and underwriting performance of the insurance company. It is especially important to calculate the premium of the contract embedded investment guarantee properly . Traditional method of pricing the contract embedded investment guarantee was assumed that lapse rate was known, because product providers believed lapse rate was not a major factor to price the contract. However, Mary hardy’s ”Investment Guarantees” page 96 specifically mentions about the lapse rate risk: Withdrawls are more problematic. Withdrawals are, to some extent ,related to the investment experience, and the withdrawal risk is, therefore, not fully diversifiable. So this article will found the model of lapse rate dependent on economic factors and further get the fair value of one kind of a contract embedded guarantee: GMMB. We will build a financial model introduced by Heston (1993) and use the methodology provided by Mercurio (1996,2001) to price the risk bearing gap of a contract embedded guarantee with utility function to depict the risk averse level between investors . And we have lapse rates affected from the fluctuation of the implying asset which is the hazard rate model used by Kolkiewicz & Tan (2006). Finally, we will simulate a set of scenarios to present the Risk bearing spreads of equity-linked life insurance embedded guarantees whose term are 5、10 and 15 years. The following are the consequences I got: (1) The longer the duration, the larger the spread. (2) The spread out of money is larger than that in the money. (3) The higher the risk aversion, the larger the buy-ask spread. (4) The deeper the influence of economy on the lapse rate, the larger the buy-ask spread. (5) The higher guarantee price insurer offer, the deeper the spread affect.