Interest Rate Models


Book Description

The field of financial mathematics has developed tremendously over the past thirty years, and the underlying models that have taken shape in interest rate markets and bond markets, being much richer in structure than equity-derivative models, are particularly fascinating and complex. This book introduces the tools required for the arbitrage-free modelling of the dynamics of these markets. Andrew Cairns addresses not only seminal works but also modern developments. Refreshingly broad in scope, covering numerical methods, credit risk, and descriptive models, and with an approachable sequence of opening chapters, Interest Rate Models will make readers--be they graduate students, academics, or practitioners--confident enough to develop their own interest rate models or to price nonstandard derivatives using existing models. The mathematical chapters begin with the simple binomial model that introduces many core ideas. But the main chapters work their way systematically through all of the main developments in continuous-time interest rate modelling. The book describes fully the broad range of approaches to interest rate modelling: short-rate models, no-arbitrage models, the Heath-Jarrow-Morton framework, multifactor models, forward measures, positive-interest models, and market models. Later chapters cover some related topics, including numerical methods, credit risk, and model calibration. Significantly, the book develops the martingale approach to bond pricing in detail, concentrating on risk-neutral pricing, before later exploring recent advances in interest rate modelling where different pricing measures are important.




Safety-First Retirement Planning


Book Description

Two fundamentally different philosophies for retirement income planning, which I call probability-based and safety-first, diverge on the critical issue of where a retirement plan is best served: in the risk/reward trade-offs of a diversified and aggressive investment portfolio that relies primarily on the stock market, or in the contractual protections of insurance products that integrate the power of risk pooling and actuarial science alongside investments. The probability-based approach is generally better understood by the public. It advocates using an aggressive investment portfolio with a large allocation to stocks to meet retirement goals. My earlier book How Much Can I Spend in Retirement? A Guide to Investment-Based Retirement Strategies provides an extensive investigation of probability-based approaches. But this investments-only attitude is not the optimal way to build a retirement income plan. There are pitfalls in retirement that we are less familiar with during the accumulation years. The nature of risk changes. Longevity risk is the possibility of living longer than planned, which could mean not having resources to maintain the retiree's standard of living. And once retirement distributions begin, market downturns in the early years can disproportionately harm retirement sustainability. This is sequence-of-returns risk, and it acts to amplify the impacts of market volatility in retirement. Traditional wealth management is not equipped to handle these new risks in a fulfilling way. More assets are required to cover spending goals over a possibly costly retirement triggered by a long life and poor market returns. And yet, there is no assurance that assets will be sufficient. For retirees who are worried about outliving their wealth, probability-based strategies can become excessively conservative and stressful. This book focuses on the other option: safety-first retirement planning. Safety-first advocates support a more bifurcated approach to building retirement income plans that integrates insurance with investments, providing lifetime income protections to cover spending. With risk pooling through insurance, retirees effectively pay an insurance premium that will provide a benefit to support spending in otherwise costly retirements that could deplete an unprotected investment portfolio. Insurance companies can pool sequence and longevity risks across a large base of retirees, much like a traditional defined-benefit company pension plan or Social Security, allowing for retirement spending that is more closely aligned with averages. When bonds are replaced with insurance-based risk pooling assets, retirees can improve the odds of meeting their spending goals while also supporting more legacy at the end of life, especially in the event of a longer-than-average retirement. We walk through this thought process and logic in steps, investigating three basic ways to fund a retirement spending goal: with bonds, with a diversified investment portfolio, and with risk pooling through annuities and life insurance. We consider the potential role for different types of annuities including simple income annuities, variable annuities, and fixed index annuities. I explain how different annuities work and how readers can evaluate them. We also examine the potential for whole life insurance to contribute to a retirement income plan. When we properly consider the range of risks introduced after retirement, I conclude that the integrated strategies preferred by safety-first advocates support more efficient retirement outcomes. Safety-first retirement planning helps to meet financial goals with less worry. This book explains how to evaluate different insurance options and implement these solutions into an integrated retirement plan.




Life Annuity Products and Their Guarantees


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.




Modelling Longevity Dynamics for Pensions and Annuity Business


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.




Pension Economics


Book Description

While not attempting to train readers as professional economists, this book aims to provide a secure grounding in the theory and practice of economics insofar as it deals with pension matters. From reading this book, the user will understand: * The key types of pension scheme * The role of pensions in maximizing individual lifetime welfare * The role of pensions in individual savings and retirement decisions * The role and consequences of the pension plan from the company's viewpoint * The role of pensions in promoting aggregate savings * The role of pensions and retirement in overlapping generations models * The economics of ageing and intergenerational accounting * The social welfare implications of pensions * The lessons of behavioural economics for pensions




The Economic Theory of Annuities


Book Description

Annuities are financial products that guarantee the holder a fixed return so long as the holder remains alive, thereby providing insurance against lifetime uncertainty. The terms of these contracts depend on the information available to insurance firms. Unlike age and gender, information about individual survival probabilities cannot be readily ascertained. This asymmetric information causes market inefficiencies, such as adverse selection. Groundbreaking in its scope, The Economic Theory of Annuities offers readers a theoretical analysis of the functioning of private annuity markets. Starting with a general analysis of survival functions, stochastic dominance, and characterization of changes in longevity, Eytan Sheshinski derives the demand for annuities using a model of individuals who jointly choose their lifetime consumption and retirement age. The relation between life insurance and annuities that have a bequest option is examined and "annuity options" are proposed as a response to the lack of secondary markets. This book also investigates the macroeconomic policy implications of annuities and changes in longevity on aggregate savings. Sheshinski utilizes statistical population theory to shed light on the debate of whether the surge in savings and growth in Asia and other countries can be attributed to higher longevity of the population and whether this surge is durable. This book shows how understanding annuities becomes essential as governments that grapple with insolvency of public social security systems place greater emphasis on individual savings accounts.




OECD Pensions Outlook 2012


Book Description

This edition looks at pension reform during the crisis and beyond, the design of automatic adjustment mechanisms, reversals of systemic pension reforms in Central and Eastern Europe, coverage of private pension systems and guarantees indefined contribution pension systems.




Annuities and Other Retirement Products


Book Description

In the 1990s many emerging economies in Central Europe and Latin America initiated their pension reforms. While most analysis to date has focused on the accumulation phase, there are a number of lessons to be shared as countries start to prepare the retirement options for their contributors, with this book addressing these issues from a public policy perspective.




Nonfinancial Defined Contribution Pension Schemes in a Changing Pension World


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.




Introduction to Insurance Mathematics


Book Description

This second edition expands the first chapters, which focus on the approach to risk management issues discussed in the first edition, to offer readers a better understanding of the risk management process and the relevant quantitative phases. In the following chapters the book examines life insurance, non-life insurance and pension plans, presenting the technical and financial aspects of risk transfers and insurance without the use of complex mathematical tools. The book is written in a comprehensible style making it easily accessible to advanced undergraduate and graduate students in Economics, Business and Finance, as well as undergraduate students in Mathematics who intend starting on an actuarial qualification path. With the systematic inclusion of practical topics, professionals will find this text useful when working in insurance and pension related areas, where investments, risk analysis and financial reporting play a major role.