两因子随机死亡率状态空间模型及长寿风险测度

引入状态空间模型对传统两因子CBD模型拟合阶段和预测阶段进行联合建模,并基于卡尔曼滤波方法对模型参数进行估计。进一步考虑到死亡率数据的小样本特征,结合Bootstrap仿真技术和生存年金组合折现模型对长寿风险进行测度。利用1996~2011年数据展开实证研究,结果表明:结合模型解释能力、参数估计结果和误差项正态分布检验结果,两因子状态空间模型要优于传统CBD模型;年金组合规模的扩大可以消除微观长寿风险,但不能消除宏观长寿风险和参数风险;宏观长寿风险占据着不可分散风险的主导地位。     

A Two-Factor Model for Low Interest Rate Regimes

This paper derives a two-factor model for the term structure of interest rates that segments the yield curve in a natural way. The first factor involves modelling a non-negative short rate process that primarily determines the early part of the yield curve and is obtained as a truncated Gaussian short rate. The second factor mainly influences the later part of the yield curve via the market index. The market index proxies the growth optimal portfolio (GOP) and is modelled as a squared Bessel process of dimension four. Although this setup can be applied to any interest rate environment, this study focuses on the difficult but important case where the short rate stays close to zero for a prolonged period of time. For the proposed model, an equivalent risk neutral martingale measure is neither possible nor required. Hence we use the benchmark approach where the GOP is chosen as numeraire. Fair derivative prices are then calculated via conditional expectations under the real world probability measure. Using this methodology we derive pricing functions for zero coupon bonds and options on zero coupon bonds. The proposed model naturally generates yield curve shapes commonly observed in the market. More importantly, the model replicates the key features of the interest rate cap market for economies with low interest rate regimes. In particular, the implied volatility term structure displays a consistent downward slope from extremely high levels of volatility together with a distinct negative skew. 1991 Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: G10, G13     

A Semiparametric Two-Factor Term Structure Model

This article proposes a semiparametric two-factor term structuremodel based on a consol rate and the spread between a shortrate and the consol rate. The diffusion functions in both theconsol rate and spread processes are nonparametrically specifiedso that the model allows for maximal flexibility of diffusionfunctions in fitting into data. The drift function of the spreadprocess is specified as a mean-reverting function, while thedrift function of the consol rate process is left unrestricted.A nonparametric procedure is developed for estimating the diffusionfunctions. The asymptotic biases of the nonparametric estimatorsare quantified when the step of discretization is fixed, whilethe asymptotic distributions of the nonparametric estimatorsare derived when the step of discretization tends to zero. Thepricing and hedging performances of the model are evaluatedin a simulated economic environment. Results show that the modelperforms quite well in the simulated economy.     

Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model

We develop a two-factor general equilibrium model of the term structure. The factors are the short-term interest rate and the volatility of the short-term interest rate. We derive closed-form expressions for discount bonds and study the properties of the term structure implied by the model. The dependence of yields on volatility allows the model to capture many observed properties of the term structure. We also derive closed-form expressions for discount bond options. We use Hansen's generalized method of moments framework to test the cross-sectional restrictions imposed by the model. The tests support the two-factor model.     

A Stochastic Model for Pensionable Service

Abstract

In this paper, a stochastic model is developed for the prediction of the employee's cumulative pensionable service over his working life, as a function of his unemployment periods and his completed lengths of service, under a service requirement constraint. Distributional and first passagetime problems are considered for the total pensionable service and a generalized renewal equation is formally solved. Further useful results are obtained and numerical applications are given.     

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.     

A Stochastic Correlation Model with Mean Reversion for Pricing Multi-Asset Options

We set up a new kind of model to price the multi-asset options. A square root process fluctuating around its mean value is introduced to describe the random evolution of correlation between two assets. In this stochastic correlation model with mean reversion term, the correlation is a random walk within the region from −1 to 1, and it is centered around its equilibrium value. The trading strategy to hedge the correlation risk is discussed. Since a solution of high-dimensional partial differential equation may be impossible, the Quasi-Monte Carlo and Monte Carlo methods are introduced to compute the multi-asset option price as well. Taking a better-of two asset rainbow as an example, we compare our results with the price obtained by the Black–Scholes model with constant correlation.     

Multiperiod Optimal Investment-Consumption Strategies with Mortality Risk and Environment Uncertainty

Abstract

In this article we investigate three related investment-consumption problems for a risk-averse investor: (1) an investment-only problem that involves utility from only terminal wealth, (2) an investment-consumption problem that involves utility from only consumption, and (3) an extended investment-consumption problem that involves utility from both consumption and terminal wealth. Although these problems have been studied quite extensively in continuous-time frameworks, we focus on discrete time. Our contributions are (1) to model these investmentconsumption problems using a discrete model that incorporates the environment risk and mortality risk, in addition to the market risk that is typically considered, and (2) to derive explicit expressions of the optimal investment-consumption strategies to these modeled problems. Furthermore, economic implications of our results are presented. It is reassuring that many of our findings are consistent with the well-known results from the continuous-time models, even though our models have the additional features of modeling the environment uncertainty and the uncertain exit time.     

The Pricing of Event Risks with Parameter Uncertainty

Financial instruments whose payoffs are linked to exogenous events, such as the occurrence of a natural catastrophe or an unusual weather pattern depend crucially on actuarial models for determining event (e.g., default) probabilities. In many instances, investors appear to receive premiums far in excess of these modeled actuarial probabilities, even for event risks that are uncorrelated with returns on other financial assets. Some have attributed these larger spreads to uncertainty in the probabilities generated by the models. We provide a simple model of such parameter uncertainty and demonstrate how it affects rational investors' demand for event risk exposures. We show that while parameter uncertainty does indeed affect bond spreads, it does not tend to increase spreads by much. Indeed, the spread increases due to parameter uncertainty in our numerical examples are on the order of only 1–2 basis points. Moreover, in many instances, including those that have the most sensible correlation settings, parameter uncertainty tends to decrease the size of bond spreads. We therefore argue that parameter uncertainty does not appear to be a satisfactory explanation for high event-risk returns.     

Bank Holding Company Risk from 1976–1989 with a Two-Factor Model

This paper employs a two-factor model of security returns to investigate the intertemporal risk of bank holding company stock returns over the 1976–1989 period. Uniquely, the two-factor model is estimated in separate regressions for each of the fourteen years between 1976 and 1989, thus exposing intertemporal changes in the model coefficients. The results show that bank holding companies have increased in risk over the sample period and also reveal that much of the controversy over the two-index model stems from the transitory nature of the interest rate coefficient through time, making long time series groupings of data misspecified. The above holds for both short-term and long-term interest rates. Interest rates have little impact on bank returns.     

A General Stationary Stochastic Regression Model for Estimating and Predicting Beta

A beta regression model is proposed where the coefficients follow a general class of stationary stochastic processes. The procedure identifies the process and estimates the parameters of the model simultaneously from the information contained in the return series. The returns of each of the Dow Jones 30 securities are examined. Betas of 5 of the securities are nonstationary and do not appear to follow a particular form of nonstationarity. Conclusions of many earlier studies may be suspect since they are based on procedures tailored to adoption of a specific form of beta nonstationarity and, thereby, based on an erroneous a priori assumption regarding such form. The ordinary least squares model is also found to be quite robust, providing reliable beta and intercept estimates not materially different from the more complex procedure with 25 of the return series.     

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.     

A Gravity Model of Mortality Rates for Two Related Populations

Abstract

The mortality rate dynamics between two related but different-sized populations are modeled consistently using a new stochastic mortality model that we call the gravity model. The larger population is modeled independently, and the smaller population is modeled in terms of spreads (or deviations) relative to the evolution of the former, but the spreads in the period and cohort effects between the larger and smaller populations depend on gravity or spread reversion parameters for the two effects. The larger the two gravity parameters, the more strongly the smaller population’s mortality rates move in line with those of the larger population in the long run. This is important where it is believed that the mortality rates between related populations should not diverge over time on grounds of biological reasonableness. The model is illustrated using an extension of the Age-Period-Cohort model and mortality rate data for English and Welsh males representing a large population and the Continuous Mortality Investigation assured male lives representing a smaller related population.     

基于动态随机一般均衡模型的金融脆弱性与货币政策新框架:理论与数值模拟

残酷的经济泡沫与频发的金融危机现实不断提醒货币当局,传统的以稳定实体经济为唯一目标的货币政策框架已经不合时宜。借鉴现有文献,在传统货币政策目标框架体系内增加了金融稳定目标。新的货币理论框架模型推导表明,中央银行增加金融稳定目标后,能有效避免最优利率被系统性低估,从而发挥中央银行最优利率在整个市场体系中的基准价格的引导作用。同时动态随机一般均衡模型模拟结果表明,中央银行最优利率水平与中央银行设定金融稳定目标权重的偏好程度、与社会福利损失水平同向变动,与银行损失成本反向变动。同时央行设定不同金融稳定目标权重后,面对外界不同冲击,实际产出与货币供给增速会发生显著性变化。根据上述研究结论,给出的政策启示一是建立"双稳定目标"货币政策新框架,二是构建"双支柱"宏观调控新格局。     

Model Uncertainty and Option Markets with Heterogeneous Beliefs

This paper provides option pricing and volume implications for an economy with heterogeneous agents who face model uncertainty and have different beliefs on expected returns. Market incompleteness makes options nonredundant, while heterogeneity creates a link between differences in beliefs and option volumes. We solve for both option prices and volumes and test the joint empirical implications using S&P500 index option data. Specifically, we use survey data to build an Index of Dispersion in Beliefs and find that a model that takes information heterogeneity into account can explain the dynamics of option volume and the smile better than can reduced‐form models with stochastic volatility.     

A Model for Analyzing the Impact of Selective Lapsation on Mortality

Abstract

This paper presents a model for examining the effect of various relationships between mortality rates and lapse rates on the mortality experience of a cohort of insured lives. The approach is individual rather than the aggregate traditionally used in analyzing selective lapsation. The model assumes that insured lives are healthy at policy issue, but later may move to an impaired state from which the lapse rate is zero. Associated with each insured is an unobservable “risk level” random variable, which reflects the heterogeneity of the insured group. Individual mortality and lapse rates are functions of the risk level. A numerical illustration provides some interesting results obtained by using this model.     

A Shrinkage Approach to Model Uncertainty and Asset Allocation

This article takes a shrinkage approach to examine the empiricalimplications of aversion to model uncertainty. The shrinkageapproach explicitly shows how predictive distributions incorporatedata and prior beliefs. It enables us to solve the optimal portfoliosfor uncertainty-averse investors. Aversion to uncertainty aboutthe capital asset pricing model leads investors to hold a portfoliothat is not mean-variance efficient for any predictive distribution.However, mean-variance efficient portfolios corresponding toextremely strong beliefs in the Fama–French model areapproximately optimal for uncertainty-averse investors. Theempirical Bayes approach does not result in optimal portfoliosfor investors who are averse to model uncertainty.     

不确定环境下我国绿色信贷交易行为的博弈分析

绿色信贷制度是我国环境保护的重要经济手段和法律政策体系的有力补充,本文运用博弈模型研究了不确定环境下我国绿色信贷交易主体的行为特征,结果发现:在缺乏外部约束的情况下银行与企业易达成合谋,强化对污染事件的处罚力度和完善对银行的绿色信贷激励约束机制应成为构建绿色信贷交易机制的主要内容,同时要配合实施相应的绿色金融配套措施,建立环保部门与银行间的畅通信息交流机制。     

Dynamic Portfolio Choice with Parameter Uncertainty and the Economic Value of Analysts' Recommendations

We derive a closed-form solution for the optimal portfolio ofa nonmyopic utility maximizer who has incomplete informationabout the alphas or abnormal returns of risky securities. Weshow that the hedging component induced by learning about theexpected return can be a substantial part of the demand. Usingour methodology, we perform an "ex ante" empirical exercise,which shows that the utility gains resulting from optimal allocationare substantial in general, especially for long horizons, andan "ex post" empirical exercise, which shows that analysts’recommendations are not very useful. (JEL C61, G11, G24)