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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… (More)

- Didier Sornette, Victoria Andersen, +11 authors Aina Johansen
- 1996

This review presents a general theory of financial crashes and of stock market instabilities that his co-workers and the author have developed over the past seven years. We start by discussing the limitation of standard analyses for characterizing how crashes are special. The study of the frequency distribution of drawdowns, or runs of successive losses… (More)

- Yannick Malevergne, Vladilen Pisarenko, Didier Sornette
- Physical review. E, Statistical, nonlinear, and…
- 2011

Fat-tail distributions of sizes abound in natural, physical, economic, and social systems. The lognormal and the power laws have historically competed for recognition with sometimes closely related generating processes and hard-to-distinguish tail properties. This state-of-affair is illustrated with the debate between Eeckhout [Amer. Econ. Rev. 94, 1429… (More)

- X Burtschell, Jon Gregory, +12 authors D. Laurent
- 2005

We compare some popular CDO pricing models, related to the bottom‐up approach. Dependence between default times is modelled through Gaussian, stochastic correlation, Student t, double t, Clayton and Marshall‐Olkin copulas. We detail the model properties and compare the semi‐analytic pricing approach with large portfolio approximation techniques. We study… (More)

Zipf’s law states that the number of firms with size greater than S is inversely proportional to S. Most explanations start with Gibrat’s rule of proportional growth but require additional constraints. We show that Gibrat’s rule, at all firm levels, yields Zipf’s law under a balance condition between the effective growth rate of incumbent firms (which… (More)

A large consensus now seems to take for granted that the distributions of empirical returns of financial time series are regularly varying, with a tail exponent b close to 3. First, we show by synthetic tests performed on time series with time dependence in the volatility with both Pareto and Stretched-Exponential distributions that for sample of moderate… (More)

We provide definitive results to close the debate between Eeckhout (2004, 2009) and Levy (2009) on the validity of Zipf’s law, which is the special Pareto law with tail exponent 1, to describe the tail of the distribution of U.S. city sizes. Because the origin of the disagreement between Eeckhout and Levy stems from the limited power of their tests, we… (More)

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… (More)

We summarize a book under publication with the above title written by the three present authors, on the theory of Zipf’s law, and more generally of power laws, driven by the mechanism of proportional growth. The preprint is available upon request from the authors. For clarity, consistence of language and conciseness, we discuss the origin and conditions of… (More)

Using a family of modified Weibull distributions, encompassing both sub-exponentials and super-exponentials, to parameterize the marginal distributions of asset returns and their natural multivariate generalizations, we give exact formulas for the tails and for the moments and cumulants of the distribution of returns of a portfolio make of arbitrary… (More)