Longevity risk and capital markets: the 2023–2024 update

Longevity risk is the risk that the promised recipient of lifetime cashflows ends up living much longer than originally anticipated, thus causing a shortfall in funding. A related risk, reimbursement risk is the risk that providers of health insurance face when new and expensive drugs are introduced and the insurer must cover their costs. Longevity and reimbursement risks are particularly acute in domains in which scientific breakthroughs can increase the speed of new drug development. An emerging asset class, research-backed obligations or RBOs (cf., Fernandez et al., 2012), provides a natural mechanism for hedging these risks: RBO equity tranches gain value as new life- extending therapies are developed and do so in proportion to the number of successful therapies introduced. We use the stylized case of annuity underwriting to show how RBO equity could be used to hedge some forms longevity risk on a retirement portfolio. Using the same framework, we then show how RBO securities may be used to hedge a much broader class of reimbursement risks faced by health insurance firms. We demonstrate how to compute hedge ratios to neutralize specific exposures. Although our analytic results are stylized, our simulation results suggest substantial potential for this asset class to reduce financial uncertainty for those institutions exposed to either longevity or reimbursement risks. For example, our simulation results indicate that the correlation between the return on RBO equity and the reimbursement shortfall for a health insurer is about 0.66 under reasonable assumptions. Even under extremely conservative assumptions, this correlation is still 0.34, suggesting that RBO equity offers substantial hedging benefits, producing more favorable outcomes in about 87% of scenarios.

The paper presents closed-form Delta and Gamma hedges for annuities and death assurances, in the presence of both longevity and interest-rate risk. Longevity risk is modeled through an extension of the classical Gompertz law, while interest rate risk is modeled via an Hull-and-White process. We theoretically provide natural hedging strategies, considering also contracts written on different generations. We provide a UK-population and bond-market calibrated example. We compute longevity exposures and explicitly calculate Delta-Gamma hedges. Re-insurance is needed in order to set-up portfolios which are Delta-Gamma neutral to both longevity and interest-rate risk.

Given the rising cost of maintaining defined benefit (DB) pensions, there has been a surge of activities in recent years by DB plan sponsors to transfer their pension risk through strategies such as buy-ins and buy-outs. As buy-in and buy-out transaction pipelines grow, insurers actively participating in the buy-in and buy-out markets are exposed to significant longevity risk embedded in pension schemes. In this paper, we investigate how to maximize a bulk annuity insurer’s value with reinsurance and/or longevity securities, subject to constraints that control longevity and investment risks as well as an overall risk. We apply duality and the martingale approach to derive an optimal longevity risk transfer strategy. Our results show that longevity risk transfer interacts with an insurer’s investment decision for value maximization. Our analysis also highlights the interdependence of different longevity risk management tools to achieve an overall risk target.

Given the rising cost of maintaining defined benefit pensions, there has been a surge of activities in recent years by defined benefit plan sponsors to transfer their pension risk through strategies such as buy-ins and buy-outs. As buy-in and buy-out transaction pipelines grow, insurers actively participating in the buy-in and buy-out markets are exposed to significant longevity risk embedded in pension schemes. In this article, we investigate how to maximize a bulk annuity insurer’s value with reinsurance and/or longevity securities, subject to constraints that control longevity and investment risks as well as an overall risk. We apply duality and the martingale approach to derive an optimal longevity risk transfer strategy. Our results show that longevity risk transfer interacts with an insurer’s investment decision for value maximization. Our analysis also highlights the interdependence of different longevity risk management tools to achieve an overall risk target.

In this article, we develop strategies of hedging multiyear mortality (longevity) risk for a life insurer (an annuity provider) through purchasing some mortality-linked securities from a financial intermediary. Under the multiyear hedges for a life insurer (an annuity provider) involving two uncertain factors—the mortality rate and the number of life insureds (annuity recipients)—we derive closed-form formulas for the optimal units of purchasing underlying mortality-linked securities. Numerical illustrations show that the downside risk of loss because of mortality (longevity) risk for the life insurer (annuity provider) can be significantly hedged by purchasing the optimal units of mortality-linked securities, and the sample risk can be reduced by increasing the number of life insureds (annuity recipients) at issue. For a financial intermediary, adopting an optimal weight of a portfolio of life and annuity business can reduce extreme losses from the longevity risk but could slightly increase losses from the mortality risk, and the sample risk cannot necessarily be eliminated by increasing the number of life insureds/annuity recipients at issue.

A particularly important issue in retirement income provision is longevity risk. There are two components to longevity risk. The first is the uncertainty over how long any particular pension scheme member is going to live after retirement. This is known as idiosyncratic longevity risk. Both individuals and schemes face idiosyncratic longevity risk. The second is uncertainty over how long members of a particular age cohort are going to live after retirement. This is known as systematic longevity risk. Only schemes face systematic longevity risk. Individuals have a poor understanding of idiosyncratic longevity risk. Pension schemes can reduce idiosyncratic longevity risk by pooling the risk amongst a large number of scheme members, i.e., by taking advantage of the law of large numbers. Systematic longevity risk, however, cannot be reduced in this way: it needs to be hedged using a suitable hedging instrument.

This Special Issue of the Insurance: Mathematics and Economics contains 16 contributions to the academic literature all dealing with longevity risk and capital markets. Draft versions of the papers were presented at Longevity 15: The Fifteenth International Longevity Risk and Capital Markets Solutions Conference that was held in Washington DC on 12-13 September 2019. It was hosted by the Pensions Institute at City, University of London. Longevity risk and related capital market solutions have grown increasingly important in recent years, both in academic research and in the markets we refer to as the Life Market, i.e., the capital market that trades longevity-linked assets and liabilities. Mortality improvements around the world are putting more and more pressure on governments, pension funds, life insurance companies, as well as individuals, to deal with the longevity risk they face. At the same time, capital markets can, in principle, provide vehicles to hedge longevity risk effectively and transfer the risk from those unwilling or unable to manage it to those willing to invest in this risk in exchange for appropriate risk-adjusted returns or to those who have a counterpoising risk that longevity risk can hedge, e.g., life offices and reinsurers with mortality risk on their books. Many new investment products have been created both by the insurance/reinsurance industry and by the capital markets. Mortality catastrophe bonds are an early example of a successful insurance-linked security. Some new innovative capital market solutions for transferring longevity risk include longevity (or survivor) bonds, longevity (or survivor) swaps, mortality (or q-) forward contracts and reinsurance sidecars. The aim of the International Longevity Risk and Capital Markets Solutions Conferences is to bring together academics and practitioners from all over the world to discuss and analyze these exciting new developments.

The impact of longevity risk has not been well studied in most developing countries because of the lack of suitable mortality data. As a result, most pension companies in these countries (especially those on the African continent) do not account for longevity risk in their annual valuation. This can even lead to their collapse if steps are not taken to address it. In this work, we develop a method of assessing longevity risk where there is a severe lack of mortality data. The method is based on the assumption that there is a nearly linear relationship between annuitant’s hazard function and their mortality at higher ages (postretirement age), which permits approximating with the Gompertz model. We tried the method on mortality data from Ghana, and the results are consistent with those in the standard literature. That is, longevity risk is a treat to pension companies in Ghana even though, in the case of Ghana, this treat has partially been mitigated by the high-interest rate in the country. With this method, pension and life companies that are not able to account for longevity risk as a result of lack of data or newly formed pension companies with even 2-year mortality data will be able to assess the longevity risk they face without relying on data or models from other countries. <b>TOPICS:</b>Long-term/retirement investing, pension funds, risk management, frontier markets <b>Key Findings</b> ▪ Longevity risk is present in Ghana, and its impact on life companies in the country is potentially high. ▪ Unlike most developed countries, longevity risk in Ghana has partially been mitigated by the high interest rate in the country. ▪ Ghana’s postretirement mortality could be approximated with the Gompertz model.

Longevity is one of the greatest risks threatening the stability of our society. An anti-ageing breakthrough that slowed down our biological clocks would cause profound challenges for our society, particularly if it was a quick and cheap intervention. The adjustment would be difficult for politicians: many countries operate pay-as-you-go state pension systems, with the current generation of workers paying for the pensions of the retired generation. Increased expectations of life expectancy require tax rises, later retirement ages or cuts to pensions in payment. The unpopularity of this economic medicine is believed to be one of the reasons why governments have habitually underestimated the scope for improvements in life expectancy, so we are currently playing catch-up with belated increases to state pension ages. The lack of preparedness for further increases in life expectancy risks could trigger a global economic recession, with the natural reaction of older people being to hoard their savings, causing a reduction in consumer demand. So, there is both an opportunity and a need for innovation to build corporate and societal resilience to longevity risk. Valuable lessons are being learned from the development of other exotic commodities—like credit risk and catastrophe bonds—to shape the new longevity trading market. In this chapter, we explore sources of longevity risk; properties of longevity risk; why organisations wish to cede longevity risk; why organisations wish to acquire longevity risk; how longevity risk is currently transferred; the lessons learned from the journey to date; and the future for longevity risk transfer.

Historical tontines promised enormous rewards to the last few survivors at the expense of those died early. And, while this design appealed to the gambling instinct, it is a suboptimal way to manage and generate retirement income. This is why fair life annuities making constant payments -- where the insurance company is exposed to longevity risk -- induces greater lifetime utility. But, tontines do not have to be structured as a fixed cash-flow shared among a shrinking number of survivors and insurance companies do not actually sell fair life annuities, partially due to aggregate longevity risk. In this paper we derive the tontine structure that maximizes lifetime utility, but doesn't expose the sponsor to any longevity risk. Technically speaking we solve the Euler Lagrange equation and examine its sensitivity to (i.) the size of the tontine pool, (ii.) individual longevity risk aversion, and (iii.) subjective health status. The optimal tontine varies with the individual's longevity risk aversion and the number of participants. And, the historical (flat, constant) tontine structure is only optimal in the limit as longevity risk aversion goes to infinity. We then introduce a structure called a natural tontine whose payout declines in exact proportion to the (expected) survival probabilities, which is near-optimal for all values of longevity risk aversion and the size of the tontine pool. We compare the utility of optimal tontines to the utility of loaded life annuities under reasonable demographic and economic conditions and find that the life annuity's advantage over tontines, is minimal. Our contribution is to leverage economic theory to design the next generation of tontine annuities.We also use our framework to review and analyze the first-ever mortality-derivative issued by the British government, known as King Williams's tontine of 1693. Although it is widely acknowledged that mortality-derivatives were mis-priced in their early years, it is worth noting that both life annuities and tontines co-existed during that period. We shed light on the preferences and beliefs of those who invested in the tontines vs. the annuities and conclude by arguing that tontines should be re-introduced and allowed to co-exist with life annuities. Individuals would likely select a portfolio of tontines and annuities that suit their personal preferences for consumption and longevity risk, as they did over 320 years ago.

The title of my talk today is Pensions, Risks, and Capital Markets, and it draws on work the UK Pensions Commission conducted as we tried to get to grips with the issues of who does bear, who can bear, and who should bear different risks in different elements of the pension system, state and private. That analysis was set out in detail in a lecture I gave at the Cass Business School in April 2005, which is available on the UK Pensions Commission's website, http:/ /www.pensionscommission.org.uk. In one crucial respect, however, our thinking evolved during last year and the conclusion we set out in our report differed from that suggested in my original lecture. I will highlight that point when we arrive at it. My lecture last year covered issues relating to investment return risk as well as to longevity risk. It asked questions such as: Do the risks of equity investment decline with the length of the holding period? In what class of assets should pension funds be invested, and is the answer different for defined benefit and defined contribution schemes? But since today's conference is about longevity risk, I will leave aside the investment return risks and concentrate entirely on issues relating to longevity risk, and in particular four: * How large is the uncertainty about future longevity and thus how great are the risks involved in underwriting longevity risk?; * How much longevity risk is being absorbed by some or other agent today, and how might demand for longevity risk absorption develop in the future?; * What are the prospects for risk absorption capacity and price?; and * Who should bear longevity risk, and with what implications for policy? First, then, how uncertain are our estimates of future life expectancy? And let me be clear, my focus today is entirely on uncertainty about the average life expectancy of an entire age cohort-not on variability in the individual life expectancies of individuals within each cohort-which is, of course, a significant risk, but one which is clearly statistically analyzable, manageable, and absorbable. For it is uncertainty over the average life expectancy of entire age cohorts which is the key problem. Figure 1 sets out three projections from the UK Government Actuary's

Project Description: To examine how portfolio size affects longevity risks in a pool of life settlements. Specifically, this research analyzes the impact of longevity risk on the investment return of a life settlement portfolio. Scope of Research/Methodology: Life settlements offer institutional investors an asset class that provides diversified returns which are not correlated or dependent on movements of the economy. Life settlement portfolios are, however, subject to life expectancy (LE) underwriter risk and longevity risk. LE underwriter risk can be mitigated somewhat by evaluating LE provider performance and allowing for diversity of LE providers within a portfolio. Longevity risk, studied closely in this research, can be statistically predicted, managed, and reduced by aggregating a sizeable portfolio of life settlements. A data set of 2,000 life settlement policies was assembled from which testing samples were extracted. Insured individuals ranged in age from 65 to 95 and estimated LEs ranged from 64 to 96 months. Policy face values ranged from $70,000 to $10,000,000. A statistical model was constructed to test the difference in deviation of LEs in different random sample distributions. The objective of this model, using basic statistical analysis, was to show that portfolio stability increases as the number of insured increases. Further, the minimum number of policies required by a portfolio to reach stability in standard deviations was estimated. Resources: Insurance and Life Settlement Industry Research & Statistics: Conning Research and Consulting, Inc., “Institute for International Research” discussion by Michael Crane, “Investment Analysis and Portfolio Management” 8th ed. by Reilly & Brown, “Life Settlement Securitization” by A.M. Best Company, Inc. Target Results and Benefits: Research determined that the optimal portfolio size for mitigating longevity risk is 300 lives. Timeline: Project research and report drafted from June, 2008 through August, 2008.

Longevity Three: The Third International Longevity Risk and Capital Markets Solutions Conference was held in Taipei, Taiwan on 20-21 July 2007. It was hosted by National Chengchi University. Mortality improvements around the world are putting more pressure on governments, pension funds, life insurance companies as well as individuals to deal with the increasing longevity risk they face. Financial markets, on the other hand, can in principle provide vehicles to hedge longevity risk effectively. Many new investment products have been created both by the insurance/reinsurance industry and by the capital markets. Mortality catastrophe bonds are an example of a successful insurance-linked security. Some new innovative capital market solutions for transferring longevity risk include survivor bonds, reverse mortgages, longevity-linked swaps and forward contracts. The aim of the International Longevity Risk and Capital Markets Solutions Conferences is to bring together academics and practitioners from all over the world to discuss and analyze these exciting new developments. The first conference was held at Cass Business School in London in February 2005. This conference was prompted by the announcement of the Swiss Re mortality catastrophe bond in December 2003 and the EIB/BNP/PartnerRe longevity bond in November 2004. The second conference was held in April 2006 in Chicago and hosted by the Katie School at Illinois State University. In the intervening period, there were further issues of mortality catastrophe bonds, as well as the release of the Credit Suisse Longevity Index. Life settlement securitizations were also beginning to take place in the US. In the UK, new life companies backed by global investment banks and private equity firms were setting up for the express purpose of buying out the defined benefit pension liabilities of UK corporations. Goldman Sachs announced it was setting up such a buy-out company itself because the issue of pension liabilities was beginning to impede its mergers and acquisitions activities. So there was now clear evidence that a new global capital market in longevity risk transference was beginning to emerge. However, as with many other economic activities, not all progress follows a smooth path. The EIB/BNP/PartnerRe longevity bond did not attract sufficient investor interest and was withdrawn in late 2005. But a great deal was learned from this about the conditions and requirements needed to launch a successful capital market.

Longevity risk may be defined as the risk of outliving one’s accumulated wealth. Although many theoretical studies have suggested that individuals will increase their precautionary saving in order to mitigate longevity risk, only a few of such studies have used empirical data to test people’s decision-making behaviour in response to longevity risk. The main purpose of this paper is to investigate how households adjust their consumption and investment plans in response to longevity risk. We find that households reduce their consumption over their entire lifespan and increase the proportion of their risky assets before retirement when they face longevity risk. Furthermore, we also discover that households with females, more children, higher health expenditure and greater risk aversion change their risky assets to a lesser extent in their whole life period in the face of longevity risk, compared with other households.

Life expectancy has been rapidly increasing and remains uncertain in all OECD countries, including Poland. One of the many economic and social consequences of this process is the increase of the longevity risk in social security systems. This article focuses on the issues of managing longevity risk in the pension system in Poland, in particular - the construction of public and supplementary pension systems and its ability to adapt to the challenges associated with longevity risk. Particular attention has been paid to the analysis of public structures and supplementary pension schemes in the phase of payment of benefits (decumulation). The research work, of which the results are presented in the article, is based on literature studies, comparative analysis, statistical analysis; as well as descriptive and explanatory methods. Also, a model of the two stages of pension risk created by T. Szumlicz has been used. The author argues that both the public pension systems as well as the supplementary pension schemes in Poland do not secure adequate protection against the risk of longevity. While in the public retirement system, the aggregate longevity risk exists, and the participants of additional pension systems are exposed to individual longevity risk. The limitation of these risks requires significant structural changes both in the public and in the additional pension schemes in Poland.