Equity-linked Annuities Research Articles

Hancocked: Manulife and the Limits of Private Health Insurance

Long-term care (LTC) insurance is a salesman's dream. Millions of well-heeled boomers, anxious to protect their estates from the random expropriation of institutional dependency - what a market! But for Manulife, bleeding $1.5 million a day in LTC claims through subsidiary John Hancock, LTC is a nightmare. Company spokesmen blame unexpected increases in life expectancy. But management's fundamental error was insuring correlated risks. Risk pooling works only when individual risks are uncorrelated. Increases in life expectancy affect all contracts together. Manulife made the same mistake selling equity-linked annuities with guaranteed floors - essentially insuring against stock market declines. Results for shareholders have been catastrophic. Top management, meanwhile, have been honoured and richly rewarded.

The Annuity Puzzle Remains a Puzzle

We examine incomplete annuity menus, background risk, bequest motives, and default risk as possible drivers of divergence from full annuitization. Contrary to what is often suggested in the literature, we find that full annuitization remains optimal if saving is possible after retirement. This holds irrespective of whether real or only nominal annuities are available. Whenever liquidity is desired, individuals save sizeable amounts out of their annuity income to smooth consumption shocks. Similarly, adding equity-linked annuities to the menu does not increase welfare significantly, since individuals can invest in stocks in order to get the desired equity exposure.

Pricing Annuity Guarantees Under a Regime-Switching Model

We consider the pricing problem of equity-linked annuities and variable annuities under a regimeswitching model when the dynamic of the market value of a reference asset is driven by a generalized geometric Brownian motion model with regime switching. In particular, we assume that regime switching over time according to a continuous-time Markov chain with a finite number state space representing economy states. We use the Esscher transform to determine an equivalent martingale measure for fair valuation in the incomplete market setting. The paper is complemented with some numerical examples to highlight the implications of our model on pricing these guarantees.

Risk Analysis of Mortality Improvement: The Case of Chinese Annuity Markets

China has experienced significant improvement in longevity (commonly referred to as mortality improvement) since the late 1930s. The rate of mortality improvement has been faster than in most developed countries. This development has resulted in a great challenge to provide retirement income to the ageing population. This challenge is increased by the increasing presence of commercial annuity products in China. Such products should become an important source of retirement benefits. In this article, we propose a model of mortality improvement and calculate its factors using Chinese life tables. We also analyze the risks to annuity providers due to mortality improvement, and compare risks of mortality improvement for two different forms of annuities: equity-linked annuity and traditional fixed annuity. Finally, we provide several suggestions for managing risks of mortality improvement. In particular, we discuss a natural hedging strategy of issuing variable annuity instead of traditional annuity.

Optimal early withdrawal and valuation of finite-horizon fund protection options

When embedded in equity-linked annuities, the dynamic fund protection option automatically increases the number of primary fund units so that their total value does not fall below the (possibly stochastic) guaranteed level. As the option payout is determined by the running maximum of a price ratio, the “standard” fund protection option can be excessively expensive. In this paper, we modify the design of the embedded option by relaxing the guarantee to take effect only when the upgraded fund value has fallen to a certain level (the “spread”) below the reference fund value. Through a change of numeraire and appealing to the Markov and scaling property of the state variables, we are led to consider the fund protection option at inception, for which a decomposition formula for the American value can be derived. For the standard option, the early withdrawal premium is given by a single integral whose integrand is an explicit function of the early withdrawal boundary, whereas for the option with spread (K, say), the early withdrawal premium is given by a double integral whose integrand is an explicit function of a continuum of early withdrawal boundaries corresponding to options with spread not exceeding K. In both cases, a piecewise linear approximation of the early withdrawal boundary substantially simplifies the evaluation of the option value. Detailed algorithms are provided for the computation of both the prices and an entire family of early withdrawal boundaries for American fund protection options. For completeness, we also determine the prices and stationary boundaries of perpetual options with spread. Our numerical results show that the introduction of a spread in the option payout is effective in maing fund protection options more economically attractive.

Estimating the Present Value and the Break-Even Participating Rate for Equity-Linked Annuity Contracts

Estimating the Present Value and the Break-Even Participating Rate for Equity-Linked Annuity Contracts

Variance of the CTE Estimator

The Conditional Tail Expectation (CTE), also called Expected Shortfall or Tail-VaR, is a robust, convenient, practical, and coherent measure for quantifying financial risk exposure. The CTE is quickly becoming the preferred measure for statutory balance sheet valuation whenever real-world stochastic methods are used to set liability provisions. We look at some statistical properties of the methods that are commonly used to estimate the CTE and develop a simple formula for the variance of the CTE estimator that is valid in the large sample limit. We also show that the formula works well for finite sample sizes. Formula results are compared with sample values from realworld Monte Carlo simulations for some common loss distributions, including equity-linked annuities with investment guarantees, whole life insurance and operational risks. We develop the CTE variance formula in the general case using a system of biased weights and explore importance sampling, a form of variance reduction, as a way to improve the quality of the estimators for a given sample size. The paper closes with a discussion of practical applications.