Copula 在商业银行组合信用风险度量中的应用

本文对比分析了正态Copula函数、t-Copula函数、Gumbel Copula函数、Frank Copula函数和Clayton Copula函数对资产组合分布尾部特征的描述特点并选择其中四种Copula函数与KMV模型相结合对商业银行组合信用风险进行度量,度量结果显示Clayton—Copula相关模式假设下的商业银行组合信用风险度量结果最符合实际。     

组合违约相关性研究综述

积极主动的组合信用风险管理技术和产品近年在国外获得迅猛发展,组合违约风险及其相关性研究成为实施此类技术和产品的关键问题。在介绍违约相关性度量指标发展的基础上,梳理了目前国外关于组合违约风险及其相关研究的现状,分析了相关研究的不足和发展趋势。     

西方商业银行行业信用风险管理经验及其启示

西方商业银行普遍认为行业信用风险的实质即为行业信用集中风险,行业信用风险管理的核心就是保持分散化、避免行业过度集中。在此基础上,形成了包括行业信用风险识别、度量、管理手段(或工具)、监测、报告等内容的管理框架。其中,开发信用组合模型以准确度量行业信用风险,广泛运用行业信用限额、信用衍生工具等有效手段或工具两方面最为突出。我国商业银行应借鉴国外成功经验,通过加强行业分析与监测工作、提高行业信用风险度量精度、综合利用各种管理手段与工具,逐步提高行业信用风险管理水平。     

西方商业银行行业信用风险管理经验及其启示

西方商业银行普遍认为行业信用风险的实质即为行业信用集中风险，行业信用风险管理的核心就是保持分散化、避免行业过度集中。在此基础上，形成了包括行业信用风险识别、度量、管理手段、监测、报告等内容的管理框架。其中，开发信用组合模型以准确度量行业信用风险，广泛运用行业信用限额、信用衍生工具等有效手段两方面最为突出。我国商业银行应借鉴国外成功经验，通过加强行业分析与监测工作、提高行业信用风险度量精度、综合利用各种管理手段，逐步提高行业信用风险管理水平。     

基于Copula方法的房地产信贷组合风险度量研究

将房地产开发商贷款和个人住房贷款这两类贷款看成一个信贷组合,考虑了两类信贷风险间的非线性相关关系,构建了基于Copula函数的两类贷款组合的信用风险度量模型和度量两类房地产信贷组合信用风险的仿真模拟步骤,并进行了实例分析。实例研究结果表明,Copula函数的应用能灵活处理两类房地产信贷风险间的相关关系,风险度量结果较完全正相关和完全独立两种情况更准确。     

我国上市公司信用风险度量及影响因素分析

首先利用KMV模型度量了样本公司的信用风险,接着以资产规模、股权结构、成长能力、流动性、行业前景、公司经营状况作为解释变量、公司违约距离作为被解释变量,建立了多元线性回归模型。实证分析表明,资产规模、股权集中度、成长能力与信用风险正相关;国有股比重、流动性与信用风险负相关;行业前景和公司经营状况对信用风险也有显著影响。     

基于半参数Copula的信用风险实证分析

随着金融市场的不断深入和发展,金融相关性分析越来越复杂,Copula技术以处理非正态联合分布的优良性质得到了国内外学术研究的广泛关注。本文通过非参数的核密度估计法估计Copula的边缘分布,用两阶段最大化方法确定Copula的参数和核密度估计的带宽,用Copula理论更加准确地描述资产的相关性,从而更加准确地量化金融市场的风险,并在KMV的框架下,讨论中国A股市场投资组合的信用风险。     

信用风险度量的CreditMetrics与KMV模型的比较研究

随着金融改革的深化和发展,信用风险度量已经越来越值得重视。文章介绍最常用的两种先进的信用风险管理模型,详尽地阐述了两个模型度量信用风险所用的方法,并在比较的基础上,指出两个模型的优点以及存在的不足,以更好地用于风险度量。     

信用风险度量的CreditMetrics与KMV模型的比较研究

随着金融改革的深化和发展,信用风险度量已经越来越值得重视。文章介绍最常用的两种先进的信用风险管理模型,详尽地阐述了两个模型度量信用风险所用的方法,并在比较的基础上,指出两个模型的优点以及存在的不足,以更好地用于风险度量。     

信用担保机构信用风险模型探析

本文通过对信用担保机构信用风险特性和四大现代信用风险度量模型的全面分析和探讨,结合我国信用担保机构进行信用风险度量时存在的主要障碍,提出了我国信用担保机构信用风险度量模型的选择原则和发展思路。     

Checking for asymmetric default dependence in a credit card portfolio: A copula approach

Traditional credit risk models adopt the linear correlation as a measure of dependence and assume that credit losses are normally-distributed. However some studies have shown that credit losses are seldom normal and the linear correlation does not give accurate assessment for asymmetric data. Therefore it is possible that many credit models tend to misestimate the probability of joint extreme defaults.This paper employs Copula Theory to model the dependence across default rates in a credit card portfolio of a large UK bank and to estimate the likelihood of joint high default rates. Ten copula families are used as candidates to represent the dependence structure. The empirical analysis shows that, when compared to traditional models, estimations based on asymmetric copulas usually yield results closer to the ratio of simultaneous extreme losses observed in the credit card portfolio.Copulas have been applied to evaluate the dependence among corporate debts but this research is the first paper to give evidence of the outperformance of copula estimations in portfolios of consumer loans. Moreover we test some families of copulas that are not typically considered in credit risk studies and find out that three of them are suitable for representing dependence across credit card defaults.     

Copula dynamics in CDOs

Values of tranche spreads of collateralized debt obligations (CDOs) are driven by the joint default performance of the assets in the collateral pool. The dependence between the entities in the portfolio mainly depends on current economic conditions. Therefore, a correlation implied from tranches can be seen as a measure of the general situation of the credit market. We analyse the European market of standardized CDOs using tranches of the iTraxx index in the periods before and during the global financial crisis. We investigate the evolution of the correlations using different copula models: the standard Gaussian, the NIG, the double-t, and the Gumbel copula model. After calibration of these models, one obtains a time varying vector of parameters. We analyse the dynamic pattern of these coefficients. That enables us to forecast future parameters and consequently calculate Value-at-Risk measures for iTraxx Europe tranches.     

Contagion models a la carte: which one to choose?

We propose a copula contagion mixture model for correlated default times. The model includes the well-known factor, copula, and contagion models as its special cases. The key advantage of such a model is that we can study the interaction of different models and their pricing impact. Specifically, we model the default times of the underlying names in a reference portfolio to follow contagion intensity processes with exponential decay coupled with a copula dependence structure. We also model the default time of the counterparty and its dependence structure with the reference portfolio. Numerical tests show that correlation and contagion have an enormous joint impact on the rates of CDO tranches and the corresponding credit value adjustments are extremely high to compensate for the wrong-way risk.     

信用衍生产品隐含相关性结构研究

信用衍生产品在信用风险管理领域日益流行。其标的资产池的违约相关性结构在信用衍生产品定价、信用组合多元化和信用组合风险管理中具有重要作用。本文通过复制信用衍生产品中存在的隐含相关性微笑曲线现象,研究信用衍生产品标的信用的违约相关性结构。结果表明,本文使用的研究方法能够较好地给出标的信用合约间的违约相关性结构,同时,本文从风险管理角度研究了算法的有效性、计算效率和稳健性,并给出了相应的解释。     

A mixed C-vine copula model for hedging price and volumetric risk in wind power trading

When energy trading companies enter into long-term agreements with wind power producers, where a fixed price is paid for the fluctuating production, they are facing a joint price and volumetric risk. Since the pay-off of such agreements is non-linear, a hedging portfolio would ideally consist of not only forwards, but also a basket of e.g. call and put options. Illiquidity and an almost non-existent market for options challenge however the optimal hedging of joint price and volumetric risk in many market places. Here, we consider the case of the Danish power market, and exploit its strong positive correlation with the much more liquid German market to construct a proxy hedge. We propose a three-dimensional mixed vine copula to model the evolution of the Danish and German spot electricity prices and the Danish wind power production. We construct a realistic hedging portfolio by identifying various instruments available in the market, such as real options in the form of the right to transfer electricity across the border and the right to convert electricity to heat. Using the proposed vine copula to determine optimal hedging decisions, we show that significant benefits are to be drawn by extending the hedging portfolio with the proposed instruments.     

CDO pricing with nested Archimedean copulas

Companies in the same industry sector are usually more correlated than firms in different sectors, as they are similarly affected by macroeconomic effects, political decisions, and consumer trends. Despite the many stock return models taking this fact into account, there are only a few credit default models that take it into consideration. In this paper we present a default model based on nested Archimedean copulas that is able to capture hierarchical dependence structures among the obligors in a credit portfolio. Nested Archimedean copulas have a surprisingly simple and intuitive interpretation. The dependence among all companies in the same sector is described by an inner copula and the sectors are then coupled via an outer copula. Consequently, our model implies a larger default correlation for companies in the same industry sector than for companies in different sectors. A calibration to CDO tranche spreads of the European iTraxx portfolio is performed to demonstrate the fitting capability of the model. This portfolio consists of CDS on 125 companies from six different industry sectors and is therefore an excellent portfolio for a comparison of our generalized model with a traditional copula model of the same family that does not take different sectors into account.     

Stock market dependence in crisis periods: Evidence from oil price shocks and the Qatar blockade

This paper examines the correlation and the dependence patterns of the Qatar stock market with other markets using copula statistical theory and exploiting new datasets covering the period August 1998 to June 2018. To examine the crisis –specific change in the average degree of dependence we decomposed the data into the time periods before and after oil price shocks and the 2017 political crisis among the Gulf Cooperation Council members (i.e. the Qatari blockade). Our findings from the static copula modelling show that the correlations between the Qatari and the other stock markets significantly change after the oil price and the blockade crisis as well. The degree of change in the correlation is time varying and differs from county-group to another. Moreover, our findings reveals that the 2008 global financial crisis has a stronger impact than the price shocks and political crisis. The findings of the paper are of interest and allow for formulating a reliable and dynamic portfolio design framework for investors and risk managers.     

Portfolio construction incorporating asymmetric dependence structures: a user's guide

We outline a method of portfolio selection incorporating asymmetric dependency structures using copula functions. Assuming normally distributed marginal returns, we illustrate how asymmetric return correlations affect the efficient frontier and subsequent portfolio performance under a dynamic rebalancing framework. Implementing this methodology within the context of tactically allocating a small set of market indices, we demonstrate several key findings. First, we establish the manner by which the efficient frontier constructed under asymmetric dependence differs from a mean‐variance frontier. By establishing a paper portfolio based on these differences, we find that asymmetric correlation structures do have real economic value. The primary source of this economic value is the ability to better protect portfolio value and reduce the size of any erosion in return relative to the normal portfolio when asymmetric return correlations are accounted for.     

Investigating the dependence structure between credit default swap spreads and the U.S. financial market

Under Basel II framework, credit risk assessment is of high significance in the light of correlation risk. Correlation risk is often envisioned along with business conditions and financial market’s impact. We employ copula methodology to identify the dependence structures that may exist between market risk fundamentals and credit risk fundamentals. Considering credit derivative spreads as credit risk fundamentals and market data as market risk determinants, we describe and quantify the asymmetric link prevailing between credit risk and market risk. Credit risk is negatively linked with market price risk whereas it becomes positively linked with market volatility risk. Such patterns give rise to interesting asymmetric dependence structures between both risk sources. We are then able to balance reliably market price risk with market volatility feedback, the market trend supporting a common correlation between securities. In the light of the previous trade-off, we propose also a simple credit risk management rule.     

Tail Dependence in International Real Estate Securities Markets

??Tail dependence?? characterizes the cross market linkages during stressful times. Analyzing tail dependence is of primary interest to portfolio managers who systematically monitor the co-movements of asset markets. However, the relevant literature on real estate securities markets is very thin. Our study extends the literature by using the flexible symmetrized Joe-Clayton (SJC) copula to estimate the tail dependences for six major global markets (U.S., U.K., Japan, Australia, Hong Kong, and Singapore). In implementing the SJC copula, we model the marginal distributions of returns through a semi-parametric method which has never been applied to real estate returns. Our major findings suggest that international markets display different strength and dynamics of tail dependence. We extensively discuss the implications of our findings for financial practices such as portfolio tail diversifications, portfolio selections, portfolio risk management and hedging strategies. Our study also demonstrates that the widely used linear correlation is an inadequate measure of market linkages, especially during periods of crisis.