股票资产组合VaR研究基于混合D藤Copula模型

本文在对上证市场五种股票资产组合的风险分析中以VaR作为风险度量指标,采用基于Pair Copula高维建模理论的混合D藤Copula模型,建立了反应多个资产组合相关结构的联合分布模型。该模型对传统D藤Copula建模方法作了进一步的改进,通过一定的选择标准,确定了D藤中每个Pair Copula函数的最优函数族,这样使得所建立的模型不仅考虑到了资产维数的影响,而且还能捕捉到组合内部因子间相关结构的差异性,从而改进后的模型能更好地描述资产组合的相关结构,并且能更精确地反映资产组合收益的实际分布。最后,以混合D藤Copula模型为基础,利用Monte Carlo方法计算了上证市场五种股票资产组合的VaR,并通过实证研究进一步证明了该模型的有效性。     

“金砖四国”股票市场间相依结构分析

金融市场间的相依关系及其结构分析是金融风险测度、资产组合管理等金融理论和实务中的一个重要问题,而基于线性相关系数是难以正确刻画非线性条件下金融资产间的相关结构,特别是尾相依关系。为研究"金砖四国"新兴股票市场间的相依结构,文章构建了一个混合Copula模型,对"金砖四国"股票市场间的相依结构进行建模分析,并将结果与单一阿基米德Copula模型进行了比较,表明混合Copula模型既能保留单一Copula模型的特性,更能灵活、全面地刻画变量间的相依关系。实证研究的结果表明:在样本数据期间,"金砖四国"股票市场间存在非对称相关关系,相依结构上存在差异;中国上证综指波动较为剧烈,与其它三国指数间以下尾相依为主;巴西、印度、俄罗斯三国股指间的相依结构相似,联动相关性相近,并无显著的下尾相依关系。     

宏观经济与股票价格波动之间的关系研究

利用Copula模型,研究宏观经济变量与上证股指收益率之间的相关关系,在选择合适的边缘分布函数的基础上,分别建立了常相关的二元正态Copula函数、t—Copula函数、FrankCopula函数、ClaytonCopula函数以及Gum—belCopula函数模型,并且利用欧氏距离方法选择出最佳拟合Copula模型。选取2001年1月至2011年12月的月度数据作为处理对象,并利用最佳拟合模型分析宏观经济变量与上证股指收益率间相关关系及相关结构,从而揭示了中国宏观经济与股票市场之间的相关性。     

国际碳期货市场间动态尾部相依及风险研究

EUA和CER已成为碳期货市场最重要的两种交易商品,文章基于BP检验将2008—2017年两资产连续期货数据分为三时期;通过VAR模型,以线性、非线性格兰杰检验和脉冲响应及方差分解方法研究两者的因果关系;进而运用GARCH-Copula分析各时期动态相依结构;基于Copula函数,结合蒙特卡罗方法计算EUA资产及投资组合的风险值。结果表明:(1)各时期两者间均存在单向或双向的先导关系,且联动性逐渐降低;(2)EUA序列用ARMA-GARCH-t模型拟合较好,而CER的非对称波动更倾向于ARMA-GJRGARCH-N模型;(3)三时期最优连接函数分别为t-Copula、Gumbel Copula和时变RG Copula,且尾部相关系数依次减小;(4)投资组合风险显著低于单个EUA资产风险,且风险降低比例较大。这些结论为以碳期货为投资主体的投资组合策略提供了决策依据。     

公共事业指数与工业指数的相关性研究

本文根据阿基米德类Copula函数与Kendall's秩相关系数的关系,通过非参数估计法得到描述沪市行业指数中的公共事业指数与工业指数组合相关结构的最佳Copula函数形式,即用来描述牛市特征的Gumbel Copula,以及相应的尾部相关系数.尾部相关性分析结果表明,两指数收益率之间存在明显的非对称的尾部相关性,而且是上尾相关程度强于下尾相关程度,说明两指数牛市期间的相关性强于熊市期间的相关性.从规避风险角度分析,公共事业指数/工业指数组合是有效的指数组合.     

Copula函数在风险管理中的应用研究--以上证A股与B股的相关结构分析为例

Copula函数为研究资产间的相关性提供了一种新方法,已被越来越多地应用于风险管理。基于对Copula函数的基本特点及其在风险管理中的作用分析,以及运用Copula函数对上海证券市场A股与B股指数的相关结构进行的分析,发现了与国外市场不同的研究结果:不论市场处于上升期或下跌期,上证A股与B股指数间均存在较强的尾部相关性。     

担保债权凭证之评价——多因子模型和KMV模型之探讨

探讨担保债权凭证商品之评价，包含缩减式模型及结构式模型两种研究方法；前者以多因子相关性模型，而後者以KMV模型为方法探讨之主轴。多因子相关性模型中资产的违约分配函数分别假设为指数、韦伯及Burr分配；再分别结合Gauss Copula或t5 Copula函数，估计商品的信用价差。实证分析以台湾“玉山银行债券资产证券化特殊目的信托2005—1受益证券”为例。实证研究结果发现，指数分配之信用价差估计值偏大，Burr分配估计值最小；t5 Copula函数之信用价差估计值都较Gauss Copula函数之估计值大。此外，将数据作适当调整後应用KMV模型之信用价差估计值比多因子相关性模型之估计值大。     

信用风险度量及其组合管理中的相关性研究——Copula函数的引进

综述了从传统过渡到现代的信用风险度量方法,并比较了它们的特点.提出组合管理思想是信用风险管理的方向,组合的相关性问题是研究重点.而Copula函数具有描述非线性相关的优势,使用Copula函数可以更加精确地度量信用风险.     

基于消费者物价指数的养老金担保成本评估模型

探讨了以消费者物价指数为最低担保的缴费确定型养老金计划,并在应用Copula函数度量投资组合回报率与消费者物价指数增长率的相关关系基础上,建立了评估这种担保成本的模型,最后给出了担保成本的随机模拟算法。     

基于Copula函数的尾部相关性度量

本文讨论了Copula函数的尾部相关性,当边缘分布是标准Frechet分布时,计算了Copula函数的尾部相关系数及缓慢变化函数,并且得出线性混合Copula函数的尾部相关性是几乎独立的或者较强的渐近相关.     

Energy portfolio risk management using time-varying extreme value copula methods

This work is concerned with the statistical modeling of the dependence structure between three energy commodity markets (WTI crude oil, natural gas and heating oil) using the concept of copulas and proposes a method for estimating the Value at risk (VaR) of energy portfolio based on the combination of time series models with models of the extreme value theory before fitting a copula. Each return series is modeled by AR-(FI) GARCH univariate model. Then, we fit the GPD distribution to the tails of the residuals to model marginal residuals distributions. The extreme value copula to the iid residuals is fitted and we simulate from it to construct N portfolios and estimate VaR. As a first step, the method is applied to a two-dimensional energy portfolio. In second step, we extend method in trivariate context to measure VaR of three-dimensional energy portfolio. Dependences between residuals are modeled using a trivariate nested Gumbel copulas. Methods proposed are compared with various univariate and multivariate conventional VaR methods. The reported results demonstrate that GARCH-t, conditional EVT and FIGARCH extreme value copula methods produce acceptable estimates of risk both for standard and more extreme VaR quantiles. Generally, copula methods are less accurate compared with their predictive performances in the case of portfolio composed of exchange market indices.     

Analyzing the dependence structure of various sectors in the Brazilian market: A Pair Copula Construction approach

In this paper we estimate the dependence structure between economic sectors in the Brazilian financial market through Pair Copula Construction. We use daily data from indices which represent telecommunications, energy, industrials, consumer, financial, basic materials and real estate sectors in BM&F/Bovespa. Results indicate predominance of student's t copula in structure. BB1, BB7, BB8, Frank and Joe copulas also fit into some relationships. Regarding dependence, tail measures obtain relevant values in most relationships. Lower tail dependence exceeds absolute, measured by Kendall's Tau, and upper tail in many cases, reflecting the asymmetry in some relationships. Further, in order to give robustness to these results, we forecast daily Value at Risk, considering distinct significance levels, of a portfolio composed of studied sectors through the estimated structure. Results allow one to conclude that VaR predictions are correct. These results permit business industry participants to construct portfolios with assets of these sectors under a proper diversification structure. Moreover, from an international point of view, investors who are interested in diversification could perform more sophisticated strategies in this country rather than simply trading the index.     

Mixed copula model with stochastic correlation for CDO pricing

This paper deals with the problem of pricing credit derivatives portfolio—CDO. The article assumes that the systematic factor and idiosyncratic factors subject to the fat-tailed mixed G-VG distribution instead of the traditional Gaussian distribution in the framework of factor model. Thus, the G-VG copula model is established. Stochastic correlation is also incorporated to account for the correlation skew problem. The semi-analytical expressions for conditional default probability, cumulative loss distribution function and expected tranche loss are explicitly derived in the G-VG copula models under large homogeneous portfolio approximation. Thus the CDO price can be determined. The numerical analysis is carried out and the properties of the new models with those of the traditional models are compared. Results show that new models not only provide a closer fit to the market quotes, but also bring more flexibility into the dependence structure.     

标准仓单质押组合的价格风险——基于中国农产品期货规范市场的实证研究

利用基于Copula函数的AR(p)-GARCH(p,q)模型计算的VaR能够对农产品标准仓单的价格风险进行准确度量。对大连商品交易所的典型期货交易品种——黄大豆一号、豆油、豆粕的期货合约日结算价进行了实证研究。研究结果显示:从对价格风险预测的盯市频率来看,时变VaR优于静态VaR,因此重视农产品价格风险的频次预测应替代传统风险判断的单次监测;从对风险因子间相依性结构的刻画来看,基于t-Copula函数计算的VaR优于基于正态Copula函数计算的VaR,因此质押物价格波动间的相关系数是度量组合风险时必须考虑的重要变量。     

Testing the Gaussian and Student's t copulas in a risk management framework

This paper introduces a semiparametric framework for selecting either a Gaussian or a Student's t copula in a d-dimensional setting. We compare the two models using four different approaches: (i) four goodness-of-fit graphical plots, (ii) a bootstrapped correlation matrix generated in each scenario with the empirical correlation matrix used as a benchmark, (iii) Value-at-Risk (VaR) and Expected Shortfall (ES) as risk measures, and (iv) co-Value-at-Risk (CoVaR) and Marginal Expected Shortfall (MES) as co-risk measures. We illustrate this four-step procedure using a portfolio of daily returns of six international stock indices. The VaR results confirm that the t-based copula model is an attractive alternative to the Gaussian. The ES analysis is less conclusive, and indicates that risk managers should jointly use the risk measure as well as the copula model. The results highlight the importance of promoting stress testing rather than ES in the risk management industry, particularly in the aftermath of a financial crisis.     

A novel nonlinear value-at-risk method for modeling risk of option portfolio with multivariate mixture of normal distributions

This paper proposes a novel nonlinear model for calculating Value-at-Risk (VaR) when the market risk factors of an option portfolio are heavy-tailed. A multivariate mixture of normal distributions is used to depict the heavy-tailed market risk factors and accordingly a closed form expression for the moment generating function that can reflect the change in option portfolio value can be derived. Moreover, in order to make use of the correlation between the characteristic function and the moment generating function, Fourier-Inversion method and adaptive Simpson rule with iterative algorithm of numerical integration into the nonlinear VaR model for option portfolio are applied for calculation of VaR values of option portfolio. VaR values of option portfolio obtained from different methods are compared. Numerical results of Fourier-Inversion method and Monte Carlo simulation method show that high accuracy VaR values can be obtained when risk factors have multivariate mixture of normal distributions than when they have normal distributions. Moreover, VaR values obtained by using the Fourier-Inversion method are not obviously different from VaR values obtained by using Monte Carlo simulation when market risk factors have normal distributions or multivariate mixture of normal distributions. However, the speed of computation is obviously faster when using Fourier-Inversion method, than when using Monte Carlo simulation method. Besides, Cornish Fisher method is faster and simpler than Monte Carlo simulation method or Fourier-Inversion method. However, this method does not offer high accuracy and cannot be used to calculate VaR values of option portfolio when market risk factors have heavy-tailed distributions.     

How to maximize golden opinions

In this article, we aim to model the level and structure of the dependence between the world's leading stock markets and those of the emerging market groups?–?Europe, Latin America and Far East. To this end we use a mixture model of Gaussian, Gumbel and Gumbel survival copulas. Our results indicate that none of the pairs of stock markets exhibit a right-tail dependence structure. All valid models exhibit a mixture of Gaussian and left-tail dependence structure. Our findings imply that Gaussian dependence structure is dominant in most of the models. The emerging equity markets in the European region exhibit the most significant dependence structure with the world leaders. Furthermore, most of the emerging equity markets have a significant dependence structure with the US stock market. We further compare our findings with the results of the conventional correlation coefficients and conclude the importance of using copula models in analysing the portfolio diversification opportunities. Our findings overall indicate two important remarks: First, the copula models reveal better indicators for global investors to establish a diversified portfolio; Second, international equity markets exhibit significant dependence, which leaves a smaller opportunity to benefit from international portfolio diversification.     

Diversification into Emerging Markets – An Australian and the US Perspective Using a Time‐varying Approach

Over the past two decades, a number of studies have examined the benefits of diversifying equity investments internationally, particularly into emerging markets. In the portfolio construction process, many researchers have criticised Markowitz's Portfolio Theory because of its inherent assumptions such as symmetric and constant correlations. In this study, we use a conditional copula model to estimate the time‐varying asymmetric correlations of stock markets and construct optimal portfolios by using estimated correlations. We find that optimised portfolios provide significant benefits for both Australian and the US investors. Out‐of‐sample results show Copula model provides results closer to the in‐sample‐estimated benefits of diversification. The results have important implications for portfolio managers who seek to diversify into emerging markets.     

Modelling VaR for foreign-asset portfolios in continuous time

VaR is widely viewed as a measure of market risk of a portfolio. The purpose of this article is to provide a VaR model for foreign-asset portfolios in continuous time. In the VaR model, the VaRs are not only a function of volatilities of asset returns and exchange rate but also a function of correlation coefficient between foreign assets and exchange rate. Moreover, by backtesting, the empirical results show that the new VaR model can efficiently evaluate the market risk of foreign-asset portfolios.