Multi-population mortality forecasting using tensor decomposition

ABSTRACT

In this paper, we formulate the multi-population mortality forecasting problem based on 3-way (age, year, and country/gender) decompositions. By applying the canonical polyadic decomposition (CPD) and the different forms of the Tucker decomposition to multi-population mortality data (10 European countries and 2 genders), we find that the out-of-sample forecasting performance is significantly improved both for individual populations and the aggregate population compared with using the single-population mortality model based on rank-1 singular value decomposition (SVD), or the Lee–Carter model. The results also shed lights on the similarity and difference of mortality among different countries. Additionally, we compare the variance-explained method and the out-of-sample validation method for rank (hyper-parameter) selection. Results show that the out-of-sample validation method is preferred for forecasting purposes.     

Stochastic mortality under measure changes

We provide a self-contained analysis of a class of continuous-time stochastic mortality models that have gained popularity in the last few years. We describe some of their advantages and limitations, examining whether their features survive equivalent changes of measures. This is important when using the same model for both market-consistent valuation and risk management of life insurance liabilities. We provide a numerical example based on the calibration to the French annuity market of a risk-neutral version of the model proposed by Lee & Carter (1992).     

The random-walk hypothesis revisited: new evidence on multiple structural breaks in emerging markets

We examine whether stock prices in 18 emerging markets follow random-walk or mean-reversion processes in the presence of sudden and gradual multiple structural breaks. Our tests endogenously determined the structural shifts and are more powerful than either the traditional random-walk (unit root) tests or the single structural break tests. In all emerging markets, we find strong evidence for multiple structural breaks. When we use single break tests, the random-walk hypothesis is rejected. However, when we use tests of double level shifts in the mean and make due allowance for multiple structural breaks, the results are consistent with the random-walk hypothesis in the vast majority of the sampled markets. The evidence proves robust to using price indexes whether denominated in U.S. dollars, in local currencies or in real terms, and also to using fractional integration tests. Our results contradict some previous studies for emerging markets which restrict structural breaks to only one-time shift.     

Lifetime asset allocation with idiosyncratic and systematic mortality risks

This paper considers a lifetime asset allocation problem with both idiosyncratic and systematic mortality risks. The novelty of the paper is to integrate stochastic mortality, stochastic interest rate and stochastic income into a unified framework. An investor, who is a wage earner receiving a stochastic income, can invest in a financial market, consume part of his wealth and purchase life insurance or annuity so as to maximize the expected utility from consumption, terminal wealth and bequest. The problem is solved via the dynamic programming principle and the Hamilton–Jacobi–Bellman equation. Analytical solutions to the problem are derived, and numerical examples are provided to illustrate our results. It is shown that idiosyncratic mortality risk has significant impacts on the investor’s investment, consumption, life insurance/annuity purchase and bequest decisions regardless of the length of the decision-making horizon. The systematic mortality risk is largely alleviated by trading the longevity bond. However, its impacts on consumption, purchase of life insurance/annuity and bequest as well as the value function are still pronounced, when the decision-making horizon is sufficiently long.     

Valuing variable annuity guarantees on multiple assets

Guarantees embedded variable annuity contracts exhibit option-like payoff features and the pricing of such instruments naturally leads to risk neutral valuation techniques. This paper considers the pricing of two types of guarantees; namely, the Guaranteed Minimum Maturity Benefit and the Guaranteed Minimum Death Benefit riders written on several underlying assets whose dynamics are given by affine stochastic processes. Within the standard affine framework for the underlying mortality risk, stochastic volatility and correlation risk, we develop the key ingredients to perform the pricing of such guarantees. The model implies that the corresponding characteristic function for the state variables admits a closed form expression. We illustrate the methodology for two possible payoffs for the guarantees leading to prices that can be obtained through numerical integration. Using typical values for the parameters, an implementation of the model is provided and underlines the significant impact of the assets’ correlation structure on the guarantee prices.     

Quantifying mortality risk in small defined-benefit pension schemes

A risk of small defined-benefit pension schemes is that there are too few members to eliminate idiosyncratic mortality risk, that is, there are too few members to effectively pool mortality risk. This means that when there are few members in the scheme, there is an increased risk of the liability value deviating significantly from the expected liability value, as compared to a large scheme. We quantify this risk through examining the coefficient of variation of a scheme's liability value relative to its expected value. We examine how the coefficient of variation varies with the number of members and find that, even with a few hundred members in the scheme, idiosyncratic mortality risk may still be significant. Next we quantify the amount of the mortality risk concentrated in the executive section of the scheme, where the executives receive a benefit that is higher than the non-executive benefit. We use the Euler capital allocation principle to allocate the total standard deviation of the liability value between the executive and non-executive sections. The results suggest that the mortality risk of the scheme should be monitored and managed within the sections of a scheme and not only on a scheme-wide basis.     

The maximum entropy mortality model: forecasting mortality using statistical moments

ABSTRACT

The age-at-death distribution is a representation of the mortality experience in a population. Although it proves to be highly informative, it is often neglected when it comes to the practice of past or future mortality assessment. We propose an innovative method to mortality modeling and forecasting by making use of the location and shape measures of a density function, i.e. statistical moments. Time series methods for extrapolating a limited number of moments are used and then the reconstruction of the future age-at-death distribution is performed. The predictive power of the method seems to be net superior when compared to the results obtained using classical approaches to extrapolating age-specific-death rates, and the accuracy of the point forecast (MASE) is improved on average by 33% respective to the state-of-the-art, the Lee–Carter model. The method is tested using data from the Human Mortality Database and implemented in a publicly available R package.     

The Lee-Carter quantile mortality model

The Lee-Carter (LC) stochastic mortality model has been widely used for making future projections of mortality rates. In the framework of the LC model, the response function is non-linear in parameters. Here, we adapt this LC framework to compute conditional quantiles. The LC quantile model can be defined as quantile non-linear regression conditioned to age and the calendar year. Two strategies for estimating coefficients based on interior-point methods are described. We show that the LC quantile model provides additional information to that furnished by the traditional LC conditional mean. An application to Spanish mortality data is reported.     

Pricing pension buy-outs under stochastic interest and mortality rates

Pension buy-out is a special financial asset issued to offload the pension liabilities holistically in exchange for an upfront premium. In this paper, we concentrate on the pricing of pension buy-outs under dependence between interest and mortality rates risks with an explicit correlation structure in a continuous time framework. Change of measure technique is invoked to simplify the valuation. We also present how to obtain the buy-out price for a hypothetical benefit pension scheme using stochastic models to govern the dynamics of interest and mortality rates. Besides employing a non-mean reverting specification of the Ornstein–Uhlenbeck process and a continuous version of Lee–Carter setting for modeling mortality rates, we prefer Vasicek and Cox–Ingersoll–Ross models for short rates. We provide numerical results under various scenarios along with the confidence intervals using Monte Carlo simulations.     

The impact of tax rate changes on intercorporate investment

We examine how tax rates impact investment by corporations in the stock market. We regress changes in intercorporate investment on changes in the various individual and corporate top statutory marginal tax rates (MTRs). We find a significant negative association between changes in individual capital gains MTRs and changes in intercorporate investment, while no such association is evident for changes in either individual ordinary or dividend MTRs. These results support the notion that corporations respond to the after-tax rate of return and/or market efficiency consequences brought about by a change in individual capital gains MTRs. We find a significant positive relation between changes in intercorporate investment and changes in corporate MTRs on ordinary income. These results are consistent with corporations scaling back expansion plans and instead investing free cash flows in equity securities as MTRs increase.     

Meeting user information needs: The impact of major changes in FASB and GASB standards on financial reporting by colleges and universities

This longitudinal study reports the impact of changes in generally accepted accounting principles on financial statement disclosures for 100 public and private institutions of higher education. Disclosures from the period when all colleges and universities followed the same accounting standards are compared with disclosures in periods after major changes in accounting and reporting standards were made by the Financial Accounting Standards Board (FASB) for private institutions and by the Governmental Accounting Standards Board (GASB) for public institutions. We find that an importance-weighted disclosure index shows that user needs are better met using the new reporting standards for public but not private institutions. An expanded unweighted index, however, shows improvement for both public and private colleges and universities. Using this disclosure index, the improvement for universities reporting under GASB standards exceeded the improvement for those reporting under FASB standards.     

The impact of blockchain related name changes on corporate performance

This paper examines the impact of blockchain and crypto-related name changes on corporate and financial performance of the corporations. We document several pieces of evidence suggesting that companies who partake in such “crypto-exuberant” naming practices become more volatile and offer substantial and persistent stock market premiums as a reward for their corporate identity change. However, the retroactive name changes harm firm's short-term profitability and have a dampening effect on financial leverage of the company. This paper advances the Dotcom effect literature by providing novel results on the changing traditional pathways of price discovery and information flows after the announcement of corporate name changes to blockchain-related names. The identified contagion channels display that crypto-exuberant companies become more susceptible to cryptocurrency markets, which should interest regulators and investors.     

Reference mortality K2004 of personal life insurance policies in Finland

This article presents the reference mortality model K2004 approved by the Actuarial Society of Finland and the technique that was implemented in developing it. Initially, I will present the historical development of individual mortality rates in Finland. Then, the requirements posed for a modern mortality modelling will be presented. Reference mortality model K2004 is based on total population mortality rates, which were adjusted to correspond with that portion of the population that has a life insurance policy. First, the model presents a margin of the observed life insurance mortality rate in the total population with a Lee-Carter method together with a forecast, where the downward trend in mortality rates is expected to continue at the rate illustrated since the 1960s. Then, the mortality rate has been adjusted into life insurance mortality per age so that it corresponds to the differences observed between total population and the portion of population that has a life insurance during 1991–2001. Finally, a cohort and gender-specific functional margin will be presented to obtained data.     

The double entry structural constraint on the econometric estimation of accounting variables

ABSTRACT

This paper develops a structural system for estimating accounting variables, within which the deterministic relationships inherent in financial statement articulation are clearly defined in the econometric model. The key proposition of the paper lies in the treatment of the financial statements as a matrix of codetermined information constrained by double entry, where the expected value of each of the individual items that comprise the financial statements will be mirrored elsewhere in the system with a different sign. Given that the change in net operating assets shares the same variation as the change in net financial claims, it is shown, by formally identifying the articulation, that empirical application will yield increased precision and improved efficiency by comparison to the more traditional methods that fail to specify the structural double entry property.     

供给侧结构性改革进程中技术创新效率研究

本文以生产要素内部配置结构调整对边际产出弹性影响为基础,建立包含生产要素内部配置结构的科布-道格拉斯生产函数,对中国工业企业技术创新效率进行实证分析。主要结论有:区域外商投资工业企业比例的增加能提升资本和劳动力边际产出弹性;区域内资工业企业比例的增加能提升劳动力边际产出弹性;政府科技资助与工业企业技术创新效率之间并非简单的线性关系。提高工业企业技术创新效率需要政府科技资助形成一定规模;劳动者素质提高对工业企业技术创新效率产生积极影响。政策建议是:继续加大对外开放力度,优化区域生产要素配置结构;扩大政府科技资助规模,优化政府科技资助结构;有效引导高素质人才流动。     

The impact of sovereign rating changes on the activity of European banks

We verify the effects of sovereign rating revisions on the activity of European banks, in terms of their regulatory capital ratio, profitability, liquidity, and lending supply. First, we find that a sovereign downgrade has a significant impact, primarily on capital ratios and lending supply. In contrast, upgrades do not have a significant impact, indicating an asymmetric effect of sovereign rating changes. Second, we find that three transmission channels (assets channel, funding channel, and rating channel) explain a relevant part of the impact of a sovereign downgrade. Finally, we find strong evidence that the rating-based regulation affects all measures of the activity of domestic banks, causing negative externalities for financial institutions. Our results hold also controlling for sovereign risk, estimating a GMM system, and employing an instrumental variable approach.     

The impact of rating changes in Australian financial markets

Credit ratings have only a limited role in Australian financial regulation, so the effects of rating changes on financial prices can be observed largely free from regulatory effects. We find that bond and stock prices move in the ‘expected’ direction following both positive and negative rating announcements, although the movements are small. Announcement effects are larger for small firms, for downgrades from investment to speculative grade, and where agencies have not previously indicated the rating is under review. Overall, the results suggest that agencies are not generally viewed as consistently having access to important information that is not already in the public domain.     

The valuation consequences of voluntary accounting changes

Firm management typically claims that voluntary accounting method changes (VACs) are made to enhance the informativeness of earnings by better matching accounting practices with economic reality. In contrast, skeptics argue that managers adopt new accounting procedures to opportunistically manage earnings and influence their firm’s stock price. In this paper, we investigate these alternative motives for VACs. Specifically, we investigate whether VACs cause equity prices to deviate from their fundamental values in the short-term by studying the long-run stock-price performance for a sample of firms that voluntarily change accounting methods. In addition, we investigate changes in earnings informativeness by examining the behavior of earning response coefficients and the relationship between earnings and future cash flows in years surrounding the VAC event. In contrast to prior research, we find little evidence that a strategy based solely on the earnings effect of a VAC can generate abnormal returns. While we find weak evidence of post-VAC abnormal returns for extreme VACs, this result appears to be driven by the accruals anomaly documented in Sloan [Sloan, R. G. (1996). The Accounting Review, 71, 289–315]. Our evidence further suggests that earnings informativeness is not significantly altered by voluntary changes in accounting methods. Taken together, our evidence suggests the market recognizes the financial statement effects of alternative acceptable accounting methods and efficiently processes the valuation implications of VACs.