台灣長壽風險債券設計與評價

Pricing and Designing Longevity Bond: the Experience in Taiwan

經濟醫療發展造就人類壽命逐年增長，退休基金與提供年金型商品的金融機構在獲利上受到很大衝擊。此種長壽風險（Longevity Risk），是無法經由大數法則分散之系統風險。壽命連結證券化商品（Mortality-linked Securities）提供金融機構一個移轉死亡率風險至資本市場的新工具。死亡率債券（Mortality Bonds）及長壽債券（Longevity Bonds）已在國外發行數年，本文使用國內死亡率經驗，設計長壽債券發行條件，計算發行長壽債券理論價格及隱含的風險市場價格。此外，採用二因子死亡率模型（Cairns, et al, 2006），考慮參數不確定風險之下，估計並模擬台灣未來的存活率。最後利用風險中立定價法，計算不同發行條件、天期之長壽債券價格，做為台灣金融業發行壽命連結型商品之參考。

Longevity risk is defined as the uncertainty of mortality improvement in the future. It is a significant phenomenon that the average life span is getting longer than expected, especially among higher aged (elderly) people. Recently, the mortality-linked securities star to be prevalent in the financial markets. Financial institutions successfully transfer the mortality risk to the capital market by means of these securitizations. This paper intends to derive the reasonable market price of longevity bond and the market price of longevity risk as a reference to the mortality securitizations in Taiwan. The stochastic mortality and model parameter uncertainty are taken into consideration. We show how the risk-neutral valuation is applied on longevity bond. Last, we demonstrate an issuance of longevity bond in Taiwan as an example.