以結構模型評價違約風險的死亡率債券

Abstract

死亡率債券(Mortality Bond)是近年來重要的金融創新商品之一，將壽險業之死亡率風險(Mortality Risk)轉移至資本市場。最為代表的是瑞士再保險公司在2003年12月發行高達4億的死亡率債券，吸引許多投資客的湧入並成為全球投資標的，因此評價死亡率債券成為一個重要的議題。本文發展一個結構模型來評價有違約風險的死亡率債券，此模型結合隨機利率的資本動態、隨機死亡率的動態，並用蒙地卡羅(Monte Carlo)數值方法模擬無違約風險和有違約風險(Default Risk)的死亡率債券價格。在最後，將基差風險(Basis Risk)、道德風險(Moral Hazard)放入模型中討論且比較之間的債券價格。

Mortality bond is one of the innovation commodity in the financial market recently, and mortality risk is successfully transferred from life assurance industry to capital market. A famous example is that Swiss Re mortality bond whose issue size was $400 million was issued in December 2003, attracting attention of investors and becoming an underlying investment all over the world. Therefore, pricing mortality bond become an important issue. This article develops a structural model to price a default-risky mortality bond, incorporating asset dynamics of stochastic interest rates and mortality model and we use the Monte Carlo method to compute default-free and default-risky mortality bond. Last, we put moral hazard and basis risk into model and discuss difference of these bond prices.