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The life insurance industry has been exposed to high levels of longevity risk born from the mismatch between realized mortality trends and anticipated forecast. Annuity providers are exposed to extended periods of annuity payments. There are no immediate instruments in the market to counter the risk directly. This paper aims to develop appropriate instruments for hedging longevity risk and providing an insight on how existing products can be tailor-made to effectively immunize portfolios consisting of life insurance using a cointegration vector error correction model with regime-switching (RS-VECM), which enables both short-term fluctuations, through the autoregressive structure [AR(1)] and long-run equilibria using a cointegration relationship. The authors also develop synthetic products that can be used to effectively hedge longevity risk faced by life insurance and annuity providers who actively hold portfolios of life insurance products. Models are derived using South African data. The authors also derive closed-form expressions for hedge ratios associated with synthetic products written on life insurance contracts as this will provide a natural way of immunizing the associated portfolios. The authors further show how to address the current liquidity challenges in the longevity market by devising longevity swaps and develop pricing and hedging algorithms for longevity-linked securities. The use of a cointergrating relationship improves the model fitting process, as all the VECMs and RS-VECMs yield greater criteria values than their vector autoregressive model (VAR) and regime-switching vector autoregressive model (RS-VAR) counterpart’s, even though there are accruing parameters involved.

The market model adopted from Ngai and Sherris (2011) is a cointegration RS-VECM for this enables both short-term fluctuations, through the AR(1) and long-run equilibria using a cointegration relationship (Johansen, 1988, 1995a, 1995b), with a heteroskedasticity through the use of regime-switching. The RS-VECM is seen to have the best fit for Australian data under various model selection criteria by Sherris and Zhang (2009). Harris (1997) (Sajjad et al., 2008) also fits a regime-switching VAR model using Australian (UK and US) data to four key macroeconomic variables (market stock indices), showing that regime-switching is a significant improvement over autoregressive conditional heteroscedasticity (ARCH) and generalised autoregressive conditional heteroscedasticity (GARCH) processes in the account for volatility, evidence similar to that of Sherris and Zhang (2009) in the case of Exponential Regressive Conditional Heteroscedasticity (ERCH). Ngai and Sherris (2011) and Sherris and Zhang (2009) also fit a VAR model to Australian data with simultaneous regime-switching across many economic and financial series.

The authors develop a longevity swap using nighttime data instead of usual income measures as it yields statistically accurate results. The authors also develop longevity derivatives and annuities including variable annuities with guaranteed lifetime withdrawal benefit (GLWB) and inflation-indexed annuities. Improved market and mortality models are developed and estimated using South African data to model the underlying risks. Macroeconomic variables dependence is modeled using a cointegrating VECM as used in Ngai and Sherris (2011), which enables both short-run dependence and long-run equilibrium. Longevity swaps provide protection against longevity risk and benefit the most from hedging longevity risk. Longevity bonds are also effective as a hedging instrument in life annuities. The cost of hedging, as reflected in the price of longevity risk, has a statistically significant effect on the effectiveness of hedging options.

This study relied on secondary data partly reported by independent institutions and the government, which may be biased because of smoothening, interpolation or extrapolation processes.

An examination of South Africa’s mortality based on industry experience in comparison to population mortality would demand confirmation of the analysis in this paper based on Belgian data as well as other less developed economies. This study shows that to provide inflation-indexed life annuities, there is a need for an active market for hedging inflation in South Africa. This would demand the South African Government through the help of Actuarial Society of South Africa (ASSA) to issue inflation-indexed securities which will help annuities and insurance providers immunize their portfolios from longevity risk.

In South Africa, there is an infant market for inflation hedging and no market for longevity swaps. The effect of not being able to hedge inflation is guaranteed, and longevity swaps in annuity products is revealed to be useful and significant, particularly using developing or emerging economies as a laboratory. This study has shown that government issuance or allowing issuance, of longevity swaps, can enable insurers to manage longevity risk. If the South African Government, through ASSA, is to develop a projected mortality reference index for South Africa, this would allow the development of mortality-linked securities and longevity swaps which ultimately maximize the social welfare of life assurance policy holders.

The paper proposes longevity swaps and static hedging because they are simple, less costly and practical with feasible applications to the South African market, an economy of over 50 million people. As the market for MLS develops further, dynamic hedging should become possible.

The improvements of longevity are intensifying the need for capital markets to be used to manage and transfer the risk through longevity-linked securities. Nevertheless, the difference between the reference population of the hedging instrument and the population of members of a pension plan, or the beneficiaries of an annuity portfolio, determines a significant heterogeneity causing the so-called basis risk. In particular, it is shown that if insurers use financial instruments based on national indices to hedge longevity risk, this hedge can become imperfect. For this reason, it is fundamental to arrange a model allowing to quantify the basis risk for minimising it through a correct calibration of the hedging instrument.

The paper provides a framework for measuring the basis risk impact on the. To this aim, we propose a model that measures the population basis risk involved in a longevity hedge, in the functional data model setting. hedging strategies.

The innovative contribution of the paper occurs in two key points: the modelling of mortality and the hedging strategy. Regarding the first point, the paper proposes a functional demographic model framework (FDMF) for capturing the basis risk. The FDMF model generally designed for single population combines functional data analysis, nonparametric smoothing and robust statistics. It allows to capture the variability of the mortality trend, by separating out the effects of several orthogonal components. The novelty is to set the FDMF for modelling the mortality of the two populations, the hedging and the exposed one. Regarding the second point, the basic idea is to calibrate the hedging strategy determining a suitable mixture of q-forwards linked to mortality rates to maximise the degree of longevity risk reduction. This calibration is based on the key q-duration intended as a measure allowing to estimate the price sensitivity of the annuity portfolio to the changes in the underlying mortality curve.

The novelty lies in linking the shift in the mortality curve to the standard deviation of the historical mortality rates of the exposed population. This choice has been determined by the observation that the shock in a mortality rate is age dependent. The main advantage of the presented framework is its strong versatility, being the functional demographic setting a generalisation of the Lee-Carter model commonly used in mortality forecasting, it allows to adapt to different demographic scenarios. In the next developments, we set out to compare other common factor models to assess the most effective longevity hedge. Moreover, the parsimony for considering together two trajectories of the populations under consideration and the convergence of long-term forecast are important aspects of our approach.

The demographic risk is the risk due to the uncertainty in the demographic scenario assumptions by which life insurance products are designed and valued. The uncertainty lies both in the accidental (insurance risk) and systematic (longevity risk) deviations of the number of deaths from the value anticipated for it. This last component gives rise to the risk due to the randomness in the choice of the survival model for valuations (model risk or projection risk). If the insurance risk component can be assumed negligible for well‐diversified portfolios, as in the case of pension annuities, longevity risk is crucial in the actuarial valuations. The question is particularly decisive in contexts in which the longevity phenomenon of the population is strong and pension annuity portfolios constitute a meaningful slice of the financial market – both typical elements of Western economies. The paper aims to focus on the solvency appraisal for a portfolio of life annuities, deepening the impact of the demographic risk according to suitable risk indexes apt to describe its evolution in time.

The financial quantity proposed for representing the economic wealth of the life insurance company is the stochastic surplus, and the paper analyses the impact on it of different demographic assumptions by means of risk indicators as the projection risk index, the quantile surplus valuation and the ruin probability. By means of the proposed models, the longevity risk is mainly taken into account in a stochastic scenario for the financial risk component, in order to consider their interactions, too. In order to furnish practical details significant in the portfolio risk management, several numerical applications clarify the practical meaning of the models in the solvency context.

This paper studies the impact on the portfolio surplus of the systematic demographic risk, taking into account their interaction with the financial risk sources. In this order of ideas, the internal risk profile of a life annuity portfolio is deeply investigated by means of suitable risk indexes: in a solvency analysis perspective, some possible scenarios for the evolution of death rates (generated by different survival models) are considered and this paper evaluates the impact on the portfolio surplus caused by different choices of the demographic model. The first index is deduced by a variance decomposition formula, the other ones involve the conditional quantile calculus and the ruin probability. Such indexes constitute benchmarks, whose conjoined use provides useful information to the meeting of the solvency requirements.

With respect to the recent actuarial literature, in which the most important contribution on the surplus analysis has been given by Lisenko et al. – where the analysis focuses on the financial aspect applied to portfolios of temporary and endowment contracts – the paper considers life annuity portfolios, taking into account the effect of the systematic demographic risk and its interactions with the financial risk components.

The purpose of this paper is to present a clear path to securitize the longevity risk with two distinct swaps in order to inspire a new Chinese life market.

Studies on longevity risk securitization consist of three aspects, respectively, instrument design, pricing methodology and mortality projection. The swaps designed are referenced, respectively, to vanilla and complex survivor swaps (Dowd et al., 2006; Lin and Cox, 2005). Methods applied are RHH model and Gompertz law for mortality projection, as well as two-factor Wang transformation for pricing.

This paper figures out the market price of risk in Chinese annuity market, checks for the sensitivity of the price to parameters and tests the hedging effects by Monte Carlo simulation.

Based on the theoretical and numerical results, this paper suggests an effective way to possibly witness the birth of New Life Market in China.

Systematic mortality risk, i.e. the risk of unexpected changes in mortality and survival rates, can substantially impact a life insurers' risk and solvency situation. By using the “natural hedge” between life insurance and annuities, insurance companies have an effective tool for reducing their net‐exposure. The purpose of this paper is to analyze this risk management tool and to quantify its effectiveness in hedging against changes in mortality with respect to default risk measures.

To achieve this goal, the paper models the insurance company as a whole and takes into account the interaction between assets and liabilities. Systematic mortality risk is considered in two ways. First, systematic mortality risk is modeled using scenario analyses and, second, empirically observed changes in mortality rates for the last 10‐15 years are used.

The paper demonstrates that the consideration of both the asset and liability side is vital to obtain deeper insight into the impact of natural hedging on an insurer's risk situation and shows how to reach a desired safety level while simultaneously immunizing the portfolio against changes in mortality rates.

The paper contributes to the literature by considering the insurance company as a whole in a multi‐period setting and taking into account both, assets and liabilities, as well as their interaction. Furthermore, the paper shows how to obtain a desired safety level while simultaneously immunizing a portfolio against changes in default risk.

The purpose of this study is to develop new type of reverse mortgage contract. How to provide adequate services and housing for an increasing number of people that are dependent on the help of others is a crucial question in the European Union (EU). The housing stock in Europe is not fit to support a shift from institutional care to the home-based independent living. Some 90% of houses in the UK and 70%–80% in Germany are not adequately built, as they contain accessibility barriers for people with emerging functional impairments. The available reverse mortgage contracts do not allow for relocation to their own adapted facilities. How to finance the adaptation from housing equity is discussed.

The authors have extended the existing loan reverse mortgage model. Actuarial methods based on the equivalence of the actuarial present values and the multiple decrement approach are used to evaluate premiums for flexible longevity and lifetime long-term care (LTC) insurance for financing adequate facilities.

The adequate, age-friendly housing provision that is appropriate to support the independence and autonomy of seniors with declining functional capacities can lower the cost of health care and improve the well-being of older adults. For financing the development of this kind of facilities for seniors, the authors developed the reverse mortgage scheme with embedded longevity and LTC insurance as a possible financial instrument for better LTC services and housing with care in assisted-living facilities. This kind of facilities should be available for the rapid growth of older cohorts.

The numerical example is based on rather crude numbers, because of lack of data, as the developed reverse mortgage product with LTC insurance is a novelty. Intensity of care and probabilities of care in certain category of care will change after the introduction of this product.

The model results indicate that it is possible to successfully tie an insurance product to the insured and not to the object.

The introduction of this insurance option will allow many older adult with low pension benefits and a substantial home equity to safely opt for a reverse mortgage and benefit from better social care.

While currently available reverse mortgage contracts lapse when the homeowner moves to assisted-living facilities in any EU Member State, in the paper a new method is developed where multiple adjustments of housing to the functional capacities with relocation is possible, under the same insurance and reverse mortgage contract. The case of Slovenia is presented as a numerical example. These insurance products, as a novelty, are portable, so the homeowner can move in own specialised housing unit in assisted-living facilities and keep the existing reverse mortgage contract with no additional costs, which is not possible in the current insurance products. With some small modifications, the method is useful for any EU Member State.

Bodies with responsibilities for paying pensions to individuals face a mortality risk in that the pensioners may prove longer lived than expected. The significant scale and uncertainity of this risk is becoming increasingly clear. Various measures are available to control this risk and new innovations such as mortality linked bonds and derivatives have been proposed. The purpose of this paper is to evaluate the alternative methods of controlling morality risk and discuss their potential policy implications.

The paper considers the various parties affected by mortaling risk and assesses the difficulties of predicting mortality. Different methods of predicting mortality are discussed. Policy issues are considered and conclusions presented.

There is a huge demand for methods of hedging and trading mortality risk. Financial markets are responding to this with a number of insurers moving into the bulk annuity market. New products, such as survivor bands and mortality derivatives, are just appearing in the market, it is still to be seen whether this major financial problem will be best be solved by the financial markets or by government intervention.

The paper offers an evaluation of the alternative methods of controlling mortality risk together with the potential policy implications.

Two strands of the literature are combined, namely the modeling of disability insurance and the design, valuation and discussion of insurance-linked securities.

This paper provides a discussion regarding the advantages and detriments of disability-linked securities in comparison with mortality-linked bonds and swaps as well as regarding potential disability-linked indices and the potential use. The discussion is followed by an introduction of a potential design and a corresponding valuation of disability bonds and swaps.

This securitization will provide useful tools for the risk management of disability risk in a risk-based regulatory framework.

No disability-linked securities have been defined and discussed so far.

This paper examines the role of illiquidity and duration factor in understanding the momentum profit in the Korean stock market. We find that the foreigner/institutional illiquidity factor explains the momentum effect. In addition, this paper finds that duration factor defined as the difference in returns of short-duration and long-duration stocks captures well the momentum profits. That is, a two-factor model with the market and duration factor performs much better than competing asset pricing models in explaining the momentum effect. Finally, when controlling for the duration factor, the explanatory power of the foreign/institutional illiquidity factor on the momentum profits disappears. In sum, our empirical finding indicates that the duration factor is the most important ingredient in understanding the momentum effect in the Korean stock market.

The purpose of this paper is to propose a framework based on cash flow matching for computing the Solvency Capital Requirement under Solvency II.

The time horizon of the insurance liabilities is typically longer than the maturities of bonds available in the market. With the assumption that a collection of bonds will be available for purchase in the future, the authors study the cash flow matching program under interest rate lattice models.

The solution can be interpreted as the worst‐case cost and the economic capital can be found accordingly.

The paper illustrates the methodology of computing the Solvency Capital Requirement using a dynamic cash flow matching framework under lattice models. The proposed method is particularly useful for insurance products with a typical long time horizon when most duration matching techniques are not easily applicable.