Variable Annuity Contracts Research Articles

A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities

Variable Annuities with embedded guarantees are very popular in the US market. There exists a great variety of products with both, guaranteed minimum death benefits (GMDB) and guaranteed minimum living benefits (GMLB). Although several approaches for pricing some of the corresponding guarantees have been proposed in the academic literature, there is no general framework in which the existing variety of such guarantees can be priced consistently. The present paper fills this gap by introducing a model, which permits a consistent and extensive analysis of all types of guarantees currently offered within Variable Annuity contracts. Besides a valuation assuming that the policyholder follows a given strategy with respect to surrender and withdrawals, we are able to price the contract under optimal policyholder behavior. Using both, Monte-Carlo methods and a generalization of a finite mesh discretization approach, we find that some guarantees are overpriced, whereas others, e.g. guaranteed annuities within guaranteed minimum income benefits (GMIB), are offered significantly below their risk-neutral value.

A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities

Variable Annuities with embedded guarantees are very popular in the US market. There exists a great variety of products with both, guaranteed minimum death benefits (GMDB) and guaranteed minimum living benefits (GMLB). Although several approaches for pricing some of the corresponding guarantees have been proposed in the academic literature, there is no general framework in which the existing variety of such guarantees can be priced consistently. The present paper fills this gap by introducing a model, which permits a consistent and extensive analysis of all types of guarantees currently offered within Variable Annuity contracts. Besides a valuation assuming that the policyholder follows a given strategy with respect to surrender and withdrawals, we are able to price the contract under optimal policyholder behavior. Using both, Monte-Carlo methods and a generalization of a finite mesh discretization approach, we find that some guarantees are overpriced, whereas others, e.g. guaranteed annuities within guaranteed minimum income benefits (GMIB), are offered significantly below their risk-neutral value.

Optimal asset allocation in life annuities: a note

In this note, we derive the optimal utility-maximizing asset allocation between a risky and risk-free asset within a variable annuity (VA) contract, which is a US-based savings and decumulation investment product. We are interested in the interaction between financial risk, mortality risk and consumption, towards the end of the life cycle. Our main result is that for constant relative risk aversion (CRRA) preferences and geometric Brownian motion (GBM) dynamics, the optimal asset allocation during the annuity decumulation (payout) phase is identical to the accumulation (savings) phase, which is the classical Merton [J. Econ. Theory 3 (1971) 373] solution.

Optimal Annuitization Policies

At, or about, the age of retirement, most individuals must decide what additional fraction of their marketable wealth, if any, should be annuitized. Annuitization means purchasing a nonrefundable life annuity from an insurance company, which then guarantees a lifelong consumption stream that cannot be outlived. The decision of whether or not to annuitize additional liquid assets is a difficult one, since it is clearly irreversible and can prove costly in hindsight. Obviously, for a large group of people, the bulk of financial wealth is forcefully annuitized, for example, company pensions and social security. For others, especially as it pertains to personal pension plans, such as 401(k), 403(b), and IRA plans as well as variable annuity contracts, there is much discretion in the matter. The purpose of this paper is to focus on the question of when and if to annuitize. Specifically, my objective is to provide practical advice aimed at individual retirees and their advisors. My main conclusions are as follows: • Annuitization of assets provides unique and valuable longevity insurance and should be actively encouraged at higher ages. Standard microeconomic utility-based arguments indicate that consumers would be willing to pay a substantial “loading” in order to gain access to a life annuity. • The large adverse selection costs associated with life annuities, which range from 10% to 20%, might serve as a strong deterrent to full annuitization. • Retirees with a (strong) bequest motive might be inclined to self-annuitize during the early stages of retirement. Indeed, it appears that most individuals—faced with expensive annuity products—can effectively “beat” the rate of return from a fixed immediate annuity until age 75�80. I call this strategy consume term and invest the difference. • Variable immediate annuities (VIAs) combine equity market participation together with longevity insurance. This financial product is currently underutilized (and not available in certain jurisdictions) and can only grow in popularity.

Option-Adjusted Equilibrium Valuation of Guaranteed Minimum Death Benefits in Variable Annuities

In the United States, variable annuity contracts are mutual funds with tax-deferred investment gains containing an additional embedded put option with a stochastic maturity date. At death, the beneficiary - or estate - of the policy owner is assured to receive the greater of the account market value and the original investment premium, perhaps with a minimally guaranteed roll rate. Payment for this life-contingent claim, is not made up front, but rather deducted continuously from the account in the form of a constant insurance expense ratio. This proportional expense stands in contrast to a fixed periodic - or initial - insurance premium and is what differentiates our research from previous analysis of similar equity-linked life products. In this paper we value the guaranteed minimum death benefit (GMDB) of a variable annuity by melding the tools of continuous-time financial economics and the actuarial theory of mortality functions. Specifically, we solve for the equilibrium insurance expense ratio that funds the embedded put option. We demonstrate that the equilibrium expense ratio solves a type of fixed point equation that relates the risk-neutral expected present value of costs and benefits. From an analytic perspective, with an assumed constant force of mortality, we show that the present value of the guaranteed minimum death benefit is the Laplace transform - in time - of the classical Black-Scholes/Merton equation adjusted for dividends, where the dividend is the insurance expense ratio. Remarkably, the final expression can be obtained in closed form and does not even involve the normal density. On the other hand, when the mortality is given a more realistic continuous time Gompertz structure, we obtain quite robust expressions and numerical values for the equilibrium insurance expense ratio. Finally, using a cross section of average insurance expense ratios (known as Mortality and Expense charges) provided by Morningstar Data - and reasonable estimates of market volatility - we conclude that in most cases the insurance industry is charging variable annuity holders approximately five to ten times the economic value of the guarantee.

Life insurance companies as investment managers: New implications for consumers

This paper examines the attractiveness of the equity portfolios of life insurance companies as an alternative investment to mutual funds. In particular, this study analyzes the risk-adjusted investment performance of the stock portfolios of life insurance companies, attributable to their stock selection and market timing abilities. Using conventional measures of risk-adjusted portfolio performance, we find that life insurance companies exhibit performance similar to mutual funds. The evidence suggests that the life insurance companies, like their mutual fund counterparts, fail to exhibit differential stock selection or market timing abilities that are statistically significant. While the risk-adjusted investment performance of the two investment vehicles is similar, the variable annuity contracts of life insurance companies may offer an edge over mutual funds due to their ability to defer taxes.

Securities Regulation: SEC Reiterates Decision That Issuers of Variable Annuity Contracts Are Subject to Federal Regulation under Investment Company Act of 1940

Securities Regulation: SEC Reiterates Decision That Issuers of Variable Annuity Contracts Are Subject to Federal Regulation under Investment Company Act of 1940

A COMMENT ON VARIABLE ANNUITIES

Variable Annuities are the subject of considerable discussion by individuals who identify themselves with life insurance companies and security dealers. The paper by Mr. Albert Linton published in the May, 1956, issue of the Journal of Finance is a case in point. This comment does not attempt to marshall arguments for or against variable annuities, but is concerned only with the major factors determining the size of the payments to be made from a variable annuity fund during the payment period. In Mr. Linton's Table 2, the assumption is made that the variable annuity payment would follow Standard and Poor's index of stock prices.1 The other major factor influencing the size of the annuity payment, the cash dividends that will be received by and added to the annuity fund during the period of the annuity payments, is omitted. This is comparable to omitting interest on the standard annuity contract. The purpose of Table 2 was evidently to display the magnitude of the fluctuations in variable annuity payments in contrast to the absolute dollar stability of the payments made under the terms of a traditional annuity contract. Mr. Linton emphasizes that “irate and disillusioned policyholders” might write letters to insurance commissioners and even congressmen when payments fall under variable annuity contracts. Such pressure might have been (or may be) the opportunity for federal regulation of those life insurance companies that issue variable annuity contracts. Column 1, Table 1, in this comment sets forth the fixed payment of $100 per month specified by Mr. Linton, Column 2 reproduces the assumed monthly payment made under a variable annuity contract as shown by Mr. Linton in his. Table 2, and Column 3 presents a revised statement of the monthly payment under a variable annuity contract taking cognizance of the dividends received by the annuity fund during each year of the life of the annuity. The period 1926 to 1954 is the period selected by Mr. Linton. According to Mr. Linton's presentation, the payments made under the variable annuity were less than those under the traditional contract in twelve of the twenty-nine years. The revised variable annuity payments fall below the fixed monthly payments of $100 in only three years. Furthermore, the lowest payment under the revised computation is $83 per month as compared with $49 per month shown by Mr. Linton. Certainly the intensity of the remarks in the policyholders' letters would be different if the variable annuity payments fell 17 per cent rather than 51 per cent below a norm established by the payment of a fixed number of dollars under a fixed annuity contract. Fixed annuity policyholders may well complain about the opportunities missed when they compare their $100 with the more than $200 monthly income in 1954 that might have been possible under a variable annuity contract. In the computation of Column 3, Table 1, the advantages accruing to the variable annuitant during the accumulation period have been foregone. Mr. Linton recognizes this advantage in suggesting that the rate of growth of funds during the accumulation period invested in a well-selected, properly diversified group of stocks has been larger than the rate of interest achieved by the investment portfolios that are the basis for traditional annuity contracts. We believe that such higher yields on equities are not dependent on inflation given the maintenance of our long-run rate of economic growth and that this relationship is very likely to continue. This position, however, must be left undefended since the space that may be alloted to a comment is very limited. Let the case of the conservative be admitted, however. The holder of a variable annuity contract, the annuitant, would take more risk with respect to the number of dollars he will eventually receive. Life insurance companies, other financial institutions, and even the structure of the capital markets will be affected by any considerable growth in the use of variable annuities. Such changes are certain to follow whether the life insurance companies themselves or some newly developed type of financial institution handles variable valued annuities.