Research stay at UC3M: DEPARTMENT OF STATISTICS
Project: The goal of the research is the development of statistical and econometric methods for risk quantification in vast dimensional and complex financial systems. More in particular, develop inference for large dimensional heavy-tailed distributions.
Extreme movements in asset prices are responsible for tail risk. Benoit Mandelbrot, back in 1963, already pointed out fat tails in financial returns, but they have received little attention among the practitioners since most of the financial models rely on Gaussianity. This distributional assumption is the basis of the modern portfolio analysis and option pricing. However, the last financial crisis, characterized by large and unexpected extreme movements in asset prices, has clearly shown the failure of such assumption.
Among the existing heavy-tailed distributions, the family of alpha-stable distributions, of which the Gaussian is a special case, represents a natural generalization due to its own Central Limit Theorem. Numerous studies have found this family of distributions to be more appropriate for modeling asset returns. Extensions to the vast dimensional framework are not straightforward. The general multivariate alpha-stable distribution is intractable due to the spectral measure.
Prof. Veredas will develop a methodology for vast dimensional heavy tailed models. The building block will be the Method of Simulated Quantiles of Dominicy and Veredas (Journal of Econometrics, 2013) and its extension to the elliptical distributions of Dominicy, Ogata and Veredas (Computational Statistics, 2013). First he will provide simple, reliable and fast estimators while applicable to vast dimensions. Second, he will develop the asymptotic results that show the theoretical appropriateness of the method.
Stay Period: FEB 2014 - JUL 2014