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Title: 具傳染效果的隨機死亡風險模型之建立及其應用
Modeling Infectious Mortality Risk and Its Application
Authors: 陳芬英
Chen, Fen-Ying
Contributors: 黃泓智
Huang, Hong-Chih
Chen, Fen-Ying
Keywords: 死亡風險傳染模型
Infectious mortality risk
Mortality-linked bond
Wang transform
Jump model
Floating-coupon bond
Date: 2018
Issue Date: 2018-07-24 10:59:48 (UTC+8)
Abstract: 本論文首次提出兩個死亡風險傳染模型,並將此兩個傳染模型分別應用於與死亡率連動的零息債券和附息債券的評價上。過去的文獻皆以跳躍模型(jump model)捕捉國與國之間死亡率共同移動的現象,但是當一國的死亡率受巨災影響而產生跳躍時,其他國家的死亡率未必會隨之跳躍,例如2002年的SARS。然而,當某些國家的死亡率因巨災而有顯著的跳躍時,其他國家的死亡率往往也會受之影響,隨之跳躍,例如1918年的Spanish flu。然而過去的死亡率模型並未能描述這種跳躍的現象。因此本論文主要是提出可以解釋此種現象的傳染模型,並推導與死亡率連動的零息債券和固定票息債券的封閉解,進而分析死亡傳染效果對這些債券價格之影響。實證分析結果發現在高度傳染的情況下,與死亡率連動的零息債券和附息債券的合理價格是少於低度傳染的狀況。因此忽略死亡率的傳染效果,與死亡率連動的債券其合理價格是會被高估。此結果希冀能提供再保險公司對於與死亡率連動債券的訂價和避險一個參考依據。
This thesis examines the valuation of mortality-linked bonds in two infectious mortality models in two main parts:
(1)Valuation and Analysis of the Swiss Re Bond without Coupons in an Infectious Mortality Model
(2)Valuation and Analysis of Fixed-Coupon and Floating-Coupon Mortality Bonds in an Infectious Mortality Model
The two main parts of this dissertation focus on infectious mortality risk, and two infectious models are developed to analyze the impacts of infectious mortality risk on mortality-linked bonds. This approach is different from that in the literature. To capture the infectious mortality dynamics across countries, two mortality jumps are considered in the mortality modeling: infectious jumps and specific country jumps. An infectious jump occurs only when there is a catastrophic event that causes considerable mortality. Furthermore, the mortality experience in France, the United Kingdom, the United States, Italy, and Switzerland is employed to fit the proposed infectious mortality model.
Using the two infectious mortality models, this dissertation explores the impacts of infectious mortality risk on the two types of mortality-linked bonds: zero-coupon mortality bonds and coupon mortality bonds. The first part demonstrates the structure of a zero-coupon mortality bond, namely Vital Capital I, which is a type of Swiss Re bond without coupons and was first issued as a 3-year catastrophic mortality bond in 2003. Under the infectious mortality framework, the closed-form solution of Vital Capital I is derived using Wang’s transform (2000). An empirical analysis reveals that the fair price of Vital Capital I in the model is lower than face value (market price). Sensitivity analyses illustrate that the sensitivity of the volatilities of the magnitudes of infectious mortality is the largest among the model parameters, whereas that of threshold values is the smallest.
In the second part, coupon mortality bonds, namely fixed-coupon and floating-coupon bonds, are examined. These bonds are similar to the Swiss Re bond. The closed-form solution of a fixed-coupon mortality bond is derived, and it is assumed that the coupons of floating-coupon mortality bonds are linked to a stochastic interest rate, which follows the Cox–Ingersoll–Ross interest rate model. Monte Carlo simulation is employed to evaluate the sensitivities of fair prices of floating-coupon bonds. The empirical results show the fair spreads of these two types of bonds are also higher than the spreads of 0.45% indicated by Cox et al. (2006) and closer to the market prices of 1.35% of the Swiss Re bond.
A common phenomenon is revealed in the first and second parts, which specifies that the fair prices of mortality-linked securities in high-infectious mortality model are fewer than those of mortality-linked securities in low-infectious mortality model. Therefore, ignoring the effects of infectious mortality rates significantly overestimates the par spread of mortality bonds; by contrast, considering this phenomenon provides a par spread of the mortality security that is closer to real-world values. This is helpful for pricing mortality securities and for managing catastrophic mortality risk for reinsurers.
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Description: 博士
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Data Type: thesis
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