以VAR法計算長壽債券定價 台灣資料為例

Abstract

隨著醫療水平的進步，人們的死亡率逐年下降。造成許多保險公司或退休基金等年金支付者必須支付比以往還要更多的年金給付，而可能面臨破產問題。然而，長壽風險難以藉由其他資本市場的金融工具轉移。因此，將長壽風險資產證券化的概念已經行之有年。本文將以台灣資料為例，試算出65歲以上老年人口存活率為聯結的長壽債券定價。 過往的長壽債券多採用二因子死亡率模型估計死亡率且運用風險中立評價法算出風險價格。本篇則同樣運用二因子死亡率模型。但在風險貼水的計算上，採用VaR 的概念算出債券發行方的損失比率及所需風險貼水的關聯。在無信用風險的假設下，本篇建議長壽債券由政府或是信用良好之金融機構來發行。

Longevity risk refers to uncertainty of mortality improvement in the future caused by medical development and economy growth. It may leads to solvency issues for annuity provider. However, mortality-linked securities provide the hedging instrument which transfer longevity risk from annuity provider to capital market. In this article, we use the two-factor model for stochastic mortality to predict the evolution of mortality rate in Taiwan. In addition, we use the concept of VaR(value at risk) to compute possible longevity risk premium in certain cohort and maturity of a longevity bond. Under these conditions, we derive the price of this bond. Last, we extend the calculations to longevity bonds with different cohorts and maturities to obtain the longevity risk premium and pricing longevity bond base on risk-neutral valuation.