所謂的存活交換是指雙方簽訂一紙合約，約定在未來的數個時點交換期初約定的金額，且此金額的多寡決定於未來的死亡率（或生存率）。而所謂的訂定存活交換的價格則是指在期初決定一個固定比率的貼水，使得該交換未來雙方的現金流相同。為了要能準確訂定像存活交換這種死亡率衍生性商品，我們必須要有一個適當的死亡率預測模型。現存的大多數死亡率衍生性商品定價模型都忽略死亡率會隨機跳躍的情形，因此本篇論文運用了Cox, Lin and Wang (2006)的模型來建構考慮隨機跳躍的死亡率過程。由於本篇文章主要探討巨幅變動因子以及風險的市場價格對此貼水的影響，故假設模型中的其餘參數和Cox, Lin and Wang (2006)估計的結果相同，然後檢驗在不同的巨幅變動因子及風險的市場價格下存活交換的貼水會如何的改變。除此之外此篇文章也考慮到關於違約發生的問題，在評價交換時忽略違約風險是不合理的，因此我們利用同樣的模型並增加一個卜瓦松過程來描述違約事件，然後在不同的違約率下比較模型所求得的貼水。 A survivor swap (SS) is an agreement to exchange cash flows in the future based on the mortality-dependent index. Pricing survivor swaps means to determine the fixed proportional premium which makes the initial value of the swaps is zero to each party. In order to price the mortality derivatives as SS precisely, an appropriate model to forecast mortality rate is necessary. Most of the existing mortality derivatives pricing and modeling papers ignore mortality jumps. This paper applies the Cox, Lin and Wang (2006) model to construct an individual mortality process with jumps. Because this article is interested in how jump factors and market price of risk affect premiums, it assumes that the other parameters of the model are like Cox, Lin and Wang (2006) and then examines how the premiums might vary under the different situation of jump factors and market price of risk. In addition, this article also considers that a default event may occur for the duration of a swap. It is irrational that to price a swap ignores the issue of counterparty risk. We use the same model but add a Poisson process to describe the default events, and then assume different default rates to compare the premiums.
