Parametric mortality indexes: From index construction to hedging strategies |
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| Affiliation: | 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. Department of Banking and Finance, National Chiayi University, Chiayi, Taiwan;2. Department of Risk Management and Insurance, Feng Chia University, Taichung, Taiwan;3. Department of Insurance and Finance, National Taichung University of Science and Technology, Taichung, Taiwan;4. Department of Financial and Economic Law, CTBC Financial Management College, Tainan, Taiwan;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. Centro de Gestión de la Calidad y del Cambio, Universitat Politècnica de València, Spain;2. Cass Business School, City, University of London, United Kingdom;3. Grupo de Sistemas de Optimización Aplicada, Instituto Tecnológico de Informática, Universitat Politècnica de València, Spain;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: | In this paper, we investigate the construction of mortality indexes using the time-varying parameters in common stochastic mortality models. We first study how existing models can be adapted to satisfy the new-data-invariant property, a property that is required to ensure the resulting mortality indexes are tractable by market participants. Among the collection of adapted models, we find that the adapted Model M7 (the Cairns–Blake–Dowd model with cohort and quadratic age effects) is the most suitable model for constructing mortality indexes. One basis of this conclusion is that the adapted model M7 gives the best fitting and forecasting performance when applied to data over the age range of 40–90 for various populations. Another basis is that the three time-varying parameters in it are highly interpretable and rich in information content. Based on the three indexes created from this model, one can write a standardized mortality derivative called K-forward, which can be used to hedge longevity risk exposures. Another contribution of this paper is a method called key K-duration that permits one to calibrate a longevity hedge formed by K-forward contracts. Our numerical illustrations indicate that a K-forward hedge has a potential to outperform a q-forward hedge in terms of the number of hedging instruments required. |
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| Keywords: | Cairns–Blake–Dowd model Mortality indexes Securitization Hedging strategies Longevity risk reduction |
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