Forecasting models for the Chinese macroeconomy in a data-rich environment: Evidence from large dimensional approximate factor models with mixed-frequency data

Our paper contributes to the nascent literature on forecasting the Chinese macroeconomy in a data-rich environment. We perform a horse race among a large set of traditional models and two classes of factor models with 251 monthly and 34 quarterly macroeconomic variables over the period from January 2002 to June 2018. We find evidence that mixed-frequency factor models provide superior forecasts of the CPI, RPI, investment, and consumption when compared to the simple benchmark. During the Global Financial Crisis period, we find little evidence of superiority of factor models over the simple benchmark AR(p) model.     

On Bayesian Value at Risk: From Linear to Non-Linear Portfolios

This paper proposes the use of Bayesian approach to implement Value at Risk (VaR) model for both linear and non-linear portfolios. The Bayesian approach provides risk traders with the flexibility of adjusting their VaR models according to their subjective views. First, we deal with the case of linear portfolios. By imposing the conjugate-prior assumptions, a closed-form expression for the Bayesian VaR is obtained. The Bayesian VaR model can also be adjusted in order to deal with the ageing effect of the past data. By adopting Gerber-Shiu's option-pricing model, our Bayesian VaR model can also be applied to deal with non-linear portfolios of derivatives. We obtain an exact formula for the Bayesian VaR in the case of a single European call option. We adopt the method of back-testing to compare the non-adjusted and adjusted Bayesian VaR models with their corresponding classical counterparts in both linear and non-linear cases.     

长寿风险对基本医疗保险统筹基金的冲击效应研究——基于VaR与CVaR模型的综合测算

借鉴金融风险管理中VaR和CVaR模型对尾部风险的测量思路,通过构建有限数据Lee-Carter死亡率预测模型,测算了人口的长寿风险及其对基本医疗保险统筹基金的冲击效应,结果表明:2015-2060年基本医疗保险参保人群将面临巨大的长寿风险,极端情况下长寿风险将给统筹基金收支结余超预期下降造成不容忽视的尾部损失;推迟退休年龄、提高生育率、调整个人账户和报销比例、提高职工缴费工资和控制住院费用增长均可以在一定程度上缓解长寿风险的冲击.建议明确政府在基本医疗保险长寿风险管理中的主导作用,构建医疗、养老和长期护理保险的三险联动保障机制.     

基于动态VaR模型和Copula函数的省级政府平台公司投资风险测度

省级政府投融资平台公司在城镇化建设中发挥着重要作用,其投融资风险问题亦逐渐引起重视。基于平台公司的投资收益会随着市场等宏观环境的变化而波动的考虑,将平台公司的项目投资资产视为金融资产而度量其风险状况。考虑单笔投资的情形,建立极值理论和SV-t模型的相结合平台公司一维融资风险动态VaR模型;进而考虑多笔投资间的非线性关系,结合Copula函数和蒙特卡洛模拟思路,建立平台公司多维融资风险度量模型。所构建的模型避免了传统研究的强主观性,并实现了投资风险的实时、动态度量。     

Testing linear factor models on individual stocks using the average F-test

In this paper, we propose the average F-statistic for testing linear asset pricing models. The average pricing error, captured in the statistic, is of more interest than the ex post maximum pricing error of the multivariate F-statistic that is associated with extreme long and short positions and excessively sensitive to small perturbations in the estimates of asset means and covariances. The average F-test can be applied to thousands of individual stocks and thus is free from the information loss or the data-snooping biases from grouping. This test is robust to ellipticity, and more importantly, our simulation and bootstrapping results show that the power of the average F-test continues to increase as the number of stocks increases. Empirical tests using individual stocks from 1967 to 2006 demonstrate that the popular four-factor model (i.e. Fama–French three factors and momentum) is rejected in two sub-periods from 1967 to 1971 and from 1982 to 1986.     

Follow the leader: Index tracking with factor models

We propose a new methodology to select a subset of assets for (partial) index replication, based on the latest research on factor models of large dimensions. Our method selects a set of leader stocks that fully captures the factor structure of the index to be replicated. Our selection methodology is consistent as the sample size and the number of assets jointly approach infinity. Monte Carlo experiments show that our estimated index replica tracks the underlying index with relatively small tracking errors in finite samples. We show the applicability of the method by tracking the S&P 500 equally weighed index and the MSCI USA Small Cap index with promising out-of-sample performance. Our method can be easily adapted for synthetic index replication, and to incorporate measures of liquidity or transaction cost.     

Forecasting stock returns with large dimensional factor models

We study equity premium out-of-sample predictability by extracting the information contained in a high number of macroeconomic predictors via large dimensional factor models. We compare the well-known factor model with a static representation of the common components with the Generalized Dynamic Factor Model, which accounts for time series dependence in the common components. Using statistical and economic evaluation criteria, we empirically show that the Generalized Dynamic Factor Model helps predicting the equity premium. Exploiting the link between business cycle and return predictability, we find accurate predictions also by combining rolling and recursive forecasts in real-time.     

具有破裂风险的讨价还价模型研究

Rubinstein和Muthoo所建立的具有破裂风险的讨价还价模型,是基于将参与人对自身退出谈判的主观概率等价于参与人对谈判破裂风险的主观概率这一假设的基础之上的,但该假设却存在着缺陷。通过对讨价还价破裂风险内在机理的分析可以看出,参与人对谈判对手退出谈判的主观概率才是参与人对谈判破裂风险的主观概率。根据此结论修正后的模型,在本质上反映了参与人的均衡支付与其对谈判破裂风险的主观概率之间的关系,以及参与人的均衡支付与市场竞争之间的关系。     

Unconditional distributions obtained from conditional specification models with applications in risk theory

Bivariate distributions, specified in terms of their conditional distributions, provide a powerful tool to obtain flexible distributions. These distributions play an important role in specifying the conjugate prior in certain multi-parameter Bayesian settings. In this paper, the conditional specification technique is applied to look for more flexible distributions than the traditional ones used in the actuarial literature, as the Poisson, negative binomial and others. The new specification draws inferences about parameters of interest in problems appearing in actuarial statistics. Two unconditional (discrete) distributions obtained are studied and used in the collective risk model to compute the right-tail probability of the aggregate claim size distribution. Comparisons with the compound Poisson and compound negative binomial are made.     

Portfolio Optimization under Lower Partial Risk Measures

Portfolio management using lower partial risk (downside risk) measures is attracting more attention of practitioners in recent years. The purpose of this paper is to review important characteristics of these riskmeasures and conduct simulation using four alternative measures, lower semi-variance, lower semi-absolute deviation, first order below targetrisk and conditional value-at-risk.We will show that these risk measures are useful to control downside risk whenthe distribution of assets is non-symmetric. Further, we will propose a computational scheme to resolve the difficultyassociated with solving a large dense linear programming problems resulting from these models. We will demonstrate that this method can in fact solve problems consisting of10⁴ assets and 10⁵ scenarios within a practical amount of CPU time.     

Capturing hedge fund risk factor exposures: Hedge fund return replication with ETFs

We develop a new factor selection methodology of spanning the space of hedge fund risk factors with all available exchange traded funds (ETFs). We demonstrate the efficacy of the methodology with out-of-sample individual hedge fund return replication by ETF clone portfolios. This is consistent with our interpretation of ETF returns as proxies to risk factors driving hedge fund returns. We further consider portfolios of “cloneable” and “noncloneable” hedge funds, defined as top and bottom in-sample R² matches, and demonstrate that our ETF clone portfolios slightly outperform cloneable hedge funds out of sample.     

Asset Pricing with a Bank Risk Factor

This paper studies how the state of the banking sector influences stock returns of nonfinancial firms. We consider a two‐factor pricing model, where the first factor is the traditional market excess return and the second factor is the change in the average distance to default of commercial banks. We find that this bank factor is priced in the cross section of U.S. nonfinancial firms. Controlling for market beta, the expected excess return for a stock in the top quintile of bank risk exposure is on average 2.83% higher than for a stock in the bottom quintile.     

Potential measures and expected present value of operating costs until ruin in renewal risk models with general interclaim times

In this paper, a Sparre Andersen risk process with arbitrary interclaim time distribution is considered. We analyze various ruin-related quantities in relation to the expected present value of total operating costs until ruin, which was first proposed by Cai et al. [(2009a). On the expectation of total discounted operating costs up to default and its applications. Advances in Applied Probability 41(2), 495–522] in the piecewise-deterministic compound Poisson risk model. The analysis in this paper is applicable to a wide range of quantities including (i) the insurer's expected total discounted utility until ruin; and (ii) the expected discounted aggregate claim amounts until ruin. On one hand, when claims belong to the class of combinations of exponentials, explicit results are obtained using the ruin theoretic approach of conditioning on the first drop via discounted densities (e.g. Willmot [(2007). On the discounted penalty function in the renewal risk model with general interclaim times. Insurance: Mathematics and Economics 41(1), 17–31]). On the other hand, without any distributional assumption on the claims, we also show that the expected present value of total operating costs until ruin can be expressed in terms of some potential measures, which are common tools in the literature of Lévy processes (e.g. Kyprianou [(2014). Fluctuations of L'evy processes with applications: introductory lectures, 2nd ed. Berlin Heidelberg: Springer-Verlag]). These potential measures are identified in terms of the discounted distributions of ascending and descending ladder heights. We shall demonstrate how the formulas resulting from the two seemingly different methods can be reconciled. The cases of (i) stationary renewal risk model and (ii) surplus-dependent premium are briefly discussed as well. Some interesting invariance properties in the former model are shown to hold true, extending a well-known ruin probability result in the literature. Numerical illustrations concerning the expected total discounted utility until ruin are also provided.     

Affine Models for Credit Risk Analysis

Continuous-time affine models have been recently introducedin the theoretical financial literature on credit risk. Theyprovide a coherent modeling, rather easy to implement, but havenot yet encountered the expected success among practitionersand regulators. This is likely due to a lack of flexibilityof these models, which often implied poor fit, especially comparedto more ad hoc approaches proposed by the industry. The aimof this article is to explain that this lack of flexibilityis mainly due to the continuous-time assumption. We developa discrete-time affine analysis of credit risk, explain howdifferent types of factors can be introduced to capture separatelythe term structure of default correlation, default heterogeneity,correlation between default, and loss-given-default; we alsoexplain why the factor dynamics are less constrained in discretetime and are able to reproduce complicated cycle effects. Thesemodels are finally used to derive a credit-VaR and various decompositionsof the spreads for corporate bonds or first-to-default basket.     

An approximate distribution of delta-hedging errors in a jump-diffusion model with discrete trading and transaction costs

We introduce a jump-diffusion model for asset returns with jumps drawn from a mixture of normal distributions and show that this model adequately fits the historical data of the S&P500 index. We consider a delta-hedging strategy (DHS) for vanilla options under the diffusion model (DM) and the proposed jump-diffusion model (JDM), assuming discrete trading intervals and transaction costs, and derive an approximation for the probability density function (PDF) of the profit-and-loss (P&L) of the DHS under both models. We find that, under the log-normal model of Black–Scholes–Merton, the actual PDF of the P&L can be well approximated by the chi-squared distribution with specific parameters. We derive an approximation for the P&L volatility in the DM and JDM. We show that, under both DM and JDM, the expected loss due to transaction costs is inversely proportional to the square root of the hedging frequency. We apply mean–variance analysis to find the optimal hedging frequency given the hedger's risk tolerance. Since under the JDM it is impossible to reduce the P&L volatility by increasing the hedging frequency, we consider an alternative hedging strategy, following which the P&L volatility can be reduced by increasing the hedging frequency.     

Ruin probabilities in multivariate risk models with periodic common shock

We propose a multidimensional risk model where the common shock affecting all classes of insurance business is arriving according to a non-homogeneous periodic Poisson process. In this multivariate setting, we derive upper bounds of Lundberg-type for the probability that ruin occurs in all classes simultaneously using the martingale approach via piecewise deterministic Markov processes theory. These results are numerically illustrated in a bivariate risk model, where the beta-shape periodic claim intensity function is considered. Under the assumption of dependent heavy-tailed claims, asymptotic bounds for the finite-time ruin probabilities associated to three types of ruin in this multivariate framework are investigated.     

Counterparty Risk for Credit Default Swaps: Markov Chain Interacting Intensities Model with Stochastic Intensity

We analyze the counterparty risk for credit default swaps using the Markov chain model of portfolio credit risk of multiple obligors with interacting default intensity processes. The default correlation between the protection seller and underlying entity is modeled by an increment in default intensity upon the occurrence of an external shock event. The arrival of the shock event is a Cox process whose stochastic intensity is assumed to follow an affine diffusion process with jumps. We examine how the correlated default risks between the protection seller and the underlying entity may affect the credit default premium in a credit default swap.     

Bayesian analysis of the factor model with finance applications

The factor analysis model has been widely applied to study finance problems. The purpose of this paper is to introduce a Bayesian approach for analysing the factor analysis model. The advantages of the proposed Bayesian approach over the classical maximum likelihood rest on its capability to incorporate additional prior information, to determine the number of factors in an objective manner, and to produce parameter and factor score estimates with good statistical properties. Based on recently developed tools in statistical computing, such as the Gibbs sampler and path sampling, methods for obtaining the Bayesian estimates of the parameters and factor scores, and a procedure for computing the Bayes factor for selecting the appropriate number of factors in the model, are developed. The proposed new methodologies are applied to analyse a data set taken from the Hong Kong stock security market. It is found that a three-factor model with a generic market factor can be used to describe the systematic components of asset returns.     

CreditRisk+ Model with Dependent Risk Factors

The CreditRisk⁺ model is widely used in industry for computing the loss of a credit portfolio. The standard CreditRisk⁺ model assumes independence among a set of common risk factors, a simplified assumption that leads to computational ease. In this article, we propose to model the common risk factors by a class of multivariate extreme copulas as a generalization of bivariate Fréchet copulas. Further we present a conditional compound Poisson model to approximate the credit portfolio and provide a cost-efficient recursive algorithm to calculate the loss distribution. The new model is more flexible than the standard model, with computational advantages compared to other dependence models of risk factors.     

Expected exponential utility maximization of insurers with a Linear Gaussian stochastic factor model

In this paper, we consider the problem of optimal investment by an insurer. The wealth of the insurer is described by a Cramér–Lundberg process. The insurer invests in a market consisting of a bank account and m risky assets. The mean returns and volatilities of the risky assets depend linearly on economic factors that are formulated as the solutions of linear stochastic differential equations. Moreover, the insurer preferences are exponential. With this setting, a Hamilton–Jacobi–Bellman equation that is derived via a dynamic programming approach has an explicit solution found by solving the matrix Riccati equation. Hence, the optimal strategy can be constructed explicitly. Finally, we present some numerical results related to the value function and the ruin probability using the optimal strategy.