The Impact of Systematic Trend and Uncertainty on Mortality and Disability in a Multistate Latent Factor Model for Transition Rates

Multiple state functional disability models do not generally include systematic trend and uncertainty. We develop and estimate a multistate latent factor intensity model with transition and recovery rates depending on a stochastic frailty factor to capture trend and uncertainty. We estimate the model parameters using U.S. Health and Retirement Study data between 1998 and 2012 with Monte Carlo maximum likelihood estimation method. The model shows significant reductions in disability and mortality rates during this period and allows us to quantify uncertainty in transition rates arising from the stochastic frailty factor. Recovery rates are very sensitive to the stochastic frailty. There is an increase in expected future lifetimes as well as an increase in future healthy life expectancy. The proportion of lifetime spent in disability on average remains stable with no strong support in the data for either morbidity compression or expansion. The model has widespread application in costing of government-funded aged care and pricing and risk management of long-term-care insurance products.     

Default prediction with dynamic sectoral and macroeconomic frailties

This paper extends the macroeconomic frailty model to include sectoral frailty factors that capture default correlations among firms in a similar business. We estimate sectoral and macroeconomic frailty factors and their effects on default intensity using the data for Japanese firms from 1992 to 2010. We find strong evidence for the presence of sectoral frailty factors even after accounting for the effects of observable covariates and macroeconomic frailty on default intensity. The model with sectoral frailties performs better than that without. Results show that accounting for the sources of unobserved sectoral default risk covariations improves the accuracy of default probability estimation.     

The Impact of the Secondary Market on Life Insurers' Surrender Profits

Life insurers often claim that the life settlement industry reduces their surrender profits and leads to an adverse shift in their portfolio of insured risks; that is, high risks remain in the portfolio instead of surrendering. In this article, we aim to quantify the effect of altered surrender behavior––subject to the health status of an insured––in a portfolio of life insurance contracts on the surrender profits of primary insurers. Our model includes mortality heterogeneity by applying a stochastic frailty factor to a mortality table. We additionally analyze the impact of the premium payment method by comparing results for annual and single premium payments.     

Common Failings: How Corporate Defaults Are Correlated

We test the doubly stochastic assumption under which firms' default times are correlated only as implied by the correlation of factors determining their default intensities. Using data on U.S. corporations from 1979 to 2004, this assumption is violated in the presence of contagion or “frailty” (unobservable explanatory variables that are correlated across firms). Our tests do not depend on the time‐series properties of default intensities. The data do not support the joint hypothesis of well‐specified default intensities and the doubly stochastic assumption. We find some evidence of default clustering exceeding that implied by the doubly stochastic model with the given intensities.     

Big locational unemployment differences despite high labor mobility

Considerable labor mobility exists across US states, enough that, if migration arbitrages local unemployment, one might expect very low unemployment differences across states. However, cross-state data reveal large unemployment differences. An equilibrium multi-location model with stochastic worker-location match productivity and within-location trading frictions can account for these facts. In the model, some workers move to, or stay in, a location with high unemployment because they are more productive there than elsewhere. According to the model, labor mobility and aggregate unemployment are negatively related. This prediction is in stark contrast to standard sectoral reallocation theory, but consistent with the US data.     

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.     

Authors’ Reply: Economic Valuation Models for Insurers - Discussion by Jacques F. Carriere

Abstract

This article employs a longitudinal form of the Grade of Membership (GoM) model to specify and estimate a multivariate model of the trajectories of morbidity, disability, and mortality among longitudinally followed elderly respondents to the National Long-Term Care Survey (NLTCS) of 1984, 1989, 1994, and 1999. A distinct trajectory was constructed for each individual respondent to the survey. The trajectories described the progressive declines over time in physical and cognitive functioning among a nationally representative sample of the U.S. elderly population.

The model was structured to represent simultaneously the essential features of the fixed frailty model of Vaupel, Manton, and Stallard and Strehler and Mildvan’s model of linearly declining vitality. Unlike those models, however, the longitudinal GoM model was designed for easy and direct application to existing longitudinal data sets.

The measurement space in the NLTCS application included from one to four sets of repeated measures for each survey respondent on 95 independent variables characterizing the nature and intensity of limitations in activities of daily living (ADLs), instrumental activities of daily living (IADLs), physical functioning, and cognitive functioning, as well as indicators of behavioral characteristics, medical conditions, subjective health, age, race, sex, institutional status, and survival status.

The application showed that the model can be fitted to existing data and that the results were interpretable as generalizations of fixed frailty with linearly declining vitality.     

How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes

We propose a discrete-time stochastic volatility model in whichregime switching serves three purposes. First, changes in regimescapture low-frequency variations. Second, they specify intermediate-frequencydynamics usually assigned to smooth autoregressive transitions.Finally, high-frequency switches generate substantial outliers.Thus a single mechanism captures three features that are typicallyviewed as distinct in the literature. Maximum-likelihood estimationis developed and performs well in finite samples. Using exchangerates, we estimate a version of the process with four parametersand more than a thousand states. The multifractal outperformsGARCH, MS-GARCH, and FIGARCH in- and out-of-sample. Considerablegains in forecasting accuracy are obtained at horizons of 10to 50 days.     

Common stochastic volatility trends in international stock returns

The aim of this work is to capture common stochastic trends in weekly volatilities of the Dow Jones, Nikkei, Hang Seng and Strait Times index using a multivariate stochastic volatility (SV) model. The results suggest a very high correlation among the volatility innovations, so that it is examined whether the four series share any common stochastic trends. A Principal Component Analysis and a Factor Analysis in the state space setting reveal that two common stochastic trends can be found to underlie the volatility series. The resulting linear combinations of the volatility series no more exhibit any stochastic trend but are stationary in the state space framework. Thus, it can be concluded that volatilities of the four stock indexes are in essence co-persistent.     

Asset price and wealth dynamics under heterogeneous expectations

In order to characterize asset price and wealth dynamics arising from the interaction of heterogeneous agents with CRRA utility, a discrete-time stationary model in terms of return and wealth proportions (among different types of agents) is established. When fundamentalists and chartists are the main heterogeneous agents in the model, it is found that in the presence of heterogeneous agents the stationary model can have multiple steady states. The steady state is unstable when the chartists extrapolate strongly and (locally) stable when they extrapolate weakly. The convergence to the steady state follows an optimal selection principle - the return and wealth proportions tend to the steady state which has relatively higher return. More importantly, heterogeneity can generate instability which, under the stochastic processes of the dividend yield and extrapolation rates, results in switching of the return among different states, such as steady-state, periodic and aperiodic cycles from time to time. The model that is finally developed displays the essential characteristics of the standard asset price dynamics model assumed in continuous-time finance, in that the asset price is fluctuating around a geometrically growing trend. The model also displays the volatility clustering that is an essential feature of empirically observed asset returns.     

Loss Given Default,Loan Seasoning and Financial Fragility: Evidence from Commercial Real Estate Loans at Failed Banks

Commercial real estate (CRE) loan losses are a recurring contributor to bank failures and financial instability, yet they are not well understood. We examine a unique and proprietary data set of CRE loan defaults at banks that failed and were resolved by the FDIC after the 2008 financial crisis. We build upon an existing literature relating stochastic collateral values to loss given default (LGD). Consistent with model predictions, we show that CRE loans defaulting sooner after origination are more sensitive to declining economic conditions and exhibit LGDs that are more severe. These results are robust to a number of factors, including the declining balance of the loan over time. Our findings point to an inherent fragility associated with high CRE loan growth, even without necessarily a deterioration in lending standards, due to the changing composition of CRE loan seasoning in the industry. This reflects an unexplored risk in the literature concerning rapid and cyclical expansions in CRE credit.

     

Real Options Models of the Firm,Capacity Overhang,and the Cross Section of Stock Returns

We use a stochastic frontier model to obtain a stock‐level estimate of the difference between a firm's installed production capacity and its optimal capacity. We show that this “capacity overhang” estimate relates significantly negatively to the cross section of stock returns, even when controlling for popular pricing factors. The negative relation persists among small and large stocks, stocks with more or less reversible investments, and in good and bad economic states. Capacity overhang helps explain momentum and profitability anomalies, but not value and investment anomalies. Our evidence supports real options models of the firm featuring valuable divestment options.     

Multiple time scales and the exponential Ornstein–Uhlenbeck stochastic volatility model

We study the exponential Ornstein–Uhlenbeck stochastic volatility model and observe that the model shows a multiscale behaviour in the volatility autocorrelation. It also exhibits a leverage correlation and a probability profile for the stationary volatility which are consistent with market observations. All these features make the model quite appealing since it appears to be more complete than other stochastic volatility models also based on a two-dimensional diffusion. We finally present an approximate solution for the return probability density designed to capture the kurtosis and skewness effects.     

The compensating behavior of smokers: taxes, tar, and nicotine

Using data from the 1979 and 1987 National Health Interview Survey (NHIS), we test whether smokers alter their smoking habits in the face of higher taxes. Smokers in high-tax states are more likely to smoke cigarettes higher in tar and nicotine. Although taxes reduce the number of cigarettes consumed per day among remaining smokers, total daily tar and nicotine intake is unaffected. Young smokers, aged 18-24, are much more responsive to changes in taxes than are older smokers, and their total daily tar and nicotine intake actually increases after a tax hike. We illustrate that tax-induced compensating behavior may eliminate some health benefits generated by reduced smoking participation. A more appropriate tax might be based on the tar and nicotine content of cigarettes.     

Backtesting Stochastic Mortality Models

Abstract

This study sets out a backtesting framework applicable to the multiperiod-ahead forecasts from stochastic mortality models and uses it to evaluate the forecasting performance of six different stochastic mortality models applied to English & Welsh male mortality data. The models considered are the following: Lee-Carter’s 1992 one-factor model; a version of Renshaw-Haberman’s 2006 extension of the Lee-Carter model to allow for a cohort effect; the age-period-cohort model, which is a simplified version of Renshaw-Haberman; Cairns, Blake, and Dowd’s 2006 two-factor model; and two generalized versions of the last named with an added cohort effect. For the data set used herein, the results from applying this methodology suggest that the models perform adequately by most backtests and that prediction intervals that incorporate parameter uncertainty are wider than those that do not. We also find little difference between the performances of five of the models, but the remaining model shows considerable forecast instability.     

二叉树利率期限结构模型应用初探——以寿险公司资产负债管理为例

近年来我国寿险公司经营风险加剧，寿险公司资产负债管理正逐渐成为实务界和学术界关注的焦点。本文在深入研究随机规划、利率期限结构、投资组合等相关理论的基础上，对比分析均衡模型和无套利模型的差异，指出无套利模型更适于构楚随机规划问题中利率情景树的构建。在无套利模型中，二叉树Black-Derman-Toy模型简单易操作，可以避免三叉树模型计算量大，效率不高等缺点。因此本文采用二叉树方法以Black-Derman-Toy模型构造利率情景树，与随机规划模型相结合的资产负偾管理方法，协调、管理寿险公司资产负偾现金流，减少了随机规划模型处理随机利率分布的技术性难度。     

Older age underwriting: frisky vs frail

The speed of the aging process is variable. Some individuals remain exceptionally fit beyond age 90, while others become frail and fragile early. Survival is better predicted by biological age (state of health, status of reserves) rather than chronological age (age in years since date of birth). The frail group shows a higher mortality compared to the robust group. When assessing the elderly in underwriting, it is important to note the usual chronic diseases such as cardiovascular disease, COPD, cancer risk, and so on. But because of its strong impact on prognosis, it is also important to assess frailty. Key features of frailty are social isolation, dependency in managing life activities and self-care, cognitive decline, shrinking of bone and muscle mass, and slow weight loss.     

Consumer Response to a National Marketplace for Individual Health Insurance

The objective of this analysis is to simulate the difference between national and state‐specific individual insurance markets on take‐up of individual health insurance. This simulation analysis was completed in three steps. First, we reviewed the literature to characterize the state‐specific individual insurance markets with respect to state regulations and to identify the effect of those regulations on health insurance premiums. Second, we used empirical data to develop premium estimates for the simulation that reflect case‐mix as well as state‐specific differences in health care markets. Third, we used a revised version of the 2005 Medical Expenditure Panel Survey (MEPS) to complete a set of simulations to identify the impact of three different scenarios for national market development. (National market estimates are based on the simulation model with competition among all 50 states and moderate impact assumptions.) We find evidence of a significant opportunity to reduce the number of uninsured under a proposal to allow the purchase of health insurance across state lines. The best scenario to reduce the uninsured, numerically, is competition among all 50 states with one clear winner. The most pragmatic scenario, with a good impact, is one winner in each regional market.     

Multi-period stochastic optimization models for dynamic asset allocation

Institutional investors manage their strategic asset mix over time to achieve favorable returns subject to various uncertainties, policy and legal constraints, and other requirements. One may use a multi-period portfolio optimization model in order to determine an optimal asset mix. The concept of scenarios is typically employed for modeling random parameters in a multi-period stochastic programming model, and scenarios are constructed via a tree structure. Recently, an alternative stochastic programming model with simulated paths was proposed by Hibiki [Hibiki, N., 2001b. A hybrid simulation/tree multi-period stochastic programming model for optimal asset allocation. In: Takahashi, H. (Ed.), The Japanese Association of Financial Econometrics and Engineering. JAFEE Journal 89–119 (in Japanese); Hibiki, N., 2003. A hybrid simulation/tree stochastic optimization model for dynamic asset allocation. In: Scherer, B. (Ed.), Asset and Liability Management Tools: A Handbook for Best Practice, Risk Books, pp. 269–294], and it is called a hybrid model. The advantage of the simulated path structure compared to the tree structure is to give a better accuracy to describe uncertainties of asset returns. In this paper, we compare the two types of multi-period stochastic optimization models, and clarify that the hybrid model can evaluate and control risk better than the scenario tree model using some numerical tests. According to the numerical results, an efficient frontier of the hybrid model with the fixed-proportion strategy dominates that of the scenario tree model when we evaluate them on simulated paths. Moreover, optimal solutions of the hybrid model are more appropriate than those of the scenario tree model.     

Cost efficiency of international insurance firms

This article examines the cost efficiency of insurance firms located in 11 countries over a five-year period, 1988–1992. Two X-inefficiency measures are derived, one from the stochastic cost frontier model and the other from the distribution-free model. The results show that X-inefficiencies not only vary by country but by size and specialization. Firms in Finland and France have the lowest X-inefficiency, while firms in the United Kingdom have the highest. On average, small firms are more cost efficient than large firms worldwide. Firms grouped into those offering single or specialized services also operate more cost efficiently than those offering a combination of life and nonlife services (combined firms). The results also indicate that the X-inefficiency estimates derived from the stochastic cost frontier model are more suitable for this sample of data than those derived from the distribution-free model.