The age pattern of transitory mortality jumps and its impact on the pricing of catastrophic mortality bonds |
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| Institution: | 1. Department of Statistics and Actuarial Science, University of Waterloo, Canada;2. Risk Management, Department of Statistics and Actuarial Science, University of Waterloo, Canada;1. Amsterdam School of Economics, University of Amsterdam, Roetersstraat 11, 1018 WB, Amsterdam, The Netherlands;2. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada;1. Towers Watson Research and Innovation Center, Youkeyuan Road 88, 430074, Wuhan, China;2. SAV, Swiss certified pension actuary, Switzerland;3. Towers Watson AG, Talstrasse 62, 8021 Zurich, Switzerland;1. School of Sciences, Hebei University of Technology, PR China;2. Department of Statistics and Actuarial Science, Simon Fraser University, Canada;1. Nanyang Business School, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore;2. Department of Mathematics and Statistics, Curtin University, Perth, Australia;3. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1;1. School of Finance, Nankai University, China;2. Department of Econometrics and Operations Research, Tilburg University, Netherlands;3. Netspar, Netherlands |
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| Abstract: | To value catastrophic mortality bonds, a number of stochastic mortality models with transitory jump effects have been proposed. Rather than modeling the age pattern of jump effects explicitly, most of the existing models assume that the distributions of jump effects and general mortality improvements across ages are identical. Nevertheless, this assumption does not seem to be in line with what we observe from historical data. In this paper, we address this problem by introducing a Lee–Carter variant that captures the age pattern of mortality jumps by a distinct collection of parameters. The model variant is then further generalized to permit the age pattern of jump effects to vary randomly. We illustrate the two proposed models with mortality data from the United States and English and Welsh populations, and use them to value hypothetical mortality bonds with similar specifications to the Atlas IX Capital Class B note that was launched in 2013. It is found that the features we consider have a significant impact on the estimated prices. |
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| Keywords: | Risk-neutral valuation Securitization The Lee–Carter model Jump effects Catastrophic mortality bonds |
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