Research on natural hedge strategy of insurance companies based on combination “Variance” effect

Managing Life Insurer Risk and Profitability: Annuity Market Development Using Natural Hedging Strategies

A feasible natural hedging strategy for insurance companies

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.

PurposeThe 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.Design/methodology/approachThe 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.FindingsThe 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.Research limitations/implicationsThis study relied on secondary data partly reported by independent institutions and the government, which may be biased because of smoothening, interpolation or extrapolation processes.Practical implicationsAn 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.Social implicationsIn 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.Originality/valueThe 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.

This article studies the optimal hedging strategy to deal with longevity risk for the life insurer considering basis risk. We build up a longevity hedging framework that incorporates not only the internal natural hedging but also the external hedging by using the q‐forwards. The optimal hedging strategy is obtained by a minimizing‐variance approach that can minimize the impact of longevity risk on the insurer's profit function. To investigate the basis risk, instead of using population mortality, we adopt a unique mortality data set of annuity and life insurance policies that enable us to calibrate the multi‐population mortality dynamics for different lines of insurance policies. We consider three different hedging strategies: the natural hedging strategy, the external hedging strategy, and combining both natural hedging, and external hedging strategies. The hedge effectiveness for different hedging strategies is evaluated. In addition, the mortality forecast model based on VECM and ARIMA are used to examine the impact of basis risk on hedge effectiveness. As a result, combining both internal and external hedging strategies is the most effective way to manage longevity risk. Ignoring the basis risk will decrease the hedge effectiveness.

Natural hedging allows life insurers to manage long‐term longevity and investment risks of life annuity products through offsetting risks in life insurance products. Benefits include a reduction in risk‐based capital. We use stochastic mortality and interest rate models to assess life insurance and annuity capital requirements and to quantify the benefits of natural hedging for a range of different types of life insurance product designs and risk measures based on probability of insurer solvency. We show that level‐premium life insurance products with a medium duration (around 20–30 years) can better hedge annuity products than whole life products. Renewable term life insurance products have less hedge effectiveness than level‐premium term insurance. Results vary with the risk measure used, with the 1‐year horizon Solvency II risk measure showing lower natural hedging benefits of life insurance compared to multiple‐period risk measures.

Preface.- Introduction.- Part 1: History.- Developments in Risk and Insurance Economics: the Past 40 Years.- Part 2 : Risk and Insurance Theory Without Information Problems.- Higher-Order Risk Attitudes.- Non-Expected Utility and the Robustness of the Classical Insurance Paradigm.- The Economics of Optimal Insurance Design.- The Effects of Changes in Risk on Risk Taking: A Survey.- Risk Measures and Dependence Modeling.- The Theory of Insurance Demand.-Prevention and Precaution.- Part 3 : Asymmetric Information: Theory.- Optimal Insurance Contracts under Moral Hazard.- Adverse Selection in Insurance Contracting.- The Theory of Risk Classification.- The Economics of Liability Insurance.- Economic Analysis of Insurance Fraud.- Part 4: Asymmetric Information: Empirical Analysis.- Asymmetric Information in Insurance Markets: Predictions and Tests.- The Empirical Measure of Information Problems with Emphasis on Insurance Fraud and Dynamic Data.- Workers' Compensation: Occupational Injury Insurance's Influence on the Workplace.- Experience Rating in Non-Life Insurance.- Part 5 : Risk Management.- On the Demand for Corporate Insurance - Creating Value.- Managing Catastrophic Risks through Redesigned Insurance: Challenges and Opportunities.- Innovations in Insurance Markets: Hybrid and Securitized Risk-Transfer Solutions.- Risk Sharing and Pricing in the Reinsurance Market.- Part 6 : Insurance Pricing.- Financial Pricing of Insurance.- Insurance Price Volatility and Underwriting Cycles.- Part 7 : Industrial Organization of Insurance Markets.- On the Choice of Organizational Form: Theory and Evidence from the Insurance Industry.- Insurance Distribution.- Corporate Governance in the Insurance Industry: A Synthesis.- Systemic Risk and the Insurance Industry.- Analyzing Firm Performance in the Insurance Industry Using Frontier Efficiency and Productivity Methods.- Capital Allocation and its Discontents.- Capital and Risks Interrelationships in the Life and Health Insurance Industries: Theories and Applications.- Insurance Market Regulation: Catastrophe Risk, Competition, and Systemic Risk.- Insurance Markets in Developing Countries: Economic Importance and Retention Capacity.- Part 8: Health and Long-Term Care Insurance, Longevity Risk, Life Insurance, and Social Insurance.- Health Insurance in the United States.- Longevity Risk and Hedging Solutions.- Long-Term Care Insurance.- New Life Insurance Financial Products.- The Division of Labor Between Private and Social Insurance.

Heterogeneity of Australian Population Mortality and Implications for a Viable Life Annuity Market

본 논문은 우리나라 생명보험산업의 장수리스크에 대한 자연헤지가 충분히 이루어지고 있는가를 평가해 보았다. 연금보험과 종신보험 준비금 계산 시 사망률 모형으로는 Lee-Carter 모형을 적용하였다. 사망률 개선 시나리오로는 연금보험과 종신보험 사망률이 모두 10%와 20% 개선되는 경우, 50세 이하 저연령 사망률은 10% 개선되고, 50세 이상 고연령 사망률은 20% 개선되는 경우, 마지막으로 연금보험 사망률은 20% 개선되지만 종신보험 사망률은 10% 개선되는 등 네 가지 시나리오를 살펴보았다. 분석결과 연금보험과 종신보험에 동일한 사망률 충격을 가하는 경우와 고연령의 사망률 개선이 저연령에 비해 빠르게 나타나는 경우 모두 연금보험과 종신보험 준비금의 합은 감소하는 것으로 나타났다. 네 번째 시나리오에서만 전체 준비금은 증가하였으나, 이 경우에도 연금보험 준비금 증가의 60% 이상이 자연헤지에 의해 상쇄하는 것으로 나타났다. 따라서 우리나라 생명보험산업의 장수리스크는 자연헤지를 통해 충분히 관리되고 있다고 판단된다. The objective of this paper is to evaluate whether longevity risk is properly managed in Korean life insurance industry by measuring longevity risk in the viewpoint of natural hedge. According to analysis, the sum of the reserve of annuity and that of whole life insurance appears to decrease in the case both reserve of annuity and whole life insurance are shocked by same degree and also the mortality rate of the aged policyholders is improved faster than that of the less aged policyholders. Although the sum of the reserves increases only when the mortality improvement of annuity policyholders is higher than that of whole life insurance policyholders by two times, more than 60% of reserve increase of annuity is found to be offset by natural hedge. Thus, it is judged that the longevity risk of Korea life insurance industry is properly managed by natural hedge.

Defining and deriving the mortality durations and convexities of the prices of life insurance and annuity products with respect to an instantaneously proportional change and an instantaneously parallel shift, respectively, in μs (the forces of mortality), qs (the one-year death probabilities), ps (the one-year survival probabilities), ln (μ)s, (q/p)s, and ln (q/p)s, this article applies 24 proposed duration/convexity matching strategies classified into seven groups to determine the weights of two products in an insurance portfolio. The hedging performances of some qualified matching strategies selected as representatives are evaluated by comparing their Value at Risk (VaR) values and variance reduction ratios for a base scenario. We also test some specific scenarios for the population basis risk, model risk, volatility and jump risks, and interest rate risk to see the impacts on the matching strategies. Numerical examples show that some convexity matching strategies overall outperform the others in the VaR value and in the effectiveness of hedging both longevity and mortality risks for two kinds of insurance portfolios.

Natural Delta Gamma Hedging of Longevity and Interest Rate Risk

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.

Ownership Structure across Lines of Property-Casualty Insurance

본 연구는 보험연구원에서 2018년 실시한 보험소비자설문조사 데이터를 기반으로 생명보험상품과 손해보험 상품별 가입채널과 각 해당 보험상품들에 대한 가입 이유를 시각화 분석방법인 대응분석을 통해 분석하였다. 생명보험 상품들의 가입채널을 보면, 실손의료보험, 종신보험, 변액유니버셜종신, 변액유니버셜연금, 질병보장보험은 주로 설계사 채널과 밀접한 관련이 있으며, 상해보험은 인터넷과 TM, 홈쇼핑 채널들과 관련이 있으며, 변액종신, 어린이보장보험과 정기사망보험은 보험회사 임직원 채널과 관련이 높았다. 저축성보험과 연금보험은 은행과 증권회사 채널과 관련이 높게 나타났다. 반면에 손해보험 상품들의 가입채널을 보면, 실손의료보험, 질병보장보험, 운전자/장해의 장기 상해보험, 간병보험은 설계사 채널과 밀접한 관련이 있으며, 자동차보험은 인터넷 채널과 설계사 채널과 관련성이 높은 것으로 나타났다. 저축성보험은 TM, 보험회사직원, GA와 관련성이 있고 종합보험은 홈쇼핑과 관련이 있는 것으로 나타났다. 생명보험 상품과 손해보험 상품들의 가입 채널을 종합해 보면 주계약과 특약이 포함되어 상품의 특성이 복잡하여 구체적인 설명이 필요한 상품들은 설계사 채널이 선호되었다. 저축성보험과 연금보험은 은행과 증권회사 채널이 선호되었고, 자동차보험과 같이 정형화가 가능한 보험상품은 인터넷 채널이 선호되는 경향을 보였다.This study analyzed the subscription channels for life insurance products and indemnity insurance products and the reasons for subscribing each of the insurance products through the corresponding analysis, a visualization analysis method, based on the insurance consumer survey data conducted in 2018 by the Korea Insurance Research Institute. Looking at the subscription channels of life insurance products, loss medical insurance, whole life insurance, variable universal life insurance, variable universal annuities, and disease coverage insurance are mainly related to the life planner channel, and injury insurance is related to the internet, TM, and home shopping channels. In addition, variable whole life insurance, children s security insurance and term death insurance were related to the insurance company s employee channels. Savings insurance and annuity insurance were highly related to banks and securities companies. On the other hand, if you look at the subscription channels of indemnity life insurance products, loss medical insurance, disease insurance, long-term injury insurance for driver/disability, and care policy are closely related to the life planner channel, and auto insurance is highly related to the internet channel and the life planner channel. Appeared. It was found that savings insurance was related to TM, insurance company employees and GA, and comprehensive insurance was related to home shopping.

Calculating Capital Requirements for Longevity Risk in Life Insurance Products Using an Internal Model in Line with Solvency II