典型事实、混合Copula函数与金融市场相依结构研究

运用ARFIMA-FIAPARCH-skst模型对沪深300指数和香港恒生指数建立收益-波动模型, 然后结合估计的参数对模型进行修正以确立最终模型, 排除金融市场典型事实对相依关系的影响, 进而运用由Clayton、Frank和Gumbel组成的混合copula模型对相依结构进行建模。研究结果表明:内地市场和香港市场均未观察到显著的杠杆效应;由Clayton、Frank和Gumbel组成的混合Copula模型能够准确地描述两个市场之间的相依结构, 且两个市场下尾相依关系要强于上尾的相依关系, 通过动态混合copula也验证了这一明显的非对称关系。     

旱灾对粮食生产影响的非线性动态效应评估

自然灾害严重威胁粮食安全,因此科学地理解和认识自然灾害与粮食产量之间的关系至为重要。基于时变Copula函数方法的实证研究结果表明,水稻、小麦、玉米在低产时和旱灾的尾部相关系数分别为0.52、0.15、0.58,但是水稻、玉米在高产时和旱灾比率的尾部相关系数近似为0,小麦在高产时和旱灾的尾部相关系数仅为0？06,这意味着粮食单产与旱灾的关联性表现出非对称性。旱灾对粮食产量影响的时变性也因不同作物而异。对于水稻而言,随着技术水平的提高,旱灾与水稻单产的关联性存在显著的下降趋势;但是,旱灾与小麦、玉米单产的关联性并没有表现出随时间推移而下降的趋势。     

A Bottom-Up Dynamic Model of Portfolio Credit Risk with Stochastic Intensities and Random Recoveries

In Bielecki et al. (2014a Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014a ). Dynamic hedging of portfolio credit risk in a markov copula model . J. Optimiz. Theor. Applic . doi: DOI 10.1007/s10957-013-0318-4 (forthcoming) .[Crossref] , [Google Scholar]), the authors introduced a Markov copula model of portfolio credit risk where pricing and hedging can be done in a sound theoretical and practical way. Further theoretical backgrounds and practical details are developed in Bielecki et al. (2014b Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014b ). A bottom-up dynamic model of portfolio credit risk - Part I: Markov copula perspective . In: Recent Adv. Fin. Eng. 2012 , World Scientific (preprint version available at http://dx.doi.org/10.2139/ssrn.1844574) . [Google Scholar],c) where numerical illustrations assumed deterministic intensities and constant recoveries. In the present paper, we show how to incorporate stochastic default intensities and random recoveries in the bottom-up modeling framework of Bielecki et al. (2014a Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014a ). Dynamic hedging of portfolio credit risk in a markov copula model . J. Optimiz. Theor. Applic . doi: DOI 10.1007/s10957-013-0318-4 (forthcoming) .[Crossref] , [Google Scholar]) while preserving numerical tractability. These two features are of primary importance for applications like CVA computations on credit derivatives (Assefa et al., 2011 Assefa , S. , Bielecki , T. R. , Crépey , S. , Jeanblanc , M. ( 2011 ). CVA computation for counterparty risk assessment in credit portfolios . In: Bielecki , T.R. , Brigo , D. , Patras , F. , Eds., Credit Risk Frontiers . Hoboken : Wiley/Bloomberg-Press . [Google Scholar]; Bielecki et al., 2012 Bielecki , T. R. , Crépey , S. , Jeanblanc , M. , Zargari , B. ( 2012 ). Valuation and Hedging of CDS counterparty exposure in a markov copula model . Int. J. Theoret. Appl. Fin. 15 ( 1 ): 1250004 .[Crossref] , [Google Scholar]), as CVA is sensitive to the stochastic nature of credit spreads and random recoveries allow to achieve satisfactory calibration even for “badly behaved” data sets. This article is thus a complement to Bielecki et al. (2014a Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014a ). Dynamic hedging of portfolio credit risk in a markov copula model . J. Optimiz. Theor. Applic . doi: DOI 10.1007/s10957-013-0318-4 (forthcoming) .[Crossref] , [Google Scholar]), Bielecki et al. (2014b Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014b ). A bottom-up dynamic model of portfolio credit risk - Part I: Markov copula perspective . In: Recent Adv. Fin. Eng. 2012 , World Scientific (preprint version available at http://dx.doi.org/10.2139/ssrn.1844574) . [Google Scholar]) and Bielecki et al. (2014c Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014c ). A bottom-up dynamic model of portfolio credit risk - Part II: Common-shock interpretation, calibration and hedging issues . Recent Adv. Fin. Eng. 2012 , World Scientific (preprint version available at http://dx.doi.org/10.2139/ssrn.2245130) . [Google Scholar]).     

Analysis of directional dependence using asymmetric copula-based regression models

The directional dependence between variables using asymmetric copula regression has drawn much attention in recent years. There are, however, some critical issues which have not been properly addressed in regards to the statistical inference of the directional dependence. For example, the previous use of asymmetric copulas failed to fully capture the dependence patterns between variables, and the method used for the parameter estimation was not optimal. In addition, no method was considered for selecting a suitable asymmetric copula or for computing the general measurements of the directional dependence when there are no closed-form expressions. In this paper, we propose a generalized multiple-step procedure for the full inference of the directional dependence in joint behaviour based on the asymmetric copula regression. The proposed procedure utilizes several novel methodologies that have not been considered in the literature of the analysis of directional dependence. The performance and advantages of the proposed procedure are illustrated using two real data examples, one from biological research on histone genes, and the other from developmental research on attention deficit hyperactivity disorder.     

Quantile regression based on a weighted approach under semi-competing risks data

In this article, we investigate the quantile regression analysis for semi-competing risks data in which a non-terminal event may be dependently censored by a terminal event. Due to the dependent censoring, the estimation of quantile regression coefficients on the non-terminal event becomes difficult. In order to handle this problem, we assume Archimedean Copula to specify the dependence of the non-terminal event and the terminal event. Portnoy [Censored regression quantiles. J Amer Statist Assoc. 2003;98:1001–1012] considered the quantile regression model under right-censoring data. We extend his approach to construct a weight function, and then impose the weight function to estimate the quantile regression parameter for the non-terminal event under semi-competing risks data. We also prove the consistency and asymptotic properties for the proposed estimator. According to the simulation studies, the performance of our proposed method is good. We also apply our suggested approach to analyse a real data.     

基于极值理论和多元Copula函数的商业银行操作风险计量研究

基于操作风险呈厚尾分布的特征,本文按照巴塞尔协议的要求,采用POT极值模型分别估计了多个操作风险单元的边缘分布,然后用多元Copula函数来刻画这些操作风险单元之间的关联性并计算在险价值。通过对中国商业银行1990-2010年操作风险数据的实证分析表明,Clayton Copula能更好地反映各操作风险单元之间的相关性结构,且采用Copula考虑操作风险相关性下的VaR值要比简单加总下的VaR值减少约32.3%。因此,应用Copula函数计量操作风险相关性,不仅可以提高估计的准确性,还能够达到资产组合的风险分散化效应,减少操作风险资本要求,为商业银行提升盈利能力创造条件。     

Ordering results on extremes of scaled random variables with dependence and proportional hazards

This study deals with random variables equipped with Archimedean copulas and following scale proportional hazards (SPHs) or revered hazards models. We build the usual stochastic order both between minimums of two SPHs samples with Archimedean survival copulas and between maximums from two scale proportional reversed hazards (PRHs) samples with Archimedean copulas. The hazard rate order between minimums of independent SPHs samples and the reversed hazard rate order between maximums of independent scale PRHs samples are both derived. Also we have a discussion on the dispersive order between minimums from samples with a common Archimedean survival copula. The present results either generalize or improve some related ones in the recent literature.     

Modeling multivariate cybersecurity risks

Modeling cybersecurity risks is an important, yet challenging, problem. In this paper, we initiate the study of modeling multivariate cybersecurity risks. We develop the first statistical approach, which is centered at a Copula-GARCH model that uses vine copulas to model the multivariate dependence exhibited by real-world cyber attack data. We find that ignoring the due multivariate dependence causes a severe underestimation of cybersecurity risks. Both simulation and empirical studies show that the proposed approach leads to accurate predictions of multivariate cybersecurity risks.     

Quantile residual life regression based on semi-competing risks data

This paper investigates the quantile residual life regression based on semi-competing risk data. Because the terminal event time dependently censors the non-terminal event time, the inference on the non-terminal event time is not available without extra assumption. Therefore, we assume that the non-terminal event time and the terminal event time follow an Archimedean copula. Then, we apply the inverse probability weight technique to construct an estimating equation of quantile residual life regression coefficients. But, the estimating equation may not be continuous in coefficients. Thus, we apply the generalized solution approach to overcome this problem. Since the variance estimation of the proposed estimator is difficult to obtain, we use the bootstrap resampling method to estimate it. From simulations, it shows the performance of the proposed method is well. Finally, we analyze the Bone Marrow Transplant data for illustrations.