Adverse selection and the market for annuities

Adverse selection is often blamed for the malfunctioning of the annuities market. We simulate the impact of adverse selection on the consumption allocation of annuitants under alternative parameter values, and explore the resulting welfare implications. We show that, for most parameter values, the welfare losses associated with equilibriums that are subject to adverse selection correspond to a loss of wealth of around one percent in a first-best equilibrium. These losses are smaller than the corresponding losses associated with equilibriums with no access to an annuity market by an order of magnitude of ten. The existence of substitutes for annuities such as a bequest motive or a social security system intensifies the adverse selection but reduces its welfare impact.

Social security, life insurance and annuities for families

In this paper we ask whether an aspect of social security, namely its role as a provider of insurance against uncertain life spans, is welfare enhancing. To this end we use an OLG model where agents have a bequest motive and differ in sex and marital status and where families are formed and destroyed and their characteristics evolve (exogenously) according to U.S. demographic patterns of marriage, divorce, fertility and mortality. We compare the implications of social security under a variety of market structures that differ in the extent to which life insurance and annuities are available. We find that social security is a bad idea. In economies where the private sector provides annuities and life insurance, it is a bad idea for the standard reason that it distorts the intertemporal margin by lowering the capital stock. In the absence of such securities social security is still a very bad idea, only marginally less so compared with economies with annuities and life insurance. We also explore these issues in a world where people live longer and we find no differences in our answers. As a by-product of our analysis we find that the existence of life insurance opportunities for people is important in welfare terms while that of annuities is not.     

Dynamic portfolio choice with deferred annuities

We derive the optimal life-cycle portfolio choice and consumption pattern for households facing uncertain labor income, risky capital market, and mortality risk. In addition to stocks and bonds, the households have access to deferred annuities. Deferred payout life annuities are financial contracts providing life-long income to the annuitant after a specified period of time conditional on survival. We find that deferred annuities play an important role in household portfolios and generate significant welfare gains. Households with high benefits from state pensions, moderate risk aversion and moderate labor income risk purchase deferred annuities from age 40 and gradually increase their portfolio share. At retirement, deferred annuities account for 78% of total financial wealth. Households with low state pensions and high labor income risk purchase more annuities and earlier. Uncertainty with respect to future mortality rates has the same effect, i.e. household hedge against longevity risks using deferred annuities.     

Fixed and variable longevity income annuities in defined contribution plans: Optimal retirement portfolios taking social security into account

This paper investigates retirees' optimal purchases of fixed and variable longevity income annuities using their defined contribution (DC) plan assets and given their expected social security benefits. As an alternative, we also evaluate using plan assets to boost social security benefits through delayed claiming. Using a calibrated life-cycle model, we determine that including deferred income annuities in DC accounts is welfare-enhancing for all sex/education groups examined. We also show that providing access to well-designed variable deferred annuities with some equity exposure further enhances retiree well-being, compared to having access only to fixed annuities. Nevertheless, for those facing the highest mortality rates, delaying claiming social security is mostly preferred, whereas those anticipating living longer than average will benefit more from using accumulated DC plan assets to purchase deferred annuities.     

Optimal exchange rate flexibility with large labor unions

We study the optimal volatility of the exchange rate in a two-country model with sectoral non-atomistic wage setters, non-traded goods, nominal rigidities and alternative pricing assumptions – producer or local currency pricing. Labor unions internalize the sectoral impact of their wage settlements through firms' labor demand. With local currency pricing, exchange rate depreciation raises sales revenue, which in turn boosts domestic consumption and labor demand. Unions anticipate this effect and set higher wages accordingly. With small unions and low wage markup, optimal monetary policy enhances exchange rate movements to improve its terms of trade. With large unions and high wage markup, optimal monetary policy curbs exchange rate movements to restrain inflationary wage demands and to stabilize employment.     

An alternative approach to determining present and future value interest factors for annuities due

This note presents an alternative approach to determining present and future annuities due interest factors. Many students find the adjustment to present and future ordinary annuities interest factors confusing and, consequently, memorize the rules without fully understanding their concepts. We encourage the use of an intuitive approach that makes adjustments with only one simple rule.     

Equity-linked annuities with multiscale hybrid stochastic and local volatility

In recent times, hybrid underlying models have become an industry standard for the pricing of derivatives and other problems in finance. This paper chooses a hybrid stochastic and local volatility model to evaluate an equity-linked annuity (ELA), which is a sort of tax-deferred annuity whose credited interest is linked to an equity index. The stochastic volatility component of the hybrid model is driven by a fast mean-reverting diffusion process while the local volatility component is given by the constant elasticity of variance (CEV) model. Since contracts of the ELA usually have long maturities over 10 years, a slowly moving factor in the stochastic volatility of stock index is expected to play a significant role in the valuation of the ELA, and thus, it is added to the aforementioned model. Based on this multiscale hybrid model, an analytic approximate formula is obtained for the price of a European option in terms of the CEV probability density function and then the result is applied to the value of the point-to-point ELA. The formula leads to the dependence structure of the ELA price on the fast and slow scale stochastic volatility and the elasticity of variance.     

Regression-based Monte Carlo methods for stochastic control models: variable annuities with lifelong guarantees

We present regression-based Monte Carlo simulation algorithm for solving the stochastic control models associated with pricing and hedging of the guaranteed lifelong withdrawal benefit (GLWB) in variable annuities, where the dynamics of the underlying fund value is assumed to evolve according to the stochastic volatility model. The GLWB offers a lifelong withdrawal benefit, even when the policy account value becomes zero, while the policyholder remains alive. Upon death, the remaining account value will be paid to the beneficiary as a death benefit. The bang-bang control strategy analysed under the assumption of maximization of the policyholder’s expected cash flow reduces the strategy space of optimal withdrawal policies to three choices: zero withdrawal, withdrawal at the contractual amount or complete surrender. The impact on the GLWB value under various withdrawal behaviours of the policyholder is examined. We also analyse the pricing properties of GLWB subject to different model parameter values and structural features.     

Longevity and adjustment in pension annuities,with application to Finland

The aim of this paper is twofold. First, the improvement in adult mortality in Finland is studied. Lee-Carter (LC) Poisson log-bilinear model is used for mortality forecasting. Secondly, the paper studies how the pension annuities are adjusted to unexpected mortality pattern. A formula for funded plan is proposed. Application is made with Finnish mortality rates predicted using the LC model.     

Variable annuities in a Lévy-based hybrid model with surrender risk

This paper proposes a market consistent valuation framework for variable annuities (VAs) with guaranteed minimum accumulation benefit, death benefit and surrender benefit features. The setup is based on a hybrid model for the financial market and uses time-inhomogeneous Lévy processes as risk drivers. Further, we allow for dependence between financial and surrender risks. Our model leads to explicit analytical formulas for the quantities of interest, and practical and efficient numerical procedures for the evaluation of these formulas. We illustrate the tractability of this approach by means of a detailed sensitivity analysis of the fair value of the VA and its components with respect to the model parameters. The results highlight the role played by the surrender behaviour and the importance of its appropriate modelling.     

Structured settlement annuities, part 1: overview and the underwriting process

Structured settlement underwriting is the underwriting of medically impaired lives for the purchase of an annuity to fund the settlement. Other than risk assessment, structured settlement (SS) underwriting has little in common with traditional life insurance underwriting. Most noteworthy of these differences is the relative lack of actuarial data on which to base decisions about mortality and the necessity for prospective thinking about risk assessment. The purpose of this paper is to provide a foundation for understanding the structured settlement business and to contrast the underwriting of structured settlements with that of traditional life insurance. This is the first part of a two-part article on SS annuities. Part 2 deals with the mortality experience in SS annuitants and the life-table methodology used to calculate life expectancy for annuitants at increased mortality risk.     

Redistribution by insurance market regulation: Analyzing a ban on gender-based retirement annuities

We illustrate how equilibrium screening models can be used to evaluate the economic consequences of insurance market regulation. We calibrate and solve a model of the United Kingdom's compulsory annuity market and examine the impact of gender-based pricing restrictions. We find that the endogenous adjustment of annuity contract menus in response to such restrictions can undo up to half of the redistribution from men to women that would occur with exogenous Social Security-like annuity contracts. Our findings indicate the importance of endogenous contract responses and illustrate the feasibility of employing theoretical insurance market equilibrium models for quantitative policy analysis.     

Portfolio choice in retirement: Health risk and the demand for annuities,housing, and risky assets

In a life-cycle model, a retiree faces stochastic health depreciation and chooses consumption, health expenditure, and the allocation of wealth between bonds, stocks, and housing. The model explains key facts about asset allocation and health expenditure across health status and age. The portfolio share in stocks is low overall and is positively related to health, especially for younger retirees. The portfolio share in housing is negatively related to health for younger retirees and falls significantly in age. Finally, out-of-pocket health expenditure as a share of income is negatively related to health and rises in age.     

A common thread linking the design of guarantee and nonescalating payments of public annuities

Motivated by recent experiences in economies adopting the defined-contribution pension system, we study public annuities in the presence of survival probability heterogeneity. It is found that the difference of annuitization-weighted and unweighted averages of survival probabilities is a useful measure of the severity of adverse selection. We then examine public annuities with a guarantee feature which bundles annuity income and bequeathable wealth components. We show that when the heterogeneity in survival probability is limited, the magnitude of guarantee proportion is irrelevant. On the other hand, an increase in the guarantee proportion mitigates adverse selection when the extent of heterogeneity is sufficiently large, because the share of annuity purchase by retirees with lower (resp., higher) survival probabilities is increased (resp., decreased). We also obtain a similar set of results for public annuities with nonescalating payments. The results have useful implications regarding the design of public annuities.     

Optimal capital controls and real exchange rate policies: A pecuniary externality perspective

A new literature studies the use of capital controls to prevent financial crises. Within this new framework, we show that when exchange rate policy is costless, there is no need for capital controls. However, if exchange rate policy entails efficiency costs, capital controls become part of the optimal policy mix. When exchange rate policy is costly, the optimal mix combines prudential capital controls in tranquil times with policies that limit exchange rate depreciation in crisis times. The optimal mix yields more borrowing, fewer and less severe financial crises, and much higher welfare than with capital controls alone.     

The valuation of GMWB variable annuities under alternative fund distributions and policyholder behaviours

In this paper, we present a dynamic programming algorithm for pricing variable annuities with Guaranteed Minimum Withdrawal Benefits (GMWB) under a general Lévy processes framework. The GMWB gives the policyholder the right to make periodical withdrawals from her policy account even when the value of this account is exhausted. Typically, the total amount guaranteed for withdrawals coincides with her initial investment, providing then a protection against downside market risk. At each withdrawal date, the policyholder has to decide whether, and how much, to withdraw, or to surrender the contract. We show how different policyholder’s withdrawal behaviours can be modelled. We perform a sensitivity analysis comparing the numerical results obtained for different contractual and market parameters, policyholder behaviours and different types of Lévy processes.     

The dynamics of premium reserves of life annuities under the regime of Solvency II

The article considers the solvency requirements for a whole portfolio of annuities under the regime of Solvency II. More precisely, the following question is investigated: Which demand of interest on the initial capital – the Solvency II premium reserves – is needed in order to fit the balance for Solvency II capital requirements in the next year? It turns out, that even for a model portfolio of simple annuities with say guaranteed interest rate of 1,25% the demand of interest in one year is greater than 3%. So even if a life insurance company fulfill the capital requirements of Solvency II in 2016 the mentioned effect causes eventually problems in future times.