| Summary: | 博士 === 國立政治大學 === 風險管理與保險學系 === 106 === 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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