考慮隨機跳躍與違約風險下存活交換合約之定價

Pricing Survivor Swaps with Mortality Jumps and Default Risk

本文利用Cox et al.(2006)所發展之模型並同時納入考慮隨機跳躍的死亡率過程與違約風險來進行存活交換合約之定價。由本文評價結果發現：市場風險價格與死亡率之隨機跳躍頻率皆與存活交換合約價格存在正向關係，且與前者的正向關係亦隨死亡率之隨機跳躍頻率上升而增強。再者我們亦發現在所考慮的各種違約風險程度下市場風險價格與死亡率之隨機跳躍頻率與存活交換合約價格之正向關係依然存在。另一方面，在其他條件不變下本文發現高（低）違約風險隱含相對高（低）的存活交換合約價格。上述結果可以清楚地提供合約發行機構與投資人於發行或購買合約時進行訂定或判斷合約價格所需考量之價格攸關因素。

A survivor swap refers to an agreement for the future exchange of cash flows based upon a mortality-dependent index. Pricing survivor swaps involves the determination of a fixed proportional premium, π, which results in an initial zero value of the swaps for each party. In order to provide a precise valuation of a mortality derivative, such as a survivor swap, an appropriate model is necessary for the forecasting of the mortality rate. The model proposed for use in this study extends the model provided by Cox et al. (2006) by simultaneously considering mortality jumps and default risk. Using this extended model to price survivor swaps in this study, we mainly find from our simulated results, based upon the data collected, that the survivor swap premium has a positive correlation with both the market price of risk and the frequency of jumps. Furthermore, we find that a stronger jump frequency will enhance the effects of the market price of risk on the premium. On the other hand, the survivor swap premium is also found to have a positive correlation with the market price of risk and the frequency of jumps at any level of default risk. However, when the market price of risk and jump frequency levels are both fixed, a higher (lower) default risk will imply a lower (higher) premium.