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Author: Moshe A. Milevsky Publisher: ISBN: Category : Languages : en Pages : 31
Book Description
Most U.S.-based insurance companies offer holders of their tax-sheltered savings plans (VAs), the long-term option to annuitize their policy at a pre-determined rate over a pre-specified period of time. Currently, there is approximately one trillion dollars invested in such policies, with guaranteed annuitization rates, in addition to any guaranteed minimum death benefit. The insurance company has essentially granted the policyholder an option on two underlying stochastic variables; future interest rates and future mortality rates. Although the (put) option on interest rates is obvious, the (put) option on mortality rates is not. Motivated by this product, this paper attempts to value (options on) mortality-contingent claims, by stochastically modelling the future hazard-plus-interest rate.Heuristically, we treat the underlying life annuity as a defaultable coupon-bearing bond, where the default occurs at the exogenous time of death. From an actuarial perspective, rather than considering the force of mortality (hazard rate) at time-t for a person now age-x, as a number, we view it as a random variable forward rate,whose expectation is the force of mortality in the classical sense.Our main qualitative observation is that both mortality and interest rate risk can be hedged, and the option to annuitize can be priced by locating a replicating portfolio involving insurance, annuities and default-free bonds. We provide both a discrete and continuous-time pricing framework.
Author: Moshe A. Milevsky Publisher: ISBN: Category : Languages : en Pages : 31
Book Description
Most U.S.-based insurance companies offer holders of their tax-sheltered savings plans (VAs), the long-term option to annuitize their policy at a pre-determined rate over a pre-specified period of time. Currently, there is approximately one trillion dollars invested in such policies, with guaranteed annuitization rates, in addition to any guaranteed minimum death benefit. The insurance company has essentially granted the policyholder an option on two underlying stochastic variables; future interest rates and future mortality rates. Although the (put) option on interest rates is obvious, the (put) option on mortality rates is not. Motivated by this product, this paper attempts to value (options on) mortality-contingent claims, by stochastically modelling the future hazard-plus-interest rate.Heuristically, we treat the underlying life annuity as a defaultable coupon-bearing bond, where the default occurs at the exogenous time of death. From an actuarial perspective, rather than considering the force of mortality (hazard rate) at time-t for a person now age-x, as a number, we view it as a random variable forward rate,whose expectation is the force of mortality in the classical sense.Our main qualitative observation is that both mortality and interest rate risk can be hedged, and the option to annuitize can be priced by locating a replicating portfolio involving insurance, annuities and default-free bonds. We provide both a discrete and continuous-time pricing framework.
Author: Moshe A. Milevsky Publisher: ISBN: Category : Languages : en Pages : 44
Book Description
Asset allocation during the retirement years has not received as much attention as allocation prior to retirement. Within the context of financial planning towards the end of the life-cycle, the economics literature is puzzled over the extremely low levels of voluntary annuitization exhibited amongst the elderly. This phenomenon is inconsistent with a strict interpretation of the Modigliani life-cycle hypothesis. Although many plausible explanations have been suggested to reconcile theory and practice, none seem to contain any rigorous normative financial advice on when and if one should purchase an immediate annuity. This is particularly relevant given the increasing number of Defined Contribution pension plans in the U.S., within which the participants have to manage the risk of outliving their resources, and the corresponding trend away from Defined Benefit plans.In contrast to a classical economic approach - and motivated by the financial derivatives literature - this paper focuses attention on the Real Option embedded in the decision to annuitize. Indeed, a fixed immediate life annuity can be viewed as a project with a positive net-present value when compared to maintaining liquid wealth in non-annuitized assets. However, this project should nevertheless be deferred, since the option to wait and annuitize later has value. This result is driven by the higher possible risk-adjusted returns from alternative asset classes in the early stages of retirement, as well as possible asymmetries in mortality rates between subjective health status and objective annuity pricing.Practically speaking, we estimate that the real option to defer annuitization (RODA) is quite valuable until the mid-70s or mid-80s (depending on one's gender and risk aversion), at which point fixed immediate life annuities become the optimal asset class. Moreover, individuals with a higher risk tolerance and greater health asymmetry are endowed with an even larger option value to wait. However, low-cost variable immediate annuities, which are currently not widely available but which provide complete control over the asset allocation process within an immediate annuity wrapper, greatly reduce the option value to wait and create large welfare gains.
Author: Jeffrey R. Brown Publisher: ISBN: Category : Annuities Languages : en Pages : 72
Book Description
This paper examines the extent of redistribution that would occur under various annuity and bequest options as part of an individual accounts retirement program. I first estimate mortality differentials by gender, race, ethnicity and level of education using the National Longitudinal Mortality Study and document substantial differences. I then use these estimates to examine the expected transfers' that would take place between socioeconomic groups under different assumptions about the structure of an annuity program. Using an expected present discounted value or money's worth' calculation as the basis for comparison, I find that the size of transfers in an individual accounts program is highly sensitive to the benefit structure. For example, mandating a single-life, real annuity can result in expected transfers of as high as 20% of the account balance, often from economically disadvantaged groups toward groups that are better off. These transfers can be substantially reduced through the use of joint life annuities, survivor provisions and bequest options. For example, the largest expected negative transfer under a joint and full survivor annuity with a fully valued 20-year guarantee option is only 2% of the account balance. However, efforts to reduce the extent of redistribution generally do so at the cost of significantly lower annuity benefits paid to the individuals who contribute to the system.
Author: Collectif Publisher: OECD ISBN: 9264267794 Category : Business & Economics Languages : en Pages : 108
Book Description
This publication helps policy makers to better understand annuity products and the guarantees they provide in order to optimise the role that these products can play in financing retirement. Product design is a crucial factor in the potential role of annuity products within the pension system, along with the cost and demand for these products, and the resulting risks that are borne by the annuity providers. Increasingly complex products, however, pose additional challenges concerning consumer protection. Consumers need to be aware of their options and have access to unbiased and comprehensible advice and information about these products.
Author: Regina C. Elandt-Johnson Publisher: John Wiley & Sons ISBN: 1119011035 Category : Mathematics Languages : en Pages : 490
Book Description
Survival analysis deals with the distribution of life times, essentially the times from an initiating event such as birth or the start of a job to some terminal event such as death or pension. This book, originally published in 1980, surveys and analyzes methods that use survival measurements and concepts, and helps readers apply the appropriate method for a given situation. Four broad sections cover introductions to data, univariate survival function, multiple-failure data, and advanced topics.
Author: Marek Musiela Publisher: Springer Science & Business Media ISBN: 3662221322 Category : Mathematics Languages : en Pages : 521
Book Description
A comprehensive and self-contained treatment of the theory and practice of option pricing. The role of martingale methods in financial modeling is exposed. The emphasis is on using arbitrage-free models already accepted by the market as well as on building the new ones. Standard calls and puts together with numerous examples of exotic options such as barriers and quantos, for example on stocks, indices, currencies and interest rates are analysed. The importance of choosing a convenient numeraire in price calculations is explained. Mathematical and financial language is used so as to bring mathematicians closer to practical problems of finance and presenting to the industry useful maths tools.
Author: Ermanno Pitacco Publisher: OUP Oxford ISBN: 0191563153 Category : Business & Economics Languages : en Pages : 417
Book Description
Mortality improvements, uncertainty in future mortality trends and the relevant impact on life annuities and pension plans constitute important topics in the field of actuarial mathematics and life insurance techniques. In particular, actuarial calculations concerning pensions, life annuities and other living benefits (provided, for example, by long-term care insurance products and whole life sickness covers) are based on survival probabilities which necessarily extend over a long time horizon. In order to avoid underestimation of the related liabilities, the insurance company (or the pension plan) must adopt an appropriate forecast of future mortality. Great attention is currently being devoted to the management of life annuity portfolios, both from a theoretical and a practical point of view, because of the growing importance of annuity benefits paid by private pension schemes. In particular, the progressive shift from defined benefit to defined contribution pension schemes has increased the interest in life annuities with a guaranteed annual amount. This book provides a comprehensive and detailed description of methods for projecting mortality, and an extensive introduction to some important issues concerning longevity risk in the area of life annuities and pension benefits. It relies on research work carried out by the authors, as well as on a wide teaching experience and in CPD (Continuing Professional Development) initiatives. The following topics are dealt with: life annuities in the framework of post-retirement income strategies; the basic mortality model; recent mortality trends that have been experienced; general features of projection models; discussion of stochastic projection models, with numerical illustrations; measuring and managing longevity risk.
Author: Robert Holzmann Publisher: World Bank Publications ISBN: 0821394797 Category : Business & Economics Languages : en Pages : 535
Book Description
Nonfinancial Defined Contribution (NDC) schemes are now in their teens. The new pension concept was born in the early 1990s, implemented from the mid-1990s in Italy, Latvia, Poland and Sweden, legislated most recently in Norway and Egypt and serves as inspiration for other reform countries. This innovative unfunded individual account scheme created high hopes at a time when the world seemed to have been locked into a stalemate between piecemeal reforms of ailing traditional defined benefit schemes and introducing pre-funded financial account schemes. The experiences and conceptual issues of NDC in its childhood were reviewed in a prior anthology (Holzmann and Palmer, 2006). This new anthology published in 2 volumes serves to review its adolescence and with the aim of contributing to a successful adulthood. Volume 1 on Progress, Lessons, Implementation includes a detailed analysis of the experience and the key policy lessons in the old and new pilot countries and the implementation of NDCs elements in other reform countries. This volume 2 on Gender, Politics, Financial Stability includes deeper and new analyses of these issues that found little or no attention in the 2006 publication. The gender perspective includes 5 chapters with, perhaps, the most complete discussion on gender and pension issues available to date. The financial stability perspective addresses in 6 chapters critical micro- and macroeconomic aspects such as the balancing mechanism, the use of a reserve fund, the handling of legacy costs, and technicalities related to the management of the longevity risk when designing annuities. While the 2 volumes address many issues it also opens a number of new questions for which good answers are not yet readily available.
Author: Moshe A. Milevsky
Author: Moshe A. Milevsky
Author: Moshe A. Milevsky
Author: Jeffrey R. Brown
Author: Laura Ballotta
Author: Collectif
Author: United States. Internal Revenue Service
Author: Regina C. Elandt-Johnson
Author: Marek Musiela
Author: Ermanno Pitacco
Author: Robert Holzmann