An Optimal Product Mix for Hedging Longevity Risk in Life Insurance Companies: The Immunization Theory Approach

This article investigates the natural hedging strategy to deal with longevity risks for life insurance companies. We propose an immunization model that incorporates a stochastic mortality dynamic to calculate the optimal life insurance–annuity product mix ratio to hedge against longevity risks. We model the dynamic of the changes in future mortality using the well‐known Lee–Carter model and discuss the model risk issue by comparing the results between the Lee–Carter and Cairns–Blake–Dowd models. On the basis of the mortality experience and insurance products in the United States, we demonstrate that the proposed model can lead to an optimal product mix and effectively reduce longevity risks for life insurance companies.     

The Implied Longevity Yield: A Note on Developing an Index for Life Annuities

I develop an index for tracking the dynamic behavior of life (pension) annuity payouts over time, based on the concept of self‐annuitization. Our implied longevity yield (ILY) value is defined equal to the internal rate of return (IRR) over a fixed deferral period that an individual would have to earn on their investable wealth if they decided to self‐annuitize using a systematic withdrawal plan. A larger ILY number indicates a greater relative benefit from immediate annuitization. I use age 65—with a 10‐year period certain—compared against the same annuity at age 75 as the standard benchmark for the index, and calibrate to a comprehensive time series of weekly (Canadian) life annuity quotes from 2000 through 2004. I find that during this period the ILY varied from 5.45 percent to 6.90 percent for males and from 5.00 percent to 6.42 percent for females and was highly correlated with a duration‐weighted average yield of 10‐year and long‐term Government of Canada bonds. I believe our ILY metric can help promote and explain the benefits of acquiring lifetime payout annuities by translating the abstract‐sounding longevity insurance into more concrete and measurable financial rates of return.     

Trading death: The implications of annuity replication for the annuity puzzle,arbitrage, speculation and portfolios

Annuities are perceived as being illiquid financial instruments, and this has limited their attractiveness to consumers and their inclusion in financial models. However, short positions in annuities can be replicated using life insurance and debt, permitting long positions in annuities to be offset, or short annuity positions to be created. The implications of this result for the annuity puzzle, arbitrage between the annuity and life insurance markets, and speculation on expected longevity are investigated. It is argued that annuity replication could help reduce the annuity puzzle, improve the price efficiency of annuity markets and promote the inclusion of annuities in household portfolios.     

动态死亡率下个人年金的长寿风险分析

传统的精算定价方法假定死亡率是静态的,实际上死亡率是随时间而变动的具有动态不确定性的变量。在动态死亡率的框架下定量分析长寿风险对于个人年金产品定价的影响:引入Wang转换的风险定价方法度量长寿风险的市场价格,并运用模拟分析的方法分析长寿风险对个人年金定价的影响。最后,基于分析结果,就保险公司如何管理这一风险给出建议。     

Application of Relational Models in Mortality Immunization

The prediction of future mortality rates by any existing mortality models is hardly exact, which causes an exposure to mortality (longevity) risk for life insurers (annuity providers). Since a change in mortality rates has opposite impacts on the surpluses of life insurance and annuity, hedging strategies of mortality and longevity risks can be implemented by creating an insurance portfolio of both life insurance and annuity products. In this article, we apply relational models to capture the mortality movements by assuming that the realized mortality sequence is a proportional change and/or a constant shift of the expected one, and the size of the changes varies in the length of the sequences. Then we create a variety of non-size-free matching strategies to determine the weights of life insurance and annuity products in an insurance portfolio for mortality immunization, where the weights depend on the sizes of the proportional and/or constant changes. Comparing the hedging performances of four non-size-free matching strategies with corresponding size-free ones proposed by Lin and Tsai, we demonstrate with simulation illustrations that the non-size-free matching strategies can hedge against mortality and longevity risks more effectively than the size-free ones.     

Longevity Risk Management in Singapore's National Pension System

Although annuities are a theoretically appealing way to manage longevity risk, in the real world relatively few consumers purchase them at retirement. To counteract the possibility of retirees outliving their assets, Singapore's Central Provident Fund, a national defined contribution pension scheme, has recently mandated annuitization of workers’ retirement assets. More significantly, the government has entered the insurance market as a public‐sector provider for such annuities. This article evaluates the money's worth of life annuities and discusses the impact of the government mandate and its role as an annuity provider on the insurance market.     

Author’s Reply: Statistical Independence and Fractional Age Assumptions - Discussion by Cecil Nesbitt; Elias S. W. Shiu; Serena Tiong,January 1997

Abstract

This paper addresses the problem of the sharing of longevity risk between an annuity provider and a group of annuitants. An appropriate longevity index is designed in order to adapt the amount of the periodic payments in life annuity contracts. This accounts for unexpected longevity improvements experienced by a given reference population. The approach described in the present paper is in contrast with group self-annuitization, where annuitants bear their own risk. Here the annuitants bear only the nondiversifiable risk that the future mortality trend departs from that of the reference forecast. In that respect, the life annuities discussed in this paper are substitutes for reinsurance and securitization of longevity risk.     

我国企业年金逆向选择和道德风险管理研究

当前形势下我国人口老龄化问题日益凸显,基本养老保险制度面临着巨大的支付压力。企业年金在缓解基本养老保险给付方面起到了重大的补充作用,但是我国现行的企业年金在实际运营管理中存在很多问题。论文从委托代理角度分析企业年金各主体之间的逆向选择和道德风险问题,并提出几点相关政策建议,以完善我国企业年金制度,使其更好地为企业职工提供更安全更实惠的社会福利。     

Hedging Longevity Risk When Interest Rates are Uncertain

Abstract

This paper proposes an asset liability management strategy to hedge the aggregate risk of annuity providers under the assumption that both the interest rate and mortality rate are stochastic. We assume that annuity providers can invest in longevity bonds, long-term coupon bonds, and shortterm zero-coupon bonds to immunize themselves from the risks of the annuity for the equity holders subject to a required profit. We demonstrate that the optimal allocation strategy can lead to the lowest risk under different yield curves and mortality rate assumptions. The longevity bond can also be regarded as an effective hedging vehicle that significantly reduces the aggregate risk of the annuity providers.     

The Effect of the Real Option to Transfer on the Value of Guaranteed Minimum Death Benefits

Variable annuity contracts frequently have many options and option‐like features embedded in the contracts. Some are obvious, such as guaranteed minimum death benefits (GMDBs), while others are less obviously option‐like. In this article, we consider the effect of the real option to transfer funds between fixed and variable accounts. If a GMDB rider is considered in isolation, it is sometimes in the policyholder's interest to transfer to the fixed fund if the fixed fund earns less than the variable fund in a risk‐neutral world. On the other hand, the option to transfer will not be used if the entire annuity and rider are considered together.     

The Political Economy of Government-Issued Longevity Bonds

This article explores the trade‐offs associated with government issuance of longevity bonds as a way of stimulating private annuity supply in the presence of aggregate mortality risk. We provide new calculations suggesting a 5 percent chance that aggregate mortality risk could ex post raise annuity costs for private insurers by as much as 5–10 percentage points, with the most likely effect based on historical patterns toward the lower end of that range. While we suspect that aggregate mortality risk does exert some upward pressure on annuity prices, evidence from private market pricing suggests that, to the extent that private insurers are accurately pricing this risk, the effect is less than 5 percentage points. We discuss ways that the private market can spread this risk, while emphasizing that the government has the unique ability to spread aggregate risk across generations. We note factors that might hamper such an efficient allocation of risk, including potential political incentives for the government to shift more than the optimal amount of risk onto future generations, and the possibility that government fiscal policy might allocate risk less efficiently within each generation than would private markets. We also discuss how large‐scale longevity bond issuance might affect government borrowing costs, as well as political economy aspects of how the proceeds from such a bond issuance might be used.     

Basis risk in static versus dynamic longevity-risk hedging

This paper provides a tractable, parsimonious model for assessing basis risk in longevity and its effect on the hedging strategies of Pension Funds and annuity providers. Basis risk is captured by a single parameter, that measures the co-movement between the portfolio and the reference population’s longevity. The paper sets out the static, full and customized swap-hedge for an annuity, and compares it with a dynamic, partial, and index-based hedge. We calibrate our model to the UK and Scottish populations. The effectiveness of static versus dynamic strategies depends on the rebalancing frequency of the second, on the relative costs, and on basis risk, which does not affect fully-customized, static hedges. We show that appropriately calibrated dynamic hedging strategies can still be reasonably effective, even at low rebalancing frequencies.     

Long guarantees with short duration: the rolling annuity

We present a new type of with-profits annuities which offer lifelong, yet hedgeable, guarantees. The rolling annuity gives a minimum lifelong guarantee at the time of contribution complemented with a series of guaranteed increases prior to retirement. Importantly, the initial guarantee and the subsequent increases are all set at prevailing market rates and hence are not known in advance. The structure of the guarantee implies that, prior to the last increase, the liability is equivalent to a zero-coupon bond maturing at the next increase and can therefore easily be hedged in the financial markets. Furthermore, the short duration implies that the financial and regulatory value will (essentially) coincide. We show financial fairness and we derive the reserve and thereby the hedging strategy. We also consider longevity risk, the duration profile, and report on a simulation study of the real value of the final payout.     

延迟退休、个人账户调整与城镇职工医疗保险基金可持续运行

文章通过构建精算模型,从城镇职工医疗保险基金可持续运行的角度对不同延迟退休和个人账户调整方案及组合进行模拟评估。研究发现:现行制度下城镇职工医疗保险统筹基金面临支付风险,延迟退休仅能够在短期内缓解城镇职工医疗保险基金的支付压力;仅依靠延迟退休难以在长期内缓解城镇职工医疗保险基金的支付压力,运用“延迟退休+个人账户调整”的模式,即在延迟退休的基础上对个人账户进行调整,更有利于基金的长期稳定运行。在现行退休制度下,建议取消个人账户,将单位缴费和个人缴纳的费用计入统筹账户,城镇职工医疗保险基金的单位缴费率可以下调1%;在延迟退休政策势在必行的情况下,建议在男性和女性不同岁退休的基础上,取消个人账户,实现城镇职工医疗保险单位缴费率降低2%。这样既有利于基金的可持续运行,也可以保证基金的运行效率,更能加强城镇职工医疗保险制度的互助共济性。     

Mortality-Indexed Annuities Managing Longevity Risk Via Product Design

Abstract

Longevity risk has become a major challenge for governments, individuals, and annuity providers in most countries. In its aggregate form, the systematic risk of changes to general mortality patterns, it has the potential for causing large cumulative losses for insurers. Since obvious risk management tools, such as (re)insurance or hedging, are less suited for managing an annuity provider’s exposure to this risk, we propose a type of life annuity with benefits contingent on actual mortality experience.

Similar adaptations to conventional product design exist with investment-linked annuities, and a role model for long-term contracts contingent on actual cost experience can be found in German private health insurance. By effectively sharing systematic longevity risk with policyholders, insurers may avoid cumulative losses.

Policyholders also gain in comparison with a comparable conventional annuity product: Using a Monte Carlo simulation, we identify a significant upside potential for policyholders while downside risk is limited.     

What Makes a Better Annuity?

Given costly and limited annuity products, we investigate how annuity market innovation could improve participation and increase individual welfare. We find that participation gains are most likely with new annuity products that concentrate on late‐life payouts. Our welfare analysis suggests that annuity innovation should focus on adding survival contingencies to assets commonly held by individuals. Finally, in a complete market setting, we find demand only for those annuity contracts with a significant time gap between purchase and payout (a rarity in current contracts). Overall, our analysis indicates ample opportunity for innovation to spur annuity demand and improve individual welfare.     

Sharing Longevity Risk: Why Governments Should Issue Longevity Bonds

Government-issued longevity bonds would allow longevity risk to be shared efficiently and fairly between generations. In exchange for paying a longevity risk premium, the current generation of retirees can look to future generations to hedge their systematic longevity risk. Longevity bonds will lead to a more secure pension savings market, together with a more efficient annuity market. By issuing longevity bonds, governments can aid the establishment of reliable longevity indices and key price points on the longevity risk term structure and help the emerging capital market in longevity-linked instruments to build on this term structure with liquid longevity derivatives.     

Lifetime asset allocation with idiosyncratic and systematic mortality risks

This paper considers a lifetime asset allocation problem with both idiosyncratic and systematic mortality risks. The novelty of the paper is to integrate stochastic mortality, stochastic interest rate and stochastic income into a unified framework. An investor, who is a wage earner receiving a stochastic income, can invest in a financial market, consume part of his wealth and purchase life insurance or annuity so as to maximize the expected utility from consumption, terminal wealth and bequest. The problem is solved via the dynamic programming principle and the Hamilton–Jacobi–Bellman equation. Analytical solutions to the problem are derived, and numerical examples are provided to illustrate our results. It is shown that idiosyncratic mortality risk has significant impacts on the investor’s investment, consumption, life insurance/annuity purchase and bequest decisions regardless of the length of the decision-making horizon. The systematic mortality risk is largely alleviated by trading the longevity bond. However, its impacts on consumption, purchase of life insurance/annuity and bequest as well as the value function are still pronounced, when the decision-making horizon is sufficiently long.     

Mortality regimes and longevity risk in a life annuity portfolio

This paper explores the presence of changes of trends or jumps in French mortality from 1947 to 2007, and assesses their implications on the longevity risk management of a life annuity portfolio. We accomplish this by extending the Poisson log-bilinear regression developed by Brouhns et al. (2002) with a regime-switching model. Estimation results show that French mortality is characterized by two distinct regimes. One refers to a strong uncertainty state, which corresponds to the longevity conditions observed during the decade following World War II. The second regime is related to the low volatility of longevity improvements observed during the last 30 years. We use these results to analyze the impact of mortality regimes on the longevity risk management of a life annuity portfolio. Simulation results suggest that the changes of trends in the mortality process have some implications for longevity risk management.     

Redistribution and Insurance: Mandatory Annuitization With Mortality Heterogeneity

This article examines the distributional implications of mandatory longevity insurance when mortality heterogeneity exists in the population. Previous research has demonstrated the significant financial redistribution that occurs under alternative annuity programs in the presence of differential mortality across groups. This article embeds that analysis into a life‐cycle framework that allows for an examination of distributional effects on a utility‐adjusted basis. It finds that the degree of redistribution that occurs from the introduction of a mandatory annuity program is substantially lower on a utility‐adjusted basis than when evaluated on a purely financial basis. In a simple life‐cycle model with no bequests, complete annuitization is welfare enhancing even for those with higher‐than‐average expected mortality rates, so long as administrative costs are sufficiently low. These findings have implications for policy toward annuitization, particularly as part of a reformed Social Security system.