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Beyond Correlation: Extreme Comovements Between Financial Assets
, 2002
"... This paper inv estigates the potential for extreme comov ements between financial assets by directly testing the underlying dependence structure. In particular, a tdependence structure, deriv ed from the Student t distribution, is used as a proxy to test for this extremal behav#a(0 Tests in three ..."
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Cited by 61 (5 self)
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This paper inv estigates the potential for extreme comov ements between financial assets by directly testing the underlying dependence structure. In particular, a tdependence structure, deriv ed from the Student t distribution, is used as a proxy to test for this extremal behav#a(0 Tests in three di#erent markets (equities, currencies, and commodities) indicate that extreme comov ements are statistically significant. Moreov er, the "correlationbased" Gaussian dependence structure, underlying the multiv ariate Normal distribution, is rejected with negligible error probability when tested against the tdependencealternativ e. The economic significance of these results is illustratedv ia three examples: comov ements across the G5 equity markets; portfoliov alueatrisk calculations; and, pricing creditderiv ativ es. JEL Classification: C12, C15, C52, G11. Keywords: asset returns, extreme comov ements, copulas, dependence modeling, hypothesis testing, pseudolikelihood, portfolio models, risk management. # The authorsw ould like to thankAndrew Ang, Mark Broadie, Loran Chollete, and Paul Glasserman for their helpful comments on an earlier version of this manuscript. Both authors arewS; the Columbia Graduate School of Business, email: {rm586,assaf.zeevi}@columbia.edu, current version available at www.columbia.edu\# rm586 1 Introducti7 Specification and identification of dependencies between financial assets is a key ingredient in almost all financial applications: portfolio management, risk assessment, pricing, and hedging, to name but a few. The seminal work of Markowitz (1959) and the early introduction of the Gaussian modeling paradigm, in particular dynamic Brownianbased models, hav e both contributed greatly to making the concept of co rrelatio almost synony...
Copula goodnessoffit testing: an overview and power comparison
, 2007
"... Abstract. Several copula goodnessoffit approaches are examined, three of which are proposed in this paper. Results are presented from an extensive Monte Carlo study, where we examine the effect of dimension, sample size and strength of dependence on the nominal level and power of the different app ..."
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Cited by 41 (1 self)
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Abstract. Several copula goodnessoffit approaches are examined, three of which are proposed in this paper. Results are presented from an extensive Monte Carlo study, where we examine the effect of dimension, sample size and strength of dependence on the nominal level and power of the different approaches. While no approach is always the best, some stand out and conclusions and recommendations are made. A novel study of pvalue variation due to permuation order, for approaches based on Rosenblatt’s transformation is also carried out. Results show significant variation due to permutation order for some of the approaches based on this transform. However, when approaching rejection regions, the additional variation is negligible.
CopulaBased models for financial time series
, 2007
"... This paper presents an overview of the literature on applications of copulas in the modelling of financial time series. Copulas have been used both in multivariate time series analysis, where they are used to charaterise the (conditional) crosssectional dependence between individual time series, ..."
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Cited by 39 (0 self)
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This paper presents an overview of the literature on applications of copulas in the modelling of financial time series. Copulas have been used both in multivariate time series analysis, where they are used to charaterise the (conditional) crosssectional dependence between individual time series, and in univariate time series analysis, where they are used to characterise the dependence between a sequence of observations of a scalar time series process. The paper includes a broad, brief, review of the many applications of copulas in finance and economics.
Selecting copulas for risk management.
, 2007
"... Abstract Copulas offer financial risk managers a powerful tool to model the dependence between the different elements of a portfolio and are preferable to the traditional, correlationbased approach. In this paper we show the importance of selecting an accurate copula for risk management. We extend ..."
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Cited by 18 (0 self)
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Abstract Copulas offer financial risk managers a powerful tool to model the dependence between the different elements of a portfolio and are preferable to the traditional, correlationbased approach. In this paper we show the importance of selecting an accurate copula for risk management. We extend standard goodnessoffit tests to copulas. Contrary to existing, indirect tests, these tests can be applied to any copula of any dimension and are based on a direct comparison of a given copula with observed data. For a portfolio consisting of stocks, bonds and real estate, these tests provide clear evidence in favor of the Student's t copula, and reject both the correlationbased Gaussian copula and the extreme valuebased Gumbel copula. In comparison with the Student's t copula, we find that the Gaussian copula underestimates the probability of joint extreme downward movements, while the Gumbel copula overestimates this risk. Similarly we establish that the Gaussian copula is too optimistic on diversification benefits, while the Gumbel copula is too pessimistic. Moreover, these differences are significant.
Goodnessoffit tests for copulas
 Physica A
, 2005
"... Copulas are often used in finance to characterize the dependence between assets. However, a choice of the functional form for the copula is an open question in the literature. This paper develops a goodnessoffit test for copulas based on positive definite bilinear forms. The suggested test avoids ..."
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Cited by 12 (2 self)
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Copulas are often used in finance to characterize the dependence between assets. However, a choice of the functional form for the copula is an open question in the literature. This paper develops a goodnessoffit test for copulas based on positive definite bilinear forms. The suggested test avoids the use of plugin estimators that is the common practice in the literature. The test statistics can be consistently computed on the basis of Vestimators even in the case of large dimensions. The test is applied to a dataset of US large cap stocks to assess the performance of the Gaussian copula for the portfolios of assets of various dimension. The Gaussian copula appears to be inadequate to characterize the dependence between assets.
Forecasting VaR and Expected Shortfall using Dynamical Systems: A Risk Management Strategy
, 2009
"... Using nonparametric and parametric models, we show that the bivariate distribution of an Asian portfolio is not stable along all the period under study. We suggest several dynamic models to compute two market risk measures, the Value at Risk and the Expected Shortfall: the RiskMetrics methodology, ..."
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Cited by 7 (6 self)
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Using nonparametric and parametric models, we show that the bivariate distribution of an Asian portfolio is not stable along all the period under study. We suggest several dynamic models to compute two market risk measures, the Value at Risk and the Expected Shortfall: the RiskMetrics methodology, the Multivariate GARCH models, the Multivariate MarkovSwitching models, the empirical histogram and the dynamic copulas. We discuss the choice of the best method with respect to the policy management of bank supervisors. The copula approach seems to be a good compromise between all these models. It permits taking financial crises into account and obtaining a low capital requirement during the most important crises.
2002a, Investigating extreme dependences: Concepts and tools, Working paper, http : //papers.ssrn.com/paper.taf?abstract id
"... We investigate the relative information content of six measures of dependence between two random variables X and Y for large or extreme events for several models of interest for financial time series. The six measures of dependence are respectively the linear correlation ρ + v and Spearman’s rho ρs( ..."
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Cited by 7 (1 self)
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We investigate the relative information content of six measures of dependence between two random variables X and Y for large or extreme events for several models of interest for financial time series. The six measures of dependence are respectively the linear correlation ρ + v and Spearman’s rho ρs(v) conditioned on signed exceedance of one variable above the threshold v, or on both variables (ρu), the linear correlation ρs v conditioned on absolute value exceedance (or large volatility) of one variable, the socalled asymptotic taildependence λ and a probabilityweighted tail dependence coefficient ¯ λ. The models are the bivariate Gaussian distribution, the bivariate Student’s distribution, and the factor model for various distributions of the factor. We offer explicit analytical formulas as well as numerical estimations for these six measures of dependence in the limit where v and u go to infinity. This provides a quantitative proof that conditioning on exceedance leads to conditional correlation coefficients that may be very different from the unconditional correlation and gives a straightforward mechanism for fluctuations or changes of correlations, based on fluctuations of volatility or changes of trends. Moreover, these various measures of dependence exhibit different and sometimes opposite behaviors, suggesting that, somewhat similarly to risks whose adequate characterization requires an extension beyond the restricted onedimensional measure in terms of the variance (volatility) to include all higher order cumulants or more generally the knowledge of the full distribution, taildependence has also a multidimensional character.
Outofsample Comparison of Copula Specifications
 in Multivariate Density Forecasts”. Australian School of Business Research Paper No. 2008 ECON
, 2008
"... Most TI discussion papers can be downloaded at ..."
The Euro and European financial market integration
 Money Macro and Finance (MMF) Research Group Conference 49
, 2004
"... We use a timevarying copula model to investigate the impact of the introduction of the Euro on the dependence between seventeen European stock markets during the period 19942003. The model is implemented with a GJRGARCHt model for the marginal distributions and the Gaussian copula for the joint ..."
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Cited by 6 (0 self)
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We use a timevarying copula model to investigate the impact of the introduction of the Euro on the dependence between seventeen European stock markets during the period 19942003. The model is implemented with a GJRGARCHt model for the marginal distributions and the Gaussian copula for the joint distribution, which allows capturing timevarying, nonlinear relationships. The results show that within the euro area, market dependence increased after the introduction of the common
Tail dependence of factor models
 Journal of Risk
, 2004
"... Using the framework of factor models, we establish the general expression of the coefficient of tail dependence between the market and a stock (i.e., the probability that the stock incurs a large loss, assuming that the market has also undergone a large loss) as a function of the parameters of the u ..."
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Cited by 4 (0 self)
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Using the framework of factor models, we establish the general expression of the coefficient of tail dependence between the market and a stock (i.e., the probability that the stock incurs a large loss, assuming that the market has also undergone a large loss) as a function of the parameters of the underlying factor model and of the tail parameters of the distributions of the factor and of the idiosyncratic noise of each stock. Our formula holds for arbitrary marginal distributions and in addition does not require any parameterization of the multivariate distributions of the market and stocks. The determination of the extreme parameter, which is not accessible by a direct statistical inference, is made possible by the measurement of parameters whose estimation involves a significant part of the data with sufficient statistics. Our empirical tests find a good agreement between the calibration of the tail dependence coefficient and the realized large losses over the period from 1962 to 2000. Nevertheless, a bias is detected which suggests the presence of an outlier in the form of the crash of October 1987.