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Working Papers

Michael Sherris

Zhiping Huang, Michael Sherris, Andrés M Villegas and Jonathan Ziveyi

Abstract: This paper assesses and compares multi-factor continuous time ane mortality models applied to age-cohort mortality curves that are well suited for theoretical and practical application in nance and insurance. Models based on Gaussian distributed mortality rates, as well as the Cox-Ingersoll-Ross (CIR) process allowing for Gamma distributed mortality rates, are compared, also quantifying the probability of negative rates in the Gaussian models. In particular, we introduce the Gaussian Arbitrage-Free Nelson-Siegel (AFNS) mortality model incorporating level, slope and curvature factors. The models have appealing features including ecient estimation and computation. We estimate models using age-cohort data to capture cohort eects more eectively and in order to explain the variability in cohort mortality curves in the continuous time framework. The models allow for Poisson variation in the model estimation using the Kalman lter. The ane mortality models facilitate the derivation of closed-form survivor curves allowing for ecient valuation of mortality-linked claims. The models can also incorporate factor dependence allowing for age-dependence in the mortality curves. Importantly we show that the Gaussian independent factor AFNS model performs very well in explaining and forecasting cohort mortality.

Keywords: mortality models, continuous time, cohort curve, affine rates, Kalman filter

media 2019

Shuanglan Li, Héloïse Labit Hardy, Michael Sherris, Andrés M. Villegas

Abstract: Pooled annuity products, where the participants share systematic and idiosyncratic mortality risks as well as investment returns and risk, provide an attractive and effective alternative to traditional guaranteed life annuity products. While longevity risk sharing in pooled annuities has received recent attention, incorporating investment risk beyond fixed interest returns is relatively unexplored. Incorporating equity investments has the potential to increase expected annuity payments at the expense of higher variability. We propose and assess a strategy for incorporating equity investments along with managed-volatility for pooled annuity funds. We show how the managed volatility strategy improves investment performance, while reducing pooled annuity income volatility and downside risk, as well as an investment strategy that reduces exposure to investment risk over time. We quantify the impact of pool size when equity investments are included, showing how these products are viable with relatively small pool sizes.

Keywords: pooled annuity, equity investment, managed volatility, longevity risk 


Michael Sherris and Pengyu Wei

Abstract: This paper proposes a multi-state model of both functional disability and health status in the presence of systematic trend and uncertainty. We classify each individual observation along two dimensions: health status (other than disability) and disability and use the multi-state latent factor intensity (MLFI) model to estimate the transitions rates. The model is then used to calculate (healthy) life expectancy and price a variety of insurance products. We illustrate the importance of various factors and quantify the potential losses from model misspecification. Our results suggest that insurers should pay great attention to health status, trend, and systematic uncertainty in disability/mortality modeling and insurance pricing. We also find that integrating LTC insurance with life annuity can help to reduce the systematic uncertainties.

Keywords: functional disability; health status; trend; systematic uncertainty


Rafal Chomik and John Piggott

Demographic and technological changes are two megatrends set to transform labour markets around the world. These shifts are already under way and are expected to accelerate, particularly in East and South East Asia, which is home to the world’s oldest and fastest ageing societies and a region with an enviable pace of economic development.

The literature on the nature and impacts of each trend is vast, but the study of the interactions between them is often incidental and rarely in the Asian setting. Yet demography, technology, structural change and economic development are all related. Rapid economic development seen in many parts of Asia is the product of beneficial demographic trends as well as technological catch-up to the production productivity frontier. And technological advancements in medicine have precipitated the increasing levels of life expectancy seen around the world. While more years in good health raise prospects of working for longer, technological and structural change risk leaving older cohorts behind.

Keywords: Asia, labour market, population ageing, technology advances

Elderly couple enjoying life

Katja Hanewald, Ruo Jia and Zining Liu

Abstract: This paper studies income inequality in old age and its development over the life cycle. We develop a theoretical framework and a new empirical method to show that income is more unequally distributed in old age than in working age. We combine the regression-based inequality decomposition method and the three-step mediating effect test to analyze the transmission of income inequality from initial socioeconomic differences to income inequality in old age. Our study is based on a panel of over 4,000 old households from the China Health and Nutrition Survey
during 1991-2015. We find that the urban-rural gap and educational inequality are the primary causes of old-age income inequality. The effect of the urban-rural gap is partially mediated by educational inequality. Inequality accumulates with age and is reinforced in old age by the Chinese public pension system, which is fragmented by occupational sector.

Keywords: Inequality; Decomposition; Urban-rural gap; Pensions; China

taxation of pension

George Smyrnis, Hazel Bateman, Isabella Dobrescu, Ben Newell and Susan Thorp.

Abstract: The implications of current balance information for retirement provision are considerably difficult to grasp or anticipate. We study how balance and/or income projections motivate the voluntary savings intentions of pension plan participants over a sequence of ten choices. To this effect, we collect savings intentions from 1,615 respondents aged 25-57 years via an online experimental survey that compares four different formats for retirement account information. The formats are (i) current balance; (ii) current balance and projected retirement balance; (iii) current balance and projected retirement income; and (iv) current balance, projected retirement balance and retirement income. Regardless of information format, merely inviting plan participants to top up their retirement account prompts substantial increases in savings, especially among older respondents. At the first choice round, the income projection triggers marginally more voluntary saving intentions than the lump sum projection alone. However at both the first choice and over sequential choices, the combination of balance and income projections is what matters most. Furthermore, even though older respondents save at a higher level across all treatments, younger respondents are more sensitive to income balance projections than the older survey respondents.



Joanne Kaa Earl, Mydair Hunter and Hazel Bateman

Abstract:Objectives: Downsizing is the term used to describe the move to a smaller dwelling and the decumulation of possessions, often taking place at older age. Two psychological theories: Selection, Optimisation and Compensation (SOC) and Time Perspective (TP); were applied to explain post-downsizing perspectives.

Method: Participants were community dwelling older adults (N = 352) aged 55 years and over who downsized during the preceding five years. An online survey was used to collect data about factors determining decision-making as well as psychological aspects of the downsizing experience including regret, retirement adjustment, satisfaction with life, stress, and distress.

Results: In general only a small proportion (17.6%) of participants indicated regret about moving. Consistent with the SOC theory younger people were more highly represented in the group expressing regret. Lower levels of satisfaction with the move were associated with a Past Negative Time Perspective, lower levels of life satisfaction and higher levels of stress and psychological distress. The top five factors for downsizing included: house was too big; to be closer to family; lifestyle preferences; yard too hard to manage; and alleviation of financial strain.

Conclusion: Whilst most people do not express regret with the move, it can be a stressful process. Some factors associated with lower levels of satisfaction such as Past Negative Time Perspective may be more difficult to change than others. Understanding the post-downsizing experience of others can help better prepare people before they move to anticipate responses and possibly contribute to better retirement adjustment.

Keywords: Downsizing, Time Perspective, Regret, Older adults


Mengyi Xu, Michael Sherris and Adam W. Shao

The transition from defined benefit to defined contribution (DC) pension schemes has increased the interest in target annuitization funds that aim to fund a minimum level of retirement income. Prior literature has studied the optimal investment strategies for DC funds that provide minimum guarantees, but far less attention has been given to portfolio insurance strategies, especially for target annuitization funds. We evaluate the performance of option-based and constant proportion portfolio insurance strategies for a DC fund that targets a minimum level of inflation-protected annuity income at retirement. We show how the portfolio allocation to an equity fund varies depending on the member’s age upon joining the fund, displaying a downward trend through time for members joining the fund before ages in the mid-30s. We demonstrate how both portfolio insurance strategies provide strong protection against downside equity risk in financing a minimum level of retirement income. The option-based strategy often leads to higher accumulated savings at retirement and is also shown to provide a more robust level of protection when equity markets are more volatile and when contributions to the pension fund are lower. 

Keywords: portfolio insurance strategies, defined contribution, pension risk management, target annuitization fund

Jennifer Garcia

Anca-Stefania Jijiie, Jennifer Alonso-García and Séverine Arnold (-Gaille)

Abstract: Many OECD countries have addressed the issue of increased longevity by mainly increasing the retirement age. However, this kind of reforms may lead to substantial transfers from those with shorter lifespans to those that will live longer than the average, as they do not necessarily take into account the socio-economic differences in mortality. The contribution of our paper is therefore twofold. Firstly, we illustrate how both a Defined Benefit and a Notional Defined Contribution Pay-As-You-Go scheme can put the lower social economic classes at a disadvantage, when compared to the actuarially fair pensions. In contrast to that, higher classes experience a gain. This is due to the fact that mortality rates per socio-economic class are not considered by either scheme. Consequently, we propose a model that determines the parameters for each scheme and class which would render the pensions fairer even when no socio-economic mortality differences are considered.

Keywords: retirement age, pay-as-you-go, public pensions, adequacy, fairness, class-specific parameters