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.     

Modeling Spatial and Temporal House Price Patterns: A Comparison of Four Models

This research reports results from a competition on modeling spatial and temporal components of house prices. A large, well-documented database was prepared and made available to anyone wishing to join the competition. To prevent data snooping, out-of-sample observations were withheld; they were deposited with one individual who did not enter the competition, but had the responsibility of calculating out-of-sample statistics for results submitted by the others. The competition turned into a cooperative effort, resulting in enhancements to previous methods including: a localized version of Dubins kriging model, a kriging version of Clapps local regression model, and a local application of Cases earlier work on dividing a geographic housing market into districts. The results indicate the importance of nearest neighbor transactions for out-of-sample predictions: spatial trend analysis and census tract variables do not perform nearly as well as neighboring residuals.     

Two Monetary Models with Alternating Markets

We present a thought‐provoking study of two monetary models: the cash‐in‐advance and the Lagos and Wright ( 2005 ) models. The different approaches to modeling money—reduced form versus explicit role—induce neither fundamental theoretical nor quantitative differences in results. Given conformity of preferences, technologies, and shocks, both models reduce to equilibrium difference equations that coincide unless price distortions are differentially imposed on cash prices, across models. Equal distortions support equally large welfare costs of inflation. Performance differences stem from unequal assumptions about the pricing mechanism that governs cash transactions, not the differential modeling of the monetary exchange process.     

Fat-Tailed Regression Modeling with Spliced Distributions

Insurance claims data usually contain a large number of zeros and exhibits fat-tail behavior. Misestimation of one end of the tail impacts the other end of the tail of the claims distribution and can affect both the adequacy of premiums and needed reserves to hold. In addition, insured policyholders in a portfolio are naturally non-homogeneous. It is an ongoing challenge for actuaries to be able to build a predictive model that will simultaneously capture these peculiar characteristics of claims data and policyholder heterogeneity. Such models can help make improved predictions and thereby ease the decision-making process. This article proposes the use of spliced regression models for fitting insurance loss data. A primary advantage of spliced distributions is their flexibility to accommodate modeling different segments of the claims distribution with different parametric models. The threshold that breaks the segments is assumed to be a parameter, and this presents an additional challenge in the estimation. Our simulation study demonstrates the effectiveness of using multistage optimization for likelihood inference and at the same time the repercussions of model misspecification. For purposes of illustration, we consider three-component spliced regression models: the first component contains zeros, the second component models the middle segment of the loss data, and the third component models the tail segment of the loss data. We calibrate these proposed models and evaluate their performance using a Singapore auto insurance claims dataset. The estimation results show that the spliced regression model performs better than the Tweedie regression model in terms of tail fitting and prediction accuracy.     

Stochastic Migration Models with Application to Corporate Risk

In this article we explain how to use rating histories providedby the internal scoring systems of banks and rating agenciesin order to predict the future risk of a set of borrowers. Themethod is developed following the steps suggested by the BasleCommittee. To introduce both migration correlation and non-Markovianserial dependence, we consider rating histories with stochastictransition matrices. We develop the methodology to estimateboth the number and dynamics of the factors influencing thetransitions and we explain how to use the model for prediction.As an illustration, the ordered probit model with unobservabledynamic factor is estimated from French data on corporate risk.     

Bayesian Evaluation of DSGE Models with Financial Frictions

We evaluate two most popular approaches to implementing financial frictions into DSGE models: the Bernanke, Gertler, and Gilchrist ( 1999 ) setup, where frictions affect the price of loans, and the Kiyotaki and Moore ( 1997 ) model, where they concern the quantity of loans. We take both models to the data and check how well they fit it on several margins. Overall, comparing the models favors the Bernanke, Gertler, and Gilchrist framework. However, even this model does not make a clear improvement over the New Keynesian benchmark in terms of marginal likelihood and similarity of impulse responses to those obtained from a VAR.     

Dynamic Investment Strategy with Factor Models Under Regime Switches

A model for dynamic investment strategy is developed where assets’ returns are represented by multiple factors. In a mean–variance framework with factor models under regime switches, we derive a semi-analytic solution for the optimal portfolio with transaction costs. Due to the existence of transaction costs, the optimal portfolio is characterized as a linear combination of current and target portfolios, the latter of which maximizes the value function in the current regime. For some special cases of interest, we also derive simplified analytical solutions. To see the effect of regime switches, the proposed model is applied to US equity market in which small minus big and high minus low are employed as factors. Investment strategy based on our model demonstrates empirically that the regime switching models exhibit superior performance over the single regime model for such performance measures as realized utility and Sharpe ratio which are of particular interest in practice. Taking a close look at the time series of portfolio returns, the result shows the usefulness of the regime switching model as investors flexibly optimize asset allocations depending on the state of the market.     

Two-Pass Tests of Asset Pricing Models with Useless Factors

In this paper we investigate the properties of the standard two-pass methodology of testing beta pricing models with misspecified factors. In a setting where a factor is useless, defined as being independent of all the asset returns, we provide theoretical results and simulation evidence that the second-pass cross-sectional regression tends to find the beta risk of the useless factor priced more often than it should. More surprisingly, this misspecification bias exacerbates when the number of time series observations increases. Possible ways of detecting useless factors are also examined.     

Numerical Approach to Asset Pricing Models with Stochastic Differential Utility

In this paper employing two heuristic numerical schemes, we study the asset pricing models with stochastic differential utility (SDU), which is formulated by either of backward stochastic differential equations (BSDEs) or forward-backward stochastic differential equations (FBSDEs).The first scheme is based upon a traditional lattice algorithm of option pricing theories, involving the discretization scheme of coupled FBSDEs, which is combined with a technique of solving numerically a certain type of nonlinear equations with respect to the backward state variables. The second one is based upon the four step scheme of Ma et al. (1994) which solves quasi-linear partial differential equations associated with the FBSDEs. We demonstrate that our practical implementation algorithms can successfully solve the asset pricing models with generalized SDU and the large investor problem with market impact which are typical examples such that the usual four step scheme is difficult to implement. As other numerical applications we study the optimal consumption and investment policies of a representative agent with SDU, and the recoverability of preferences and beliefs from observed consumption data.     

Valuation of Equity-Linked Insurance and Annuity Products with Binomial Models

Abstract

In this paper we develop a valuation method for equity-linked insurance products. We assume that the premium information of term life insurances, pure endowment insurances, and endowment insurances at all maturities is obtainable within a company or from the insurance market. Using a method similar to that of Jarrow and Turnbull (1995), we derive three martingale probability measures associated with these basic insurance products. These measures are agedependent, include an adjustment for the mortality risk, and reproduce the premiums of the respective insurance products. We then extend the martingale measures to include the financial market information using copulas and use them to evaluate equity-linked insurance contracts and equity-indexed annuities in particular. This is different from the traditional approach under which diversification of mortality risk is assumed. A detailed numerical analysis is performed for various existing equity-indexed annuities in the North American market.     

Models with Unexpected Components: The Case for Efficient Estimation

Financial models often use unexpected explanatory variables. Conventionally, these are generated as the residuals of auxiliary equations, which are then substituted into the model of interest in a second step. This induces an econometric problem into the estimates, which is typically ignored. We propose a maximum likelihood estimation method as a solution. While there may be a predisposition when using financial data to dismiss our method as difficult to specify correctly, Monte Carlo simulations show that our method is robust. Further, we show that the magnitude of errors due to the generated regressor problem is somewhat larger than that due to ignoring the effects of plausible levels of leptokurtosis. An empirical example using commercial bank stock returns finds that hypothesis test conclusions from the conventional method can often be overturned.     

投资学两种研究范式的比较

投资学的标准研究范式和行为研究范式不仅在理论体系的假设和理论体系框架上存在显著差异,而且在指导投资实践方面也存在不同.但任何理论研究均需要有参照系和研究平台,因此二者的关系决非对立的,可以把标准研究范式视为行为研究范式的理论参照系和研究平台,行为研究范式是对标准研究范式假设条件的一般化和理论体系的拓展.     

Handling Valuation Models

Valuation models are useful tools, but they need to be handled with care. When taking the form of mathematical formulas, they can easily be made to convey a false sense of precision. In particular, selective choice of long‐term growth rates and discount rates can be used to justify almost any desired valuation. The author shows how relatively simple valuation models can be applied by active investors in a way that honors the fundamentalist dictum of building valuations on the foundation of “what we know” and avoiding speculation about long‐term growth rates. The article also emphasizes the role of accounting in discovering what we know, and shows how to use accounting results in a way that not only minimizes speculation about growth rates and discount rates, but actually challenges the speculation about those rates that is implicit in current stock prices. Accounting‐based valuation models are “reverse‐engineered” to discover the forecasts of future operating performance that are effectively built into current prices, so the plausibility of such forecasts can be evaluated with fundamental analysis. In this sense, valuation models are used not so much to discover the “right” price as to identify, and then subject to critical examination, the market's current expectations about future performance.     

Interpreting Factor Models

We argue that tests of reduced‐form factor models and horse races between “characteristics” and “covariances” cannot discriminate between alternative models of investor beliefs. Since asset returns have substantial commonality, absence of near‐arbitrage opportunities implies that the stochastic discount factor can be represented as a function of a few dominant sources of return variation. As long as some arbitrageurs are present, this conclusion applies even in an economy in which all cross‐sectional variation in expected returns is caused by sentiment. Sentiment‐investor demand results in substantial mispricing only if arbitrageurs are exposed to factor risk when taking the other side of these trades.     

创新商业模式——中小企业赢取资本市场之路

企业能否可持续健康发展,需要从四大方面判断:产业背景是否健康、核心团队是否优秀、商业模式是否具备竞争力和资金储备是否充足。对创业及发展阶段的中小企业而言,产业选择及团队搭建一般在公司设立前都已经完成,但融资难问题一直困扰企业,吸     

Modeling the leverage effect with copulas and realized volatility

In this paper, we propose the use of static and dynamic copulas to study the leverage effect in the S&P 500 index. Copula models can conveniently separate the leverage effect from the marginal distributions of the return and its volatility. Daily volatility is proxied by a measure of realized volatility, which is constructed from high-frequency data. We uncover a significant leverage effect in the S&P 500 index, and this leverage effect is found to be changing over time in a highly persistent manner. Moreover the dynamic copula models are shown to outperform the static counterparts.     

Bonus-Malus Systems with Two-Component Mixture Models Arising from Different Parametric Families

Two-component mixture distributions defined so that the component distributions do not necessarily arise from the same parametric family are employed for the construction of Optimal Bonus-Malus Systems (BMSs) with frequency and severity components. The proposed modeling framework is used for the first time in actuarial literature research and includes an abundance of alternative model choices to be considered by insurance companies when deciding on their Bonus-Malus pricing strategies. Furthermore, we advance one step further by assuming that all the parameters and mixing probabilities of the two component mixture distributions are modeled in terms of covariates. Applying Bayes' theorem we derive optimal BMSs either by updating the posterior probability of the policyholders’ classes of risk or by updating the posterior mean and the posterior variance. The resulting tailor-made premiums are calculated via the expected value and variance principles and are compared to those based only on the a posteriori criteria. The use of the variance principle in a Bonus-Malus ratemaking scheme in a way that takes into consideration both the number and the costs of claims based on both the a priori and the a posterior classification criteria has not yet been proposed and can alter the resulting premiums significantly, providing the actuary with useful alternative tariff structures.     

Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates

This paper specifies a multivariate stochasticvolatility (SV) model for the S & P500 index and spot interest rateprocesses. We first estimate the multivariate SV model via theefficient method of moments (EMM) technique based on observations ofunderlying state variables, and then investigate the respective effects of stochastic interest rates, stochastic volatility, and asymmetric S & P500 index returns on option prices. We compute option prices using both reprojected underlying historical volatilities and the implied risk premiumof stochastic volatility to gauge each model's performance through direct comparison with observed market option prices on the index. Our major empirical findings are summarized as follows. First, while allowing for stochastic volatility can reduce the pricing errors and allowing for asymmetric volatility or leverage effect does help to explain the skewness of the volatility smile, allowing for stochastic interest rates has minimal impact on option prices in our case. Second, similar to Melino and Turnbull (1990), our empirical findings strongly suggest the existence of a non-zero risk premium for stochastic volatility of asset returns. Based on the implied volatility risk premium, the SV models can largely reduce the option pricing errors, suggesting the importance of incorporating the information from the options market in pricing options. Finally, both the model diagnostics and option pricing errors in our study suggest that the Gaussian SV model is not sufficientin modeling short-term kurtosis of asset returns, an SV model withfatter-tailed noise or jump component may have better explanatory power.     

公司治理模式下累积投票制的作用、问题与改进方案——基于国际比较的视角

美、英、日、德、巴西和中国台湾地区累积投票制的实践经验表明,公司治理模式很大程度上可以解释各国(地区)是否采用累积投票制、累积投票制的实施细则和作用的差异:英美模式下累积投票制作用有限,实施细则具有差异化、多元化和个性化的特征;德日模式下作用更加有限,实施细则跟随美英,流于形式;而家族模式下的作用则因股权结构而异,为中小股东赋权是良好公司治理的必要不充分条件,且立法模式偏好"强制式"。就我国而言,在控股股东和内部人对公司控制力较强的背景下,目前累积投票制存在以下问题:作用有限、强制实行的阈值过高、缺乏前置程序和事后保障程序、董监分别选举、董事会规模较小、容易成为恶意并购的工具等。针对上述问题,本文提出如下建议:对控股股东行为进行直接约束,降低强制实行累积投票制的阈值,为股东赋予董事、监事候选人的提名权和罢免权,降低中小股东选出代言人所需的股权集中程度,防止累积投票制成为恶意收购的工具。     

Hysteresis Models of Investment with Multiple Uncertainties and Exchange Rate Risk

In this article we use the hysteresis model of investment developed by Brennan and Schwartz, and Dixit, and we extend it to capture the impact of interacting uncertainties on a firm with foreign operations. We develop a three-country, four-factor model where both continuous revenues and continuous costs are stochastic and are generated in countries other than the home country of the investor, who has to carry foreign currencies' risk. All four state-variables follow geometric Brownian motion processes. A critical assumption is made that the capital outlays for switching between the idle and the active states are constant fractions of the costs. An efficient numerical solution is used to demonstrate applications of the model on a multinational corporation facing operating and exchange rate risks in a multistage investment setting with interacting investment and operating options.