The CBD Mortality Indexes: Modeling and Applications

Most extrapolative stochastic mortality models are constructed in a similar manner. Specifically, when they are fitted to historical data, one or more series of time-varying parameters are identified. By extrapolating these parameters to the future, we can obtain a forecast of death probabilities and consequently cash flows arising from life contingent liabilities. In this article, we first argue that, among various time-varying model parameters, those encompassed in the Cairns-Blake-Dowd (CBD) model (also known as Model M5) are most suitably used as indexes to indicate levels of longevity risk at different time points. We then investigate how these indexes can be jointly modeled with a more general class of multivariate time-series models, instead of a simple random walk that takes no account of cross-correlations. Finally, we study the joint prediction region for the mortality indexes. Such a region, as we demonstrate, can serve as a graphical longevity risk metric, allowing practitioners to compare the longevity risk exposures of different portfolios readily.     

Modeling Period Effects in Multi-Population Mortality Models: Applications to Solvency II

Recently Cairns et al. introduced a general framework for modeling the dynamics of mortality rates of two related populations simultaneously. Their method ensures that the resulting forecasts do not diverge over the long run by modeling the difference in the stochastic factors between the two populations with a mean-reverting autoregressive process. In this article, we investigate how the modeling of the stochastic factors may be improved by using a vector error correction model. This extension is highly intuitive, allowing us to visualize the cross-correlations and the long-term equilibrium relation between the two populations. Another key benefit is that this extension does not require the user to assume which one of the two populations is dominant. This benefit is important because, as we demonstrate, it is not always easy to identify the dominant population, even if one population is much larger than the other. We illustrate our proposed extension with data from a pair of populations and apply it to the calculation of Solvency II risk capital.     

Securitization of Mortality Risks in Life Annuities

The purpose of this article is to study mortality‐based securities, such as mortality bonds and swaps, and to price the proposed mortality securities. We focus on individual annuity data, although some of the modeling techniques could be applied to other lines of annuity or life insurance.     

Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization

Normalized exponential tilting is an extension of classical theories, including the Capital Asset Pricing Model (CAPM) and the Black–Merton–Scholes model, to price risks with general‐shaped distributions. The need for changing multivariate probability measures arises in pricing contingent claims on multiple underlying assets or liabilities. In this article, we apply it to valuation of mortality‐based securities written on mortality indices of several countries. We show how to use multivariate exponential tilting to price the first pure mortality security, the Swiss Re bond. The same technique can be applied in other mortality securitization pricing.     

On the Modeling and Forecasting of Socioeconomic Mortality Differentials: An Application to Deprivation and Mortality in England

In any country, mortality rates and indices such as life expectancy usually differ across subpopulations, for example, defined by gender, geographic area, or socioeconomic variables (e.g., occupation, level of education, or income). These differentials, and in particular those related to socioeconomic circumstances, pose important challenges for the design of public policies for tackling social inequalities, as well as for the design of pension systems and the management of longevity risk in pension funds and annuity portfolios. We discuss the suitability for the modeling and forecasting of socioeconomic differences in mortality of several multiple population extensions of the Lee-Carter model, including a newly introduced relative model based on the modeling of the mortality in socioeconomic subpopulations alongside the mortality of a reference population. Using England mortality data for socioeconomic subpopulations defined using a deprivation index, we show that this new relative model exhibits the best results in terms of goodness of fit and ex post forecasting performance. We then use this model to derive projections of deprivation specific mortality rates and life expectancies at pensioner ages and analyze the impact of socioeconomic differences in mortality on the valuation of annuities.     

Weighted Pricing Functionals With Applications to Insurance

Abstract

We explore the role of weighted distributions in pricing insurance risks. In particular, we relate the distributions to actuarial and economic premium calculation principles and in this way provide a unifying methodology for constructing new principles and analyzing known ones.     

Stochastic Mortality Modeling: Key Drivers and Dependent Residuals

This article proposes an alternative framework for modeling the stochastic dynamics of mortality rates. A simple age basis combined with two stochastic period factors is used to explain the key mortality drivers, while the remaining structure is modeled via a multivariate autoregressive residuals model. The latter captures the stationary mortality dynamics and introduces dependencies between adjacent age-period cells of the mortality matrix that, among other things, can be structured to capture cohort effects in a transparent manner and incorporate across ages correlations in a natural way. Our approach is compared with models with and without a univariate cohort process. The age- and period-related latent states of the mortality basis are more robust when the residuals surface is modeled via the multivariate time-series model, implying that the process indeed acts independently of the assumed mortality basis. Under the Bayesian paradigm, the posterior distribution of the models is considered to explore coherently the extent of parameter uncertainty. Samples from the posterior predictive distribution are used to project mortality, and an in-depth sensitivity analysis is conducted. The methodology is easily extendable in multiple ways that give a different form and degree of significance to the different components of mortality dynamics.     

Redistribution and Insurance: Mandatory Annuitization With Mortality Heterogeneity

This article examines the distributional implications of mandatory longevity insurance when mortality heterogeneity exists in the population. Previous research has demonstrated the significant financial redistribution that occurs under alternative annuity programs in the presence of differential mortality across groups. This article embeds that analysis into a life‐cycle framework that allows for an examination of distributional effects on a utility‐adjusted basis. It finds that the degree of redistribution that occurs from the introduction of a mandatory annuity program is substantially lower on a utility‐adjusted basis than when evaluated on a purely financial basis. In a simple life‐cycle model with no bequests, complete annuitization is welfare enhancing even for those with higher‐than‐average expected mortality rates, so long as administrative costs are sufficiently low. These findings have implications for policy toward annuitization, particularly as part of a reformed Social Security system.     

Securitization of Longevity Risk: Pricing Survivor Bonds With Wang Transform in the Lee-Carter Framework

Longevity risk is a major issue for insurers and pension funds, especially in the selling of annuity products. In that respect, securitization of this risk could offer great opportunities for hedging. This article proposes to design survivor bonds which could be issued directly by insurers. In order to guaranty some transparency in the product, the survivor bond is based on a public mortality index. The classical Lee‐Carter model for mortality forecasting is used to price a risky coupon survivor bond based on this index.     

住房抵押贷款证券化运作的难点及对策

目前在我国，尚不具备完善的住房抵押贷款证券化运作环境，这就使住房抵押款证券化运作面临许多难点。诸如，住房抵押贷款标准化的问题、证券化特设机构的设置问题、政府能否提供信用担保或保险的问题等。本拟在对这些难点进行研究的基础上，提出相应的对策建议，以推动我国住房抵押贷款证券化的发展。     

Longevity/Mortality Risk Modeling and Securities Pricing

Securitizing longevity/mortality risk can transfer longevity/mortality risk to capital markets. Modeling and forecasting mortality rate is key to pricing mortality‐linked securities. Catastrophic mortality and longevity jumps occur in historical data and have an important impact on security pricing. This article introduces a stochastic diffusion model with a double‐exponential jump diffusion process that captures both asymmetric rate jumps up and down and also cohort effect in mortality trends. The model exhibits calibration advantages and mathematical tractability while better fitting the data. The model provides a closed‐form pricing solution for J.P. Morgan’s q‐forward contract usable as a building block for hedging.     

资产证券化:一个文献综述

资产证券化对于宏观经济金融改革发展有着重要的意义,在国内取得了较大的发展,但也存在较多的问题,需要进一步研究解决。围绕资产证券化的产生和发展、国内外实践、国内发展存在的问题与应对这三个主题,国内外形成了较多的研究成果,也需要进一步深化和细化。对于资产证券化的后续研究,建议从强化理论研究、丰富微观层面的研究、增加创新业务的研究等方面开展。     

Excess Mortality In Asia Associated With Cigarette Smoking

Abstract

Cigarette smoking has reached epidemic proportions in many Asian countries, and epidemiologists predict massive increases in the number of smoking-related deaths in future decades. This information is of great interest to insurers who would like to sell coverage in these markets with smoker/nonsmoker-distinct pricing. This review examines excess mortality due to cigarette smoking in Asia as determined by a second-quarter 1998 Internet search of the world’s English-language medical literature for references published during the preceding five years. Studies to date which observed fairly low relative risks of mortality in smokers compared with nonsmokers in Asia despite a high prevalence of smoking can be explained by the fact that health outcome data represent early experience. Given similar associations between smoking and mortality in Asian and Western studies, it is likely that mortality patterns of smokers in Asia eventually will mirror those seen in the U.S. and the United Kingdom.     

证券化：化解不良资产的有效途径

证券化已成为化解不良资产的重要途径。在我国，不良资产证券化已具备了基本条件。在具体操作中，信用升级、品种设计、二级市场建设是存在的重要问题。     

难解的中关村"哥德巴赫猜想"

北京的中关村是高科技中小企业聚集地,也是创业人才云集的地方,但是长期以来,融资难成为一道难解的“哥德巴赫猜想”     

住房抵押贷款证券化：问题与政策建议

住房抵押贷款证券化作为一项重要的金融创新，其实质是为发放住房抵押贷款的金融机构提供了一种新的融资方式。当前，我国推行住房抵押贷款证券化任重而道远，还不具备大规模开展住房抵押贷款证券化的条件，虽然住房抵押贷款证券化在我国具有其特殊的现实意义，但由于外 部条件还不完全具备，必须为住房抵押贷款证券化创造各种市场条件和制度条件。