Linking annuity benefits to the longevity experience: Alternative solutions

The uncertainty regarding financial returns and the life expectancy, joint to the reduced social security benefits, increasingly expose individuals to the risk of outliving their post-retirement assets. However, the demand for longevity guarantees remains low, due to high costs. The providers, on their side, may be reluctant to offer non-adjustable longevity guarantees, as the risk is long term and difficult to predict. It is therefore convenient to reconsider the design of longevity guarantees. In particular, a participating structure, providing a link to some longevity experience, could allow a sharing of losses, and possibly profits, resulting in a reduction of the cost of the retained guarantee. The literature review suggests a number of alternatives to define a longevity-linking arrangement, but the topic is not yet completely explored. It is useful, in particular, to have a common framework, under which the various solutions can be interpreted and compared, also with a view to the trade-off between the retained risk and the cost of the guarantee. Developing a general structure describing longevity-linked post-retirement benefits is the main purpose of this paper. Allowing for aggregate longevity risk, we then examine suitable solutions for insurance products

Variable Annuities: Risk Identification and Risk Assessment

Life annuities and pension products usually involve a number of ‘guarantees’, such as, e.g., minimum accumulation rates, minimum annual payments and minimum total payout. Packaging different types of guarantees is the feature of the so-called Variable Annuities. Basically, these products are unit-linked investment policies providing deferred annuity benefits. The guarantees, commonly referred to as GMxBs (namely, Guaranteed Minimum Benefits of type ‘x’), include minimum benefits both in case of death and survival. Following a Risk Management-oriented approach, this paper first aims at singling out all sources of risk affecting Variable Annuities (‘risk identification phase’). Critical aspects arise from the interaction between financial and demographic issues. In particular, the longevity risk may have a dramatic impact on the technical equilibrium of a portfolio. Then, we deal with risk quantification (‘risk assessment phase’), mostly via stochastic simulation of financial and demographic scenarios. Our main contribution is to present an integrated approach to risks in Variable Annuity products, so providing a unifying and innovative point of view

Longevity-contingent deferred life annuities

Considering the substantial systematic longevity risk threatening annuity providers’ solvency, indexing benefits on actual mortality improvements appears to be an efficient risk management tool, as discussed in Denuit et al. (2011) and Richter and Weber (2011). Whereas these papers consider indexing annuity payments, the present work suggests that the length of the deferment period could also be subject to revision, providing longevity-contingent deferred life annuities

The METCRAX II Field Experiment: A Study of Downslope Windstorm-Type Flows in Arizona\u2019s Meteor Crater

The second Meteor Crater Experiment (METCRAX II) was conducted in October 2013 at Arizona\u2019s Meteor Crater. The experiment was designed to investigate nighttime downslope windstorm 12type flows that form regularly above the inner southwest sidewall of the 1.2-km diameter crater as a southwesterly mesoscale katabatic flow cascades over the crater rim. The objective of METCRAX II is to determine the causes of these strong, intermittent, and turbulent inflows that bring warm-air intrusions into the southwest part of the crater. This article provides an overview of the scientific goals of the experiment; summarizes the measurements, the crater topography, and the synoptic meteorology of the study period; and presents initial analysis results

Longevity-indexed annuities

This paper addresses the problem of the sharing of longevity risk between an annuity provider and a group of annuitants. An appropriate longevity index is designed in order to adapt the amount of the periodic payments in life annuity contracts. This accounts for unexpected longevity improvements experienced by a given reference population. The approach described in the present paper is in contrast with Group Self-Annuitization where annuitants bear their own risk. Here, the annuitants only bear the non-diversifiable risk that the future mortality trend departs from that of the reference forecast. In that respect, the life annuities discussed in this paper are substitutes for reinsurance and securitization of longevity risk

The valuation of guaranteed lifelong withdrawal benefit options in variable annuity contracts and the impact of mortality risk

n light of the growing importance of the variable annuities market, in this paper we introduce a theoretical model for the pricing and valuation of guaranteed lifelong withdrawal benefit (GLWB) options embedded in variable annuity products. As the name suggests, this option offers a lifelong withdrawal guarantee; therefore, there is no limit on the total amount that is withdrawn over the term of the policy because if the account value becomes zero while the insured is still alive, he or she continues to receive the guaranteed amount annually until death. Any remaining account value at the time of death is paid to the beneficiary as a death benefit. We offer a specific framework to value the GLWB option in a market-consistent manner under the hypothesis of a static withdrawal strategy, according to which the withdrawal amount is always equal to the guaranteed amount. The valuation approach is based on the decomposition of the product into living and death benefits. The model makes use of the standard no-arbitrage models of mathematical finance, which extend the Black-Scholes framework to insurance contracts, assuming the fund follows a geometric Brownian motion and the insurance fee is paid, on an ongoing basis, as a proportion of the assets. We develop a sensitivity analysis, which shows how the value of the product varies with the key parameters, including the age of the policyholder at the inception of the contract, the guaranteed rate, the risk-free rate, and the fund volatility. We calculate the fair fee, using Monte Carlo simulations under different scenarios. We give special attention to the impact of mortality risk on the value of the option, using a flexible model of mortality dynamics, which allows for the possible perturbations by mortality shock of the standard mortality tables used by practitioners. Moreover, we evaluate the introduction of roll-up and step-up options and the effect of the decision to delay withdrawing. Empirical analyses are performed, and numerical results are provided

The impact of longevity and investment risk on a portfolio of life insurance liabilities

In this paper we assess the joint impact of biometric and financial risk on the market valuation of life insurance liabilities. We consider a stylized, contingent claim based model of a life insurance company issuing participating contracts and subject to default risk, as pioneered by Briys and de Varenne (Geneva Pap Risk Insur Theory 19(1):53–72, 1994, J Risk Insur 64(4):673–694, 1997), and build on their model by explicitly introducing biometric risk and its components, namely diversifiable and systematic risk. The contracts considered include pure endowments, deferred whole life annuities and guaranteed annuity options. Our results stress the predominance of systematic over diversifiable risk in determining fair participation rates. We investigate the interaction of contract design, market regimes and mortality assumptions, and show that, particularly for lifelong benefits, the choice of the participation rate must be very conservative if longevity improvements are foreseeable