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Empirical properties of asset returns: stylized facts and statistical issues
 Quantitative Finance
, 2001
"... We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then des ..."
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Cited by 188 (3 self)
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We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then described: distributional properties, tail properties and extreme fluctuations, pathwise regularity, linear and nonlinear dependence of returns in time and across stocks. Our description emphasizes properties common to a wide variety of markets and instruments. We then show how these statistical properties invalidate many of the common statistical approaches used to study financial data sets and examine some of the statistical problems encountered in each case.
Asymmetric correlations of equity portfolios
 Journal of Financial Economics
, 2002
"... University. We are especially grateful for suggestions from Geert Bekaert, Bob Hodrick, and Ken Singleton. We also thank an anonymous referee whose comments and suggestions greatly improved the paper. ..."
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Cited by 169 (1 self)
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University. We are especially grateful for suggestions from Geert Bekaert, Bob Hodrick, and Ken Singleton. We also thank an anonymous referee whose comments and suggestions greatly improved the paper.
Dependence Structures for Multivariate HighFrequency Data in Finance. Quantitative Finance 3
, 2003
"... www.math.ethz.ch/finance Stylised facts for univariate high–frequency data in finance are well–known. They include scaling behaviour, volatility clustering, heavy tails, and seasonalities. The multivariate problem, however, has scarcely been addressed up to now. In this paper, bivariate series of hi ..."
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Cited by 61 (4 self)
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www.math.ethz.ch/finance Stylised facts for univariate high–frequency data in finance are well–known. They include scaling behaviour, volatility clustering, heavy tails, and seasonalities. The multivariate problem, however, has scarcely been addressed up to now. In this paper, bivariate series of high–frequency FX spot data for major FX markets are investigated. First, as an indispensable prerequisite for further analysis, the problem of simultaneous deseasonalisation of high–frequency data is addressed. In the bulk of the paper we analyse in detail the dependence structure as a function of the time scale. Particular emphasis is put on the tail behaviour, which is investigated by means of copulas and spectral measures. 1
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 44 (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...
Multivariate extremes, aggregation and dependence in elliptical distributions
, 2001
"... Abstract. In this paper we clarify dependence properties of elliptical distributions by deriving general but explicit formulas for the coefficients of upper and lower tail dependence and spectral measures with respect to different norms. We show that an elliptically distributed random vector is regu ..."
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Cited by 36 (0 self)
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Abstract. In this paper we clarify dependence properties of elliptical distributions by deriving general but explicit formulas for the coefficients of upper and lower tail dependence and spectral measures with respect to different norms. We show that an elliptically distributed random vector is regularly varying if and only if the bivariate marginal distributions have tail dependence. Furthermore, the tail dependence coefficients are fully determined by the tail index of the random vector (or equivalently of its components) and the linear correlation coefficient. Whereas Kendall’s tau is invariant in the class ofelliptical distributions with continuous marginals and a fixed dispersion matrix, we show thatthis is not true for Spearman’s rho. We also show that sums of elliptically distributed random vectors with the same dispersion matrix (up to a positive constant factor) remain elliptical if they are dependent only through their radial parts. 1.
Testing the Gaussian Copula Hypothesis for Financial Assets Dependences
 Quantitative Finance
, 2003
"... Using one of the key property of copulas that they remain invariant under an arbitrary monotonous change of variable, we investigate the null hypothesis that the dependence between financial assets can be modeled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks ..."
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Cited by 30 (2 self)
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Using one of the key property of copulas that they remain invariant under an arbitrary monotonous change of variable, we investigate the null hypothesis that the dependence between financial assets can be modeled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks are compatible with the Gaussian copula hypothesis, while this hypothesis can be rejected for the dependence between pairs of commodities (metals). Notwithstanding the apparent qualification of the Gaussian copula hypothesis for most of the currencies and the stocks, a nonGaussian copula, such as the Student’s copula, cannot be rejected if it has sufficiently many “degrees of freedom”. As a consequence, it may be very dangerous to embrace blindly the Gaussian copula hypothesis, especially when the correlation coefficient between the pair of asset is too high as the tail dependence neglected by the Gaussian copula can be as large as, i.e., three out five extreme events which occur in unison are missed.
Multivariate extremes and the aggregation of dependent risks: Examples and counterexamples
 Extremes, 2008. ISSN 13861999 (Print) 1572915X (Online). URL http://www.springerlink.com/content/ 102890/?Content+Status=Accepted
"... Properties of risk measures for extreme risks have become an important topic of research. In the present paper we discuss sub and superadditivity of quantile based risk measures and show how multivariate extreme value theory yields the ideal modeling environment. Numerous examples and counterexamp ..."
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Cited by 18 (7 self)
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Properties of risk measures for extreme risks have become an important topic of research. In the present paper we discuss sub and superadditivity of quantile based risk measures and show how multivariate extreme value theory yields the ideal modeling environment. Numerous examples and counterexamples highlight the applicability of the main results obtained.
The simple economics of bank fragility
 Journal of Banking and Finance
, 2005
"... Abstract. Banks are linked through the interbank deposit market, participations like syndicated loans and deposit interest rate risk. The similarity in exposures carries the potential for systemic breakdowns. This potential is either weak or strong, depending on whether the linkages remain or vanis ..."
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Cited by 13 (2 self)
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Abstract. Banks are linked through the interbank deposit market, participations like syndicated loans and deposit interest rate risk. The similarity in exposures carries the potential for systemic breakdowns. This potential is either weak or strong, depending on whether the linkages remain or vanish asymptotically. It is shown that the linearity of the bank portfolios in the exposures, in combination with a condition on the tails of the marginal distributions of these exposures, determines whether the potential for systemic risk is weak or strong. We show that if the exposures have marginal normal distributions the potential for systemic risk is weak, while if e.g. the Student distributions apply the potential is strong. Acknowledgement 1. Part of this work was completed while the author was visiting scholar at the Dutch Central Bank DNB. I am grateful for the hospitality, support and stimulating research environment. I would also like to thank Laurens de Haan, Philipp Hartmann and Stefan Straetmans for their comments and suggestions. A preliminary draft was presented at the September 2003 International Workshop on Risk and Regulation in Budapest. 1.