Valuation and hedging of the ruin-contingent life annuity (RCLA)

This paper analyzes a novel type of mortality contingent-claim called a ruin-contingent life annuity (RCLA). This product fuses together a path-dependent equity put option with a "personal longevity" call option. The annuitant's (i.e. long position) payoff from a generic RCLA is \$1 of income per year for life, akin to a defined benefit pension, but deferred until a pre-specified financial diffusion process hits zero. We derive the PDE and relevant boundary conditions satisfied by the RCLA value (i.e. the hedging cost) assuming a complete market where No Arbitrage is possible. We then describe some efficient numerical techniques and provide estimates of a typical RCLA under a variety of realistic parameters. The motivation for studying the RCLA on a stand-alone basis is two-fold. First, it is implicitly embedded in approximately \$1 trillion worth of U.S. variable annuity (VA) policies; which have recently attracted scrutiny from financial analysts and regulators. Second, the U.S. administration - both Treasury and Department of Labor - have been encouraging Defined Contribution (401k) plans to offer stand-alone longevity insurance to participants, and we believe the RCLA would be an ideal and cost effective candidate for that job

Failing by a Wide Margin: Methods and Findings in the 2003 Social Security Trustees Report

On March 17, 2003, the trustees of the Social Security program released their annual report on the system's financial status. Many observers took the report's extension of the trust fund's solvency one year to 2042 to mean that Social Security's financial health had improved. In fact, Social Security's actuarial balance declined and its cash flow deficits over the next 75 years increased to $25.33 trillion (in 2003 dollars). More important, the report contained significant new methodologies that are central to the debate over personal retirement accounts. The trustees now measure Social Security's deficits over the infinite horizon, providing remedies to the previous 75-year scoring window that substantially understates the costs of the current program and overstates the costs of personal account plans. Under this new perpetuity benchmark, the present value of Social Security's cash flow shortfalls totals$11.9 trillion, versus only $4.9 trillion over 75 years. To cover Social Security's cash deficits permanently would demand an immediate tax increase equal to 4.47 percent of payroll. The 2003 report also includes a "stochastic analysis" accounting for the variability of the economic and demographic factors affecting Social Security's finances, finding there is less than a 1-in-40 chance of Social Security remaining solvent for even 75 years without reform. The 2003 Trustees Report shows that Social Security's cash deficits are large, growing, and unlikely to fix themselves without action. Only personal account proposals have been certified to eliminate Social Security's multitrillion dollar cash shortfalls

Alternative framework for the fair valuation of participating life insurance contracts

In this communication, we develop suitable valuation techniques for a with-profit/unitized with profit life insurance policy providing interest rate guarantees, when a jump-diffusion process for the evolution of the underlying reference portfolio is used. Particular attention is given to the mispricing generated by the misspecification of a jumpdiffusion process for the underlying asset as a pure diffusion process, and to which extent this mispricing affects the profitability and the solvency of the life insurance company issuing these contracts

The market potential for privately financed long term care products in the UK

This paper considers the market potential for privately financed long term care products in the UK. It finds that since the present market is undeveloped there is scope to increase the range of products available to suit people with different means and circumstances. Currently the UK spends about £19 billion on long term care (LTC) of which around a third is privately funded and two thirds publicly funded. The cost of informal care for older people is estimated to be worth £58 billion a year making a total of £77 billion. The paper finds that very few people can afford to pay for LTC out of their own pockets from income alone, but that this number is increased if savings are taken into account and significantly increased if housing wealth is included as well. Insurance for LTC is normally considered to be part of the product mix usually associated with the private funding of LTC. However, as the US market demonstrates, LTC insurance products can be complex and difficult to understand and yet still not meet all needs, whilst US research suggests that policies are also over priced and unaffordable for many. In this paper the case is made for other kinds of products which produce an income at the point of need and therefore make a contribution towards LTC costs. These products include equity release, ‘top up insurance’, disability linked annuities, and immediate needs annuities. Although they may not cover all possible risks, and therefore all needs, they would bring much needed new money into LTC as well as lead to an increase in personal responsibility. With large numbers of older people on very low incomes not everybody would be able to afford these products and so the concept of LTC bonds is considered. These would work like premium bonds and pay prizes but would only be cashable at the point of need. Taken together all of the products considered would extend choice and there would be something to meet most circumstances. The government’s role would be five fold: (1) to facilitate the introduction of the LTC products and provide regulation; (2) to provide appropriate incentives for people to take them up; (3) to clarify the role of the state in terms of the minimum entitlement people can expect; (4) to make it easier to get advice and direction at points of initial contact, for example with social and health care services; and (5) to cover risks that the market cannot handle

Maximum Market Price of Longevity Risk under Solvency Regimes: The Case of Solvency II.

Longevity risk constitutes an important risk factor for life insurance companies, and it can be managed through longevity-linked securities. The market of longevity-linked securities is at present far from being complete and does not allow finding a unique pricing measure. We propose a method to estimate the maximum market price of longevity risk depending on the risk margin implicit within the calculation of the technical provisions as defined by Solvency II. The maximum price of longevity risk is determined for a survivor forward (S-forward), an agreement between two counterparties to exchange at maturity a fixed survival-dependent payment for a payment depending on the realized survival of a given cohort of individuals. The maximum prices determined for the S-forwards can be used to price other longevity-linked securities, such as q-forwards. The Cairns–Blake–Dowd model is used to represent the evolution of mortality over time that combined with the information on the risk margin, enables us to calculate upper limits for the risk-adjusted survival probabilities, the market price of longevity risk and the S-forward prices. Numerical results can be extended for the pricing of other longevity-linked securities

Valuation Perspectives and Decompositions for Variable Annuities with GMWB riders

The guaranteed minimum withdrawal benefit (GMWB) rider, as an add on to a variable annuity (VA), guarantees the return of premiums in the form of peri- odic withdrawals while allowing policyholders to participate fully in any market gains. GMWB riders represent an embedded option on the account value with a fee structure that is different from typical financial derivatives. We consider fair pricing of the GMWB rider from a financial economic perspective. Particular focus is placed on the distinct perspectives of the insurer and policyholder and the unifying relationship. We extend a decomposition of the VA contract into components that reflect term-certain payments and embedded derivatives to the case where the policyholder has the option to surrender, or lapse, the contract early.Comment: 18 pages, proof of Lemma A.1 expanded for clarit

Profitability study of the annuities of EY-Insurance

Mestrado em Ciências ActuariaisEste trabalho procura analisar a rentabilidade obtida com a venda de anuidades e produtos anuais renováveis, na seguradora Vida onde decorreu o estágio. As questões relacionadas com os desvios observados na mortalidade e a necessidade de encontrar um modelo de sobrevivência mais ajustado à experiência da companhia foram aspetos de crucial importância. Procurou assim encontrar-se bases técnicas mais adequadas para o cálculo de prémios e reservas, tanto para os produtos já em comercialização, como para novos produtos que venham a ser lançados, pois também a taxa de juro e as despesas foram afloradas, ainda que brevemente. Por motivos de confidencialidade de dados, procedeu-se a uma distorção dos valores reais. Isto não teve obviamente qualquer consequência do ponto de vista das metodologias e técnicas aplicadas no estudo. Estavam disponíveis dados para um período de quatro anos, na sua maioria relativos a rendas imediatas e rendas imediatas reversíveis. Com base nisso, foi possível detetar que a tábua de mortalidade mais adequada será 108.95% da GKF95, o que talvez permita eliminar a maior parte dos desvios. Em complemento, foi ainda feita uma análise de sensibilidade, com diferentes cenários, para se estudar o efeito sobre o nível das reservas das diferentes possibilidades consideradas. Um exercício final de profit testing revelou que as responsabilidades continuam insuficientemente cobertas, pelo que trabalho adicional é necessário para resolver o problema.This study aims to evaluate the profitability of the life annuities in the insurance company where the internship took place by concentrating on finding the best mortality table for the company portfolio to quote the price for the new annuity businesses and reserving for the ones already sold. The project is based on real data that was intentionally transformed for the purpose of this text because of confidentiality reasons. The distortion conceals reality in an appropriate manner and has obviously no effects on the methodologies applied. Data concerns immediate and immediate reversible life annuities for four years, since these products comprise the most significant part of the company population of policy holders. The best mortality table for this data is 108.95% of GKF95 table, by least square fitting. In order to forecast the future mortality, the Gompertz-Makeham mortality model was applied and there were no systematic evolution through time for the future mortality. A Sensitivity analysis was performed to show the effects of different scenarios on mathematical reserving. Finally, a profit testing revealed that the technical bases for the annuities are not enough to cover the liabilities. 108.95% of GKF 95 table can be assumed as the initial table and 104.29% of GKF 95 table can be assumed to hold extra reserve, in order to guarantee an adequate mathematical reserve

Maximum Market Price of Longevity Risk under Solvency Regimes: The Case of Solvency II.

Longevity risk constitutes an important risk factor for life insurance companies, and it can be managed through longevity-linked securities. The market of longevity-linked securities is at present far from being complete and does not allow finding a unique pricing measure. We propose a method to estimate the maximum market price of longevity risk depending on the risk margin implicit within the calculation of the technical provisions as defined by Solvency II. The maximum price of longevity risk is determined for a survivor forward (S-forward), an agreement between two counterparties to exchange at maturity a fixed survival-dependent payment for a payment depending on the realized survival of a given cohort of individuals. The maximum prices determined for the S-forwards can be used to price other longevity-linked securities, such as q-forwards. The Cairns–Blake–Dowd model is used to represent the evolution of mortality over time that combined with the information on the risk margin, enables us to calculate upper limits for the risk-adjusted survival probabilities, the market price of longevity risk and the S-forward prices. Numerical results can be extended for the pricing of other longevity-linked securities

Participating Payout Life Annuities: Lessons from Germany

This paper analyzes the regulatory framework of German immediate participating payout life annuities (PLAs), which offer guaranteed minimum benefits as well as participation in insurers’ surpluses. Our particular focus lies on the mechanics of sharing surpluses between shareholders and policyholders. We show that the process of surplus determination, allocation, and distribution mostly follows transparent and clear rules, and that an insurance company’s management has limited leeway with respect to discretionary decision making. Subsequently, we develop an Asset Liability Model for a German life insurer that offers PLAs. Based on this model, we run Monte Carlo simulations to evaluate benefit variability and insurer stability under stochastic mortality and capital market developments. Our results suggest that through PLAs guaranteed benefits can be provided with high credibility, while, at the same time, annuitants receive attractive Money’s Worth Ratios. Moreover, we show that it might be difficult to offer a fixed benefit annuity providing the same lifetime utility as a PLA for the same premium and a comparably low insolvency risk. Overall, participating life annuity schemes may be an efficient way to deal with risk factors that are highly unpredictable and difficult to hedge over the long run, such as systematic mortality and investment risks