Economics - Research Publications
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ItemDynamic Longevity Hedging in the Presence of Population Basis Risk: A Feasibility Analysis From Technical and Economic Perspectives(Wiley, 2017-04-01)In this article, we study the feasibility of dynamic longevity hedging with standardized securities that are linked to broad-based mortality indexes. On the technical front, we generalize the dynamic “delta” hedging strategy developed by Cairns (2011) to incorporate the situation when population basis risk exists. On the economic front, we discuss the potential financial benefits of an index-based hedge over a bespoke risk transfer. By considering data from a large group of national populations, we find evidence supporting the diversifiability of population basis risk. We further propose a customized surplus swap—executed between a hedger and reinsurer—to utilize the diversifiability. As standardized instruments demand less illiquidity premium, a combination of a dynamic index-based hedge and the proposed customized surplus swap may possibly be a more economical (and equally effective) alternative to a bespoke risk transfer.
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ItemA Bayesian approach to developing a stochastic mortality model for China(Wiley, 2019-10-01)Stochastic mortality models have a wide range of applications. They are particularly important for analysing Chinese mortality, which is subject to rapid and uncertain changes. However, owing to data‐related problems, stochastic modelling of Chinese mortality has not been given adequate attention. We attempt to use a Bayesian approach to model the evolution of Chinese mortality over time, taking into account all of the problems associated with the data set. We build on the Gaussian state space formulation of the Lee–Carter model, introducing new features to handle the missing data points, to acknowledge the fact that the data are obtained from different sources and to mitigate the erratic behaviour of the parameter estimates that arises from the data limitations. The approach proposed yields stochastic mortality forecasts that are in line with both the trend and the variation of the historical observations. We further use simulated pseudodata sets with resembling limitations to validate the approach. The validation result confirms our approach's success in dealing with the limitations of the Chinese mortality data.
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ItemPricing temperature derivatives with a filtered historical simulation approach(Taylor & Francis (Routledge), 2019-10-13)In this paper, we propose pricing temperature derivatives using a filtered historical simulation (FHS) approach that amalgamates model-based treatment of volatility and empirical innovation density. The FHS approach implicitly captures the risk premium with the entire risk-neutral model (except the innovation distribution), thereby providing significantly more flexibility than existing methods that use only one designated parameter to capture the risk premium. Additionally, instead of relying on the fitted innovation distribution, the FHS approach uses empirical innovations to capture excess skewness, excess kurtosis, and other non-standard features in the temperature data, all of which are important for the correct pricing of temperature derivatives. We apply the FHS approach to pricing derivatives written on the temperature of Chicago, and demonstrate that this approach yields better in-sample and out-of-sample pricing performance than the constant market price of risk method and the consumption-based method.
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ItemA strategy for hedging risks associated with period and cohort effects using q-forwards(Elsevier, 2018-01)The stochastic nature of future mortality arises from both period (time-related) and cohort (year-of-birth-related) effects. Existing index-based longevity hedging strategies mitigate the risk associated with period effects, but often overlook cohort effects. The negligence of cohort effects may lead to sub-optimal hedge effectiveness, if the liability being hedged is a deferred pension or annuity which involves cohorts that are not covered by the data sample. In this paper, we propose a new hedging strategy that incorporates both period and cohort effects. The resulting longevity hedge is a value hedge, reducing the uncertainty surrounding the -year ahead value of the liability being hedged. The proposed method is illustrated with data from the male population of England and Wales. It is found that the benefit of incorporating cohort effects into a longevity hedging strategy depends heavily on the persistence of cohort effects and the choice of q-forwards.
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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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ItemMortality Forecasting for Multiple Populations: An Augmented Common Factor Model with a Penalized Log-Likelihood(Taylor & Francis Inc., 2019-02-20)Recently, the topic of multi-population mortality forecasting has gained considerable attention among researchers and end-users. One of the most popular multi-population mortality models is the augmented common factor (ACF) model. In spite of its popularity, the ACF model is subject to the limitation of producing mortality forecasts with a jagged pattern rather than a smooth relationship with age. In this paper, we attempt to mitigate this problem by generalizing the work of Delwarde et al. (2007) to a multi-population setting. The generalization involves (np + 1) smoothing parameters, one for the common trend and one for each of the np individual populations. The smoothing parameters are determined by using an extended leave-one-out cross-validation. We illustrate the proposed extension with real mortality data. It is found that compared to the original ACF model, the proposed extension produces mortality forecasts that are more reasonable, with less jagged patterns across ages.
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ItemDelta-hedging longevity risk under the M7–M5 model: The impact of cohort effect uncertainty and population basis risk(Elsevier, 2019-01-01)In a recent project commissioned by the Institute and Faculty of Actuaries and the Life and Longevity Markets Association, a two-population mortality model called the M7–M5 model is developed and recommended as an industry standard for the assessment of population basis risk. In this paper, we contribute a delta hedging strategy for use with the M7–M5 model, taking into account of not only period effect uncertainty but also cohort effect uncertainty and population basis risk. To enhance practicality, the hedging strategy is formulated in both static and dynamic settings, and its effectiveness can be evaluated in terms of either variance or 1-year ahead Value-at-Risk (the latter is highly relevant to solvency capital requirements). Three real data illustrations are constructed to demonstrate (1) the impact of population basis risk and cohort effect uncertainty on hedge effectiveness, (2) the benefit of dynamically adjusting a delta longevity hedge, and (3) the relationship between risk premium and hedge effectiveness.
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ItemImproving Risk Sharing and Borrower Incentives in Mortgage Design(Taylor & Francis (Routledge), 2019)In a traditional fixed rate mortgage, the borrower pays a fixed amount each period regardless of the value of the mortgaged property. One problem with this contract is that the borrower is less willing to pay when the house value falls. This was clearly seen in the 2008 financial crisis and its aftermath when mortgage default rates and foreclosures skyrocketed as the housing market crashed. A more efficient contract design should link payments to house prices so that the borrower's incentive to pay is not undermined by a decline in property value. In addition this design can save the lender the deadweight foreclosure costs. In this paper we examine two proposed index linked mortgages which have this risk sharing feature. We analyze the e ect of both designs on borrower incentives in a multi-period setting.
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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.