This dissertation studies the adverse financial implications of "longevity risk" and "mortality risk", which have attracted the growing attention of insurance companies, annuity providers, pension funds, public policy decision-makers, and investment banks. Securitization of longevity/mortality risk provides insurers and pension funds an effective, low-cost approach to transferring the longevity/mortality risk from their balance sheets to capital markets. The modeling and forecasting of the mortality rate is the key point in pricing mortality-linked securities that facilitates the emergence of liquid markets. First, this dissertation introduces the discrete models proposed in previous literature. The models include: the Lee-Carter Model, the Renshaw Haberman Model, The Currie Model, the Cairns-Blake-Dowd (CBD) Model, the Cox-Lin-Wang (CLW) Model and the Chen-Cox Model. The different models have captured different features of the historical mortality time series and each one has their own advantages. Second, this dissertation introduces a stochastic diffusion model with a double exponential jump diffusion (DEJD) process for mortality time-series and is the first to capture both asymmetric jump features and cohort effect as the underlying reasons for the mortality trends. The DEJD model has the advantage of easy calibration and mathematical tractability. The form of the DEJD model is neat, concise and practical. The DEJD model fits the actual data better than previous stochastic models with or without jumps. To apply the model, the implied risk premium is calculated based on the Swiss Re mortality bond price. The DEJD model is the first to provide a closed-form solution to price the q-forward, which is the standard financial derivative product contingent on the LifeMetrics index for hedging longevity or mortality risk. Finally, the DEJD model is applied in modeling and pricing of life settlement products. A life settlement is a financial transaction in which the owner of a life insurance policy sells an unneeded policy to a third party for more than its cash value and less than its face value. The value of the life settlement product is the expected discounted value of the benefit discounted from the time of death. Since the discount function is convex, it follows by Jensen's Inequality that the expected value of the function of the discounted benefit till random time of death is always greater than the benefit discounted by the expected time of death. So, the pricing method based on only the life expectancy has the negative bias for pricing the life settlement products. I apply the DEJD mortality model using the Whole Life Time Distribution Dynamic Pricing (WLTDDP) method. The WLTDDP method generates a complete life table with the whole distribution of life times instead of using only the expected life time (life expectancy). When a life settlement underwriter's gives an expected life time for the insured, information theory can be used to adjust the DEJD mortality table to obtain a distribution that is consistent with the underwriter projected life expectancy that is as close as possible to the DEJD mortality model. The WLTDDP method, incorporating the underwriter information, provides a more accurate projection and evaluation for the life settlement products. Another advantage of WLTDDP is that it incorporates the effect of dynamic longevity risk changes by using an original life table generated from the DEJD mortality model table.

Recent turbulence in the financial markets has highlighted the need for diversified portfolios with lower correlations between the different investments. Life settlements meet this need, offering investors the prospect of high, stable returns, uncorrelated with the broader financial markets. This book provides readers of all levels of experience with essential information on the process surrounding the acquisition and management of a portfolio of life settlements; the assessment, modelling and mitigation of the associated longevity, interest rate and credit risks; and practical approaches to financing and risk management structures. It begins with the history of life insurance and looks at how the need for new financing sources has led to the growth of the life settlements market in the United States. The authors provide a detailed exploration of the mathematical formulae surrounding the generation of mortality curves, drawing a parallel between the tools deployed in the credit derivatives market and those available to model longevity risk. Structured products and securitisation techniques are introduced and explained, starting with simple vanilla products and models before illustrating some of the investment structures associated with life settlements. Capital market mechanisms available to assist the investor in limiting the risks associated with life settlement portfolios are outlined, as are opportunities to use life settlement portfolios to mitigate the risks of traditional capital markets. The last section of the book covers derivative products, either available now or under consideration, that will reduce or potentially eliminate longevity risks within life settlement portfolios. It then reviews hedging and risk management strategies and considers how to measure the effectiveness of risk mitigation.

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.

The pricing of longevity-linked securities depends not only on the stochastic uncertainty of the underlying risk factors, but also the attitude of investors towards those factors. In this research, we investigate how to estimate the market risk premium of longevity risk using investable retirement indexes, incorporating uncertain real interest rates using an affine dynamic Nelson-Siegel model. A multi-cohort aggregate, or systematic, continuous time affine mortality model is used where each risk factor is assigned a market price of mortality risk. To calibrate the market price of longevity risk, a common practice is to make use of market prices, such as longevity-linked securities and longevity indices. We use the BlackRock CoRI Retirement Indexes, which provides a daily level of estimated cost of lifetime retirement income for 20 cohorts in the U.S. Although investment in the index directly is not possible, individuals can invest in funds that track the index. For these 20 cohorts, we assume risk premiums for the common factors are the same across cohorts, but the risk premium of the factors for a specific cohort is allowed to take different values for different cohorts. The market prices of longevity risk are then calibrated by matching the risk-neutral model prices with BlackRock CoRI index values. Closed-form expressions and prices for European options on longevity zero-coupon bonds are derived using the model and compared to prices for standard options on zero coupon bonds. The impact of uncertain mortality on long term option prices is quantified and discussed.

"Luca Albertini and Pauline Barrieu are to be congratulated on this volume. Written in a period where structured projects in finance are having a difficult time, it is worthwhile to return to the cradle of securitisation: insurance. Spread out over three parts (life, non- life, and tax and regulatory issues) the 26 chapters, written mainly by practitioners, give an excellent overview of this challenging field of modern insurance. Methodology and examples nicely go hand in hand. The overall slant being towards actual analyses of concrete products. No doubt this book will become a milestone going forward for actuarial students, researchers, regulators and practitioners alike." —Paul Embrechts, Professor of Mathematics and Director of RiskLab, ETH Zurich The convergence of insurance with the capital markets has opened up an alternative channel for insurers to transfer risk, raise capital and optimize their regulatory reserves as well as offering institutions a source of relatively liquid investment with limited correlation with other exposures. One of the financial instruments allowing for the cession of insurance-related risks to the capital markets is Insurance-Linked Securities (ILS). This book provides hands-on information essential for market participants, drawing on the insights and expertise of an impressive team of international market players, representing the various aspects and perspectives of this growing sector. The book presents the state of the art in Insurance-Linked Securitization, by exploring the various roles for the different parties involved in the transactions, the motivation for the transaction sponsors, the potential inherent pitfalls, the latest developments and transaction structures and the key challenges faced by the market. The book is organized into parts, each covering a specific topic or sector of the market. After a general overview of the ILS market, the Insurance-Linked Securitization process is studied in detail. A distinction is made between non-life and life securitization, due to the specificities of each sector. The process and all the actors involved are identified and considered in a comprehensive and systematic way. The concepts are first looked at in a general way, before the analysis of relevant case studies where the ILS technology is applied. Particular focus is given to: the key stages in both non-life and life securitizations, including the general features of the transactions, the cedant's perspectives, the legal issues, the rating methodologies, the choice of an appropriate trigger and the risk modeling, the particular challenges related to longevity securitization, the investor's perspective and the question of the management of a portfolio of ILS, the general issues related to insurance-linked securitization, such as accounting and tax issues, regulatory issues and solvency capital requirements. The book is accompanied by a website www.wiley.com/go/albertini_barrieu_ILS which will feature updates and additions to the various contributions to follow market developments.

Longevity risk management is becoming increasingly important in the pension and life insurance industries. The unexpected mortality improvements observed in recent decades are posing serious concerns to the financial stability of defined-benefit pension plans and annuity portfolios. It has recently been argued that the overwhelming longevity risk exposures borne by the pension and life insurance industries may be transferred to capital markets through standardized longevity derivatives that are linked to broad-based mortality indexes. To achieve the transfer of risk, two technical issues need to be addressed first: (1) how to model the dynamics of mortality indexes, and (2) how to optimize a longevity hedge using standardized longevity derivatives. The objective of this thesis is to develop sensible solutions to these two questions. In the first part of this thesis, we focus on incorporating stochastic volatility in mortality modeling, introducing the notion of longevity Greeks, and analysing the properties of longevity Greeks and their applications in index-based longevity hedging. In more detail, we derive three important longevity Greeks--delta, gamma and vega--on the basis of an extended version of the Lee-Carter model that incorporates stochastic volatility. We also study the properties of each longevity Greek, and estimate the levels of effectiveness that different longevity Greek hedges can possibly achieve. The results reveal several interesting facts. For example, we found and explained that, other things being equal, the magnitude of the longevity gamma of a q-forward increases with its reference age. As with what have been developed for equity options, these properties allow us to know more about standardized longevity derivatives as a risk mitigation tool. We also found that, in a delta-vega hedge formed by q-forwards, the choice of reference ages does not materially affect hedge effectiveness, but the choice of times-to-maturity does. These facts may aid insurers to better formulate their hedge portfolios, and issuers of mortality-linked securities to determine what security structures are more likely to attract liquidity. We then move onto delta hedging the trend and cohort components of longevity risk under the M7-M5 model. In a recent project commissioned by the Institute and Faculty of Actuaries and the Life and Longevity Markets Association, a two-population mortality model called the M7-M5 model is developed and recommended as an industry standard for the assessment of population basis risk. We develop a longevity delta hedging strategy for use with the M7-M5 model, taking into account of not only period effect uncertainty but also cohort effect uncertainty and population basis risk. To enhance practicality, the hedging strategy is formulated in both static and dynamic settings, and its effectiveness can be evaluated in terms of either variance or 1-year ahead Value-at-Risk (the latter is highly relevant to solvency capital requirements). Three real data illustrations are constructed to demonstrate (1) the impact of population basis risk and cohort effect uncertainty on hedge effectiveness, (3) the benefit of dynamically adjusting a delta longevity hedge, and (3) the relationship between risk premium and hedge effectiveness. The last part of this thesis sets out to obtain a deeper understanding of mortality volatility and its implications on index-based longevity hedging. The volatility of mortality is crucially important to many aspects of index-based longevity hedging, including instrument pricing, hedge calibration, and hedge performance evaluation. We first study the potential asymmetry in mortality volatility by considering a wide range of GARCH-type models that permit the volatility of mortality improvement to respond differently to positive and negative mortality shocks. We then investigate how the asymmetry of mortality volatility may impact index-based longevity hedging solutions by developing an extended longevity Greeks framework, which encompasses longevity Greeks for a wider range of GARCH-type models, an improved version of longevity vega, and a new longevity Greek known as `dynamic delta'. Our theoretical work is complemented by two real-data illustrations, the results of which suggest that the effectiveness of an index-based longevity hedge could be significantly impaired if the asymmetry in mortality volatility is not taken into account when the hedge is calibrated.