Economics - Research Publications
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ItemConstructing Out-of-the-Money Longevity Hedges Using Parametric Mortality Indexes(Informa UK Limited, 2021-01-01)Proposed by Chan et al. (2014), parametric mortality indexes (i.e., indexes created using the time-varying parameters in a suitable stochastic mortality model) can be used to develop tradable mortality-linked derivatives such as K-forwards. Compared to existing indexes such as the LLMA's LifeMetrics, parametric mortality indexes are richer in information content, allowing the market to better concentrate liquidity. In this paper, we further study this concept in several aspects. First, we consider options written on parametric mortality indexes. Such options enable hedgers to create out-of-the-money longevity hedges, which, compared to at-the-money-hedges created with q-/K-forwards, may better meet hedgers' need for protection against downside risk. Second, using the properties of the time-series processes for the parametric mortality indexes, we derive analytical risk-neutral pricing formulas for K-forwards and options. In addition to convenience, the analytical pricing formulas remove the need for computationally intensive nested simulations that are entailed in, for example, the calculation of the hedging instruments' values when a dynamic hedge is adjusted. Finally, we construct static and dynamic Greek hedging strategies using K-forwards and options, and demonstrate empirically the conditions under which an out-of-the-money hedge is more economically justifiable than an at-the-money one.
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ItemAn Efficient Method for Mitigating Longevity Value-at-Risk(Routledge, 2021)Many of the existing index-based longevity hedging strategies focus on the reduction in variance. However, solvency capital requirements are typically based on the -year-ahead Value-at-Risk, with = 1 under Solvency II. Optimizing a longevity hedge using variance minimization is particularly inadequate when the cost of hedging is non-zero and mortality improvements are driven by a skewed and/or heavy-tailed distribution. In this paper, we contribute a method to formulate a value hedge that aims to minimize the Value-at-Risk of the hedged position over a horizon of years. The proposed method works with all stochastic mortality models that can be formulated in a state-space form, even when a non-normal distributional assumption is made. We further develop a technique to expedite the evaluation of a value longevity hedge. By utilizing the generic assumption that the innovations in the stochastic processes for the period and cohort effects are not serially correlated, the proposed technique spares us from the need for nested simulations that are generally required when evaluating a value hedge.
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ItemDrivers of Mortality Dynamics: Identifying Age/Period/Cohort Components of Historical U.S. Mortality Improvements(Taylor & Francis (Routledge), 2020)The goal of this paper is to obtain an Age/Period/Cohort (A/P/C) decomposition of historical U.S. mortality improvement. Two different routes to achieving this goal are considered. In the first route, the desired components are obtained by fitting an A/P/C model directly to historical mortality improvement rates. In the second route, an A/P/C model is estimated to historical crude death rates and the desired components are then obtained by differencing the estimated model parameters. For each route, various possible A/P/C model structures are experimented, and are evaluated on the basis of their robustness to several factors (e.g., changes in the calibration window) and their ability to explain historical changes in mortality improvement. Based on the evaluation results, an A/P/C decomposition for each gender is recommended. The decomposition will be examined in a follow-up project, in which the linkages between the A/P/C components and certain intrinsic factors will be identified.