Modeling the Dependence Structure between Bonds and Stocks: A Multivariate Copula Approach

2009 ◽  
Author(s):  
Long Kang
Keyword(s):  
Dependence Structure ◽  
Copula Approach ◽  
Multivariate Copula

scholarly journals Application of Copula functions in statistics

2007 ◽  
Author(s):  
Αριστείδης Νικολουλόπουλος
Keyword(s):  
Discrete Data ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Multivariate Distribution ◽  
Dependence Structure ◽  
Copula Models ◽  
Cumulative Distribution Functions ◽  
Multivariate Discrete Distributions ◽  
Dependence Properties ◽  
Multivariate Copula

Studying associations among multivariate outcomes is an interesting problem in statistical science. The dependence between random variables is completely described by their multivariate distribution. When the multivariate distribution has a simple form, standard methods can be used to make inference. On the other hand one may create multivariate distributions based on particular assumptions, limiting thus their use. Unfortunately, these limitations occur very often when working with multivariate discrete distributions. Some multivariate discrete distributions used in practice can have only certain properties, as for example they allow only for positive dependence or they can have marginal distributions of a given form. To solve this problem copulas seem to be a promising solution. Copulas are a currently fashionable way to model multivariate data as they account for the dependence structure and provide a flexible representation of the multivariate distribution. Furthermore, for copulas the dependence properties can be separated from their marginal properties and multivariate models with marginal densities of arbitrary form can be constructed, allowing a wide range of possible association structures. In fact they allow for flexible dependence modelling, different from assuming simple linear correlation structures. However, in the application of copulas to discrete data marginal parameters affect dependence structure, too, and, hence the dependence properties are not fully separated from the marginal properties. Introducing covariates to describe the dependence by modelling the copula parameters is of special interest in this thesis. Thus, covariate information can describe the dependence either indirectly through the marginalparameters or directly through the parameters of the copula . We examine the case when the covariates are used both in marginal and/or copula parameters aiming at creating a highly flexible model producing very elegant dependence structures. Furthermore, the literature contains many theoretical results and families of copulas with several properties but there are few papers that compare the copula families and discuss model selection issues among candidate copula models rendering the question of which copulas are appropriate and whether we are able, from real data, to select the true copula that generated the data, among a series of candidates with, perhaps, very similar dependence properties. We examined a large set of candidate copula families taking intoaccount properties like concordance and tail dependence. The comparison is made theoretically using Kullback-Leibler distances between them. We have selected this distance because it has a nice relationship with log-likelihood and thus it can provide interesting insight on the likelihood based procedures used in practice. Furthermore a goodness of fit test based on Mahalanobisdistance, which is computed through parametric bootstrap, will be provided. Moreover we adopt a model averaging approach on copula modelling, based on the non-parametric bootstrap. Our intention is not to underestimate variability but add some additional variability induced by model selection making the precision of the estimate unconditional on the selected model. Moreover our estimates are synthesize from several different candidate copula models and thus they can have a flexible dependence structure. Taking under consideration the extended literature of copula for multivariate continuous data we concentrated our interest on fitting copulas on multivariate discrete data. The applications of multivariate copula models for discrete data are limited. Usually we have to trade off between models with limited dependence (e.g. only positive association) and models with flexible dependence but computational intractabilities. For example, the elliptical copulas provide a wide range of flexible dependence, but do not have closed form cumulative distribution functions. Thus one needs to evaluate the multivariate copula and, hence, a multivariate integral repeatedly for a large number of times. This can be time consuming but also, because of the numerical approach used to evaluate a multivariate integral, it may produce roundoff errors. On the other hand, multivariate Archimedean copulas, partially-symmetric m-variate copulas with m − 1 dependence parameters and copulas that are mixtures of max-infinitely divisible bivariate copulas have closed form cumulative distribution functions and thus computations are easy, but allow only positive dependence among the random variables. The bridge of the two above-mentioned problems might be the definition of a copula family which has simple form for its distribution function while allowing for negative dependence among the variables. We define such a multivariate copula family exploiting the use of finite mixture of simple uncorrelated normal distributions. Since the correlation vanishes, the cumulative distribution is simply the product of univariate normal cumulative distribution functions. The mixing operation introduces dependence. Hence we obtain a kind of flexible dependence, and allow for negative dependence.

scholarly journals Modeling Portfolio Credit Risk Taking into Account the Default Correlations Using a Copula Approach: Implementation to an Italian Loan Portfolio

2020 ◽  
Vol 13 (6) ◽  
pp. 129
Author(s):  
Annalisa Di Clemente
Keyword(s):  
Credit Risk ◽  
Value At Risk ◽  
Risk Measure ◽  
Dependence Structure ◽  
Quantitative Methodology ◽  
Loan Portfolio ◽  
Recovery Rates ◽  
Asset Return ◽  
Portfolio Credit Risk ◽  
Copula Approach

This work aims to illustrate an advanced quantitative methodology for measuring the credit risk of a loan portfolio allowing for diversification effects. Also, this methodology can allocate the credit capital coherently to each counterparty in the portfolio. The analytical approach used for estimating the portfolio credit risk is a binomial type based on a Monte Carlo Simulation. This method takes into account the default correlations among the credit counterparties in the portfolio by following a copula approach and utilizing the asset return correlations of the obligors, as estimated by rigorous statistical methods. Moreover, this model considers the recovery rates as stochastic and dependent on each other and on the time until defaults. The methodology utilized for coherently allocating credit capital in the portfolio estimates the marginal contributions of each obligor to the overall risk of the loan portfolio in terms of Expected Shortfall (ES), a risk measure more coherent and conservative than the traditional measure of Value-at-Risk (VaR). Finally, this advanced analytical structure is implemented to a hypothetical, but typical, loan portfolio of an Italian commercial bank operating across the overall national country. The national loan portfolio is composed of 17 sub-portfolios, or geographic clusters of credit exposures to 10,500 non-financial firms (or corporates) belonging to each geo-cluster or sub-portfolio. The outcomes, in terms of correlations, portfolio risk measures and capital allocations obtained from this advanced analytical framework, are compared with the results found by implementing the Internal Rating Based (IRB) approach of Basel II and III. Our chief conclusion is that the IRB model is unable to capture the real credit risk of loan portfolios because it does not take into account the actual dependence structure among the default events, and between the recovery rates and the default events. We underline that the adoption of this regulatory model can produce a dangerous underestimation of the portfolio credit risk, especially when the economic uncertainty and the volatility of the financial markets increase.

scholarly journals Examining the Interdependence between the Exchange Rates of China and ASEAN Countries: A Canonical Vine Copula Approach

2019 ◽  
Vol 11 (19) ◽  
pp. 5487 ◽  
Author(s):  
Liu ◽  
Wang ◽  
Sriboonchitta
Keyword(s):  
Exchange Rates ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Positive Dependence ◽  
Asymmetric Dependence ◽  
Before And After ◽  
Copula Approach ◽  
Asean Countries ◽  
Vine Copula ◽  
Vine Copulas

Based on the canonical vine (C-vine) copula approach, this paper examines the interdependence between the exchange rates of the Chinese Yuan (CNY) and the currencies of major Association of Southeast Asian Nations (ASEAN) countries. The differences in the dependence structure and degree between currencies before and after the Belt and Road (B&R) Initiative were compared in order to investigate the changing role of the Renminbi (RMB) in the ASEAN foreign exchange markets. The results indicate a positive dependence between the exchange rate returns of CNY and the currencies of ASEAN countries and show the rising power of RMB in the regional currency markets after the B&R Initiative was launched. Besides this, the Malaysian Ringgit proved to be most relevant to the other ASEAN currencies, thus playing an important role in the stability of regional financial markets. Moreover, evidence of tail dependence was found in the returns of three currency pairs after the B&R Initiative, which implies the presence of asymmetric dependence between exchange rates. The results from time-varying C-vine copulas further confirmed the robustness of the results from the static C-vine copulas.

Diversification in Firm Valuation: A Multivariate Copula Approach

2011 ◽  
Author(s):  
Stefan Erdorf ◽  
Thomas Hartmann-Wendels ◽  
Nicolas Heinrichs
Keyword(s):  
Firm Valuation ◽  
Copula Approach ◽  
Multivariate Copula
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