次贷危机下中国股市与国外股市相依性分析——基于Markov机制转换模型

文章通过选取2004年1月1日到2009年6月30日中国、香港、日本、英国和澳大利亚五个股票市场日收盘价的道琼斯数据,采用三状态Markov机制转换模型研究这些股市间相依性结构的变化。通过对目标股市结构变化的研究,可以描述并预测股市的波动性,从而指导风险管理。实证分析表明,在有机制转换条件下,澳大利亚与英国、日本股市间的相依性比无机制转换条件下均有所下降,而中国与香港股市间相依性却大幅上升。同时,本文采用总体拟合效果法来选取合适的copula函数并运用基于copula理论的相关系数法进行对比研究,发现次贷危机后各股市间的尾部相依性出现不同的变化,市场收益率呈现下降趋势,波动性均有所增加。其中,澳大利亚与英国股市间的尾部相依性最强,而中国股市与其他股市之间的相依性较弱,说明受到影响的程度较小。     

Distribution modeling for reliability analysis: Impact of multiple dependences and probability model selection

Reliability analysis requires modeling of joint probability distribution of uncertain parameters, which can be a challenge since the random variables representing the parameter uncertainties may be correlated. For convenience, a Gaussian data dependence is commonly assumed for correlated random variables. This paper first investigates the effect of multidimensional non-Gaussian data dependences underlying the multivariate probability distribution on reliability results. Using different bivariate copulas in a vine structure, various data dependences can be modeled. The associated copula parameters are identified from available statistical information by moment matching techniques. After the development of the vine copula model for representing the multivariate probability distribution, the reliability involving correlated random variables is evaluated based on the Rosenblatt transformation. The impact of data dependence is significant because a large deviation in failure probability is observed, which emphasizes the need for accurate dependence characterization. A practical method for dependence modeling based on limited data is thus provided. The result demonstrates that the non-Gaussian data dependences can be real in practice, and the reliability can be biased if the Gaussian dependence is used inappropriately. Moreover, the effect of conditioning order on reliability should not be overlooked except that the vine structure contains only one type of copula.     

Measuring the subprime crisis contagion: Evidence of change point analysis of copula functions

In this paper, we first determine the existence of structural changes in the dependence between time series of equity index returns of two markets using the change point testing method. The method is based on Archimedean copula functions, which are able to comprehensively describe dependence characteristics of random variables. The degree of financial contagion between markets is subsequently estimated using the tail dependence coefficient of copula functions before and after the change point. We empirically test our method by investigating financial contagion during the subprime crisis between the US S&P 500 index and five Asian markets, namely China, Japan, Korea, Hong Kong and Taiwan. Our results show that a statistically significant change point exists in the dependence between the US market and all Asian stock markets except Taiwan. The upper tail dependence is larger after the time of change, implying the existence of contagion during the banking crisis between the US and the Asian economies. The degree of financial contagion is also estimated and found to be consistent with market events and media reports during that period.     

Asymmetric extreme interdependence in emerging equity markets

We assess the extent of integration between stock markets during stressful periods using the concept of copulas. Our methodology consists of fitting copulas to simultaneous exceedances of high thresholds, and computing copula‐based measures of interdependence and contagion. Using 21 pairs of emerging stock markets daily returns, we investigate if dependence increases with crisis, and analyse the chances of both markets crashing together. Dependence at joint positive and negative extreme returns levels may differ. This type of asymmetry is captured by the upper and lower tail dependence coefficients. Propagation of crisis may be faster in one direction, and this feature is captured by asymmetric copulas. Copyright © 2005 John Wiley & Sons, Ltd.     

次贷危机后国际股票市场相关性变动的Copula分析

基于C opu la函数导出的尾部相关性,以四个国家的股票指数的对数收益率序列为研究对象,分析了次贷危机前后国际股票市的相关结构变动,结果表明次贷危机后国际股票市场尾部相关系数比危机前大,这说明次贷危机对国际股票市场的相关结构产生了重大影响,危机期间各国的股票市场联系更加紧密.     

Robust pair‐copula based forecasts of realized volatility

A useful application for copula functions is modeling the dynamics in the conditional moments of a time series. Using copulas, one can go beyond the traditional linear ARMA (p,q) modeling, which is solely based on the behavior of the autocorrelation function, and capture the entire dependence structure linking consecutive observations. This type of serial dependence is best represented by a canonical vine decomposition, and we illustrate this idea in the context of emerging stock markets, modeling linear and nonlinear temporal dependences of Brazilian series of realized volatilities. However, the analysis of intraday data collected from e‐markets poses some specific challenges. The large amount of real‐time information calls for heavy data manipulation, which may result in gross errors. Atypical points in high‐frequency intraday transaction prices may contaminate the series of daily realized volatilities, thus affecting classical statistical inference and leading to poor predictions. Therefore, in this paper, we propose to robustly estimate pair‐copula models using the weighted minimum distance and the weighted maximum likelihood estimates (WMLE). The excellent performance of these robust estimates for pair‐copula models are assessed through a comprehensive set of simulations, from which the WMLE emerged as the best option for members of the elliptical copula family. We evaluate and compare alternative volatility forecasts and show that the robustly estimated canonical vine‐based forecasts outperform the competitors. Copyright © 2013 John Wiley & Sons, Ltd.     

Dynamic asset allocation for varied financial markets under regime switching framework

Asset allocation among diverse financial markets is essential for investors especially under situations such as the financial crisis of 2008. Portfolio optimization is the most developed method to examine the optimal decision for asset allocation. We employ the hidden Markov model to identify regimes in varied financial markets; a regime switching model gives multiple distributions and this information can convert the static mean–variance model into an optimization problem under uncertainty, which is the case for unobservable market regimes. We construct a stochastic program to optimize portfolios under the regime switching framework and use scenario generation to mathematically formulate the optimization problem. In addition, we build a simple example for a pension fund and examine the behavior of the optimal solution over time by using a rolling-horizon simulation. We conclude that the regime information helps portfolios avoid risk during left-tail events.     

Modeling dependence dynamics through copulas with regime switching

Measuring dynamic dependence between international financial markets has recently attracted great interest in financial econometrics because the observed correlations rose dramatically during the 2008–09 global financial crisis. Here, we propose a novel approach for measuring dependence dynamics. We include a hidden Markov chain (MC) in the equation describing dependence dynamics, allowing the unobserved time-varying dependence parameter to vary according to both a restricted ARMA process and an unobserved two-state MC. Estimation is carried out via the inference for the margins in conjunction with filtering/smoothing algorithms. We use block bootstrapping to estimate the covariance matrix of our estimators. Monte Carlo simulations compare the performance of regime switching and no switching models, supporting the regime-switching specification. Finally the proposed approach is applied to empirical data, through the study of the S&P500 (USA), FTSE100 (UK) and BOVESPA (Brazil) stock market indexes.     

房地产产业链相依结构演化及其危机传染效应研究

以钢铁、有色金属、家用电器、房地产、建筑材料、建筑装饰、银行、非银金融和机械设备九大申万一级行业指数所代表的房地产产业链为研究对象,通过采用R-Vine Copula方法来刻画房地产产业链上行业间相依结构及其在2008年金融危机冲击下的结构演化特征.研究结果表明:房地产产业链上各行业间普遍存在对称、厚尾的相依结构,行业间相依性水平较高;机械设备业在整个房地产产业链上起到了枢纽中心的连接作用;金融危机的发生增强了房地产产业链的总体相依性水平,危机传染效应显著;与CVine Copula和D-Vine Copula方法相比,R-Vine Copula更适合来刻画我国房地产产业链的相依结构特征.     

金融风险在股票市场的传染效应及联动行为分析

近年来金融危机频发并表现出了易传染性,引起了众多学者的高度关注。以动态条件相关模型研究美欧股市与中、日、韩股市间的时变相关性,并结合内生多重结构突变模型划分危机传染阶段,选用溢出指数模型分析股市间的风险溢出特性;随后,定义股市间相互影响的联动模式并构建不同传染阶段的加权有向网络图分析股市间的联动行为。研究表明:美欧股市对中日韩股市有明显的传染效应,被传染的速度和持续时间均不相同;金融传染和风险溢出展现出一定的不一致性,危机期间日股的风险溢出效应强于美股;传染效应在联动网络中表现为联动模式的高聚类性和高联动性,相比欧债危机,次贷危机时期股市间展现出更强的联动行为;日股与美欧股市在两次危机中均表现出最强的联动性,其所受影响也最大。     

Dependence Properties of Conditional Distributions of some Copula Models

For multivariate data from an observational study, inferences of interest can include conditional probabilities or quantiles for one variable given other variables. For statistical modeling, one could fit a parametric multivariate model, such as a vine copula, to the data and then use the model-based conditional distributions for further inference. Some results are derived for properties of conditional distributions under different positive dependence assumptions for some copula-based models. The multivariate version of the stochastically increasing ordering of conditional distributions is introduced for this purpose. Results are explained in the context of multivariate Gaussian distributions, as properties for Gaussian distributions can help to understand the properties of copula extensions based on vines.     

基于极值统计和高维动态C藤Copula的股市行业集成风险计算

股市诸多行业风险之间存在着波动相依性,集成计量多维风险对投资决策意义重大。藤Copula是Copula函数高维化拓展的一个方向,其动态化是新的研究前沿。将极值理论的GPD模型和高维动态C藤Copula方法结合起来研究沪深300指数中地产、基建、银行和运输四个行业风险,能够有效描述尾部极值形态,突出关键变量的作用。再运用动态Pair-Copula分解,刻画高维行业风险变量间的动态关系,以仿真出动态集成风险变量VaR序列。VaR计算结果通过了回溯检验和稳定性测试,表明高维动态C藤Copula模型可以作为风险集成计量的一种新的有效方法。     

Tail dependence functions and vine copulas

Tail dependence and conditional tail dependence functions describe, respectively, the tail probabilities and conditional tail probabilities of a copula at various relative scales. The properties as well as the interplay of these two functions are established based upon their homogeneous structures. The extremal dependence of a copula, as described by its extreme value copulas, is shown to be completely determined by its tail dependence functions. For a vine copula built from a set of bivariate copulas, its tail dependence function can be expressed recursively by the tail dependence and conditional tail dependence functions of lower-dimensional margins. The effect of tail dependence of bivariate linking copulas on that of a vine copula is also investigated.     

Spatial contagion between financial markets: a copula‐based approach

A method is proposed for defining and investigating spatial contagion between two financial markets X and Y by using the information contained in their copula. A practical illustration of the introduced method is also given by examining the presence of contagion among two European stock indices (namely, FTSE 100 and DAX). Copyright © 2009 John Wiley & Sons, Ltd.     

Portfolio value-at-risk estimation in energy futures markets with time-varying copula-GARCH model

This paper combines copula functions with GARCH-type models to construct the conditional joint distribution, which is used to estimate Value-at-Risk (VaR) of an equally weighted portfolio comprising crude oil futures and natural gas futures in energy market. Both constant and time-varying copulas are applied to fit the dependence structure of the two assets returns. The findings show that the constant Student t copula is a good compromise for effectively fitting the dependence structure between crude oil futures and natural gas futures. Moreover, the skewed Student t distribution has a better fit than Normal and Student t distribution to the marginal distribution of each asset. Asymmetries and excess kurtosis are found in marginal distributions as well as in dependence. We estimate VaR of the underlying portfolio to be 95% and 99%, by using the Monte Carlo simulation. Then using backtesting, we compare the out-of-sample forecasting performances of VaR estimated by different models.     

The dynamics of the relationship between spot and futures markets under high and low variance regimes

This investigation is one of the first studies to examine the dynamics of the relationship between spot and futures markets using the Markov‐switching vector error correction model. Three mature stock markets including the U.S. S&P500, the U.K. FTSE100 and the German DAX 30, and two emerging markets including the Brazil Bovespa and the Hungary BSI, are used to test the model, and the differences between the two sets of markets are examined. The empirical findings of this study are consistent with the following notions. First, after filtering out the high variance regime, the futures price is shown to lead the spot price in the price discovery process, as demonstrated by prior studies; conversely, the spot market is more informationally efficient than the futures market under the high variance condition. Second, the price adjustment process triggered by arbitrage trading between spot and futures markets during a high variance state is greater in scale than that based on a low variance state, and the degree of the co‐movement between spot and futures markets is significantly reduced during the high variance state. Third, a crisis condition involved in the high variance state is defined for the two emerging markets, whereas an unusual condition is presented for the three mature markets. Last, the lagged spot–futures price deviations perform as an information variable for the variance‐turning process. However, the portion of the variance‐switching process accounted for by this signal variable is statistically marginal for the three mature markets selected for this study. Copyright © 2008 John Wiley & Sons, Ltd.     

相关系数与相关性度量

研究了度量相关性的两个主要工具:线性相关系数和尾部相关系数.线性相关系数反映了变量间的线性相关性,这对于一般的椭圆型分布是合适的.但如果随机变量具有不对称的尾部变化特征时,要用尾部相关系数描述它们之间的相关性.通过相关函数C opu la,对沪深股市的尾部相关系数进行了定量分析.结果表明:沪深股市具有较强的相关性.     

Modelling dependence structure with Archimedean copulas and applications to the iTraxx CDS index

In this paper we model the dependence structure between credit default swap (CDS) and jump risk using Archimedean copulas. The paper models and estimates the different relationships that can exist in different ranges of behaviour. It studies the bivariate distributions of CDS index spreads and the kurtosis of equity return distribution. To take into account nonlinear relationships and different structures of dependency, we employ three Archimedean copula functions: Gumbel, Clayton, and Frank. We adopt nonparametric estimation of copula parameters and we find an extreme co-movement of CDS and stock market conditions. In addition, tail dependence indicates the extreme co-movements and the potential for a simultaneous large loss in stock markets and a significant default risk. Ignoring the tail dependence would lead to underestimation of the default risk premium.     

Statistical mechanics of nonlinear nonequilibrium financial markets

An approach to understanding the nature of markets is modelled using methods of modern nonlinear nonequilibrium statistical mechanics. This permits examination of the premise that markets can be described by nonlinear nonequilibrium Markovian distributions. Corrections to previous nonlinear continuous time models are explicitly presented. A quite general microscopic model is presented of individual agents operating on a market, and explicit relationships are derived between variables describing these agents and the macroscopic market.     

Contagion-based distortion risk measures

We propose a class of distortion measures based on contagion from an external “scenario” variable. The dependence between the scenario and the variable whose risk is measured is modeled with a copula function with horizontal concave sections. Special cases are the perfect dependence copula, which generates expected shortfall, the Marshall–Olkin family and the Placket family. As an application, we evaluate distortion measures bank liabilities with respect to a country risk scenario in the current European debt crisis.