Category Archives: Statistics

Exposé à Toulouse sur l’estimation (nonparamétrique) de quantiles

Exposé à Toulouse 1, sur l’estimation nonparamétrique de quantiles.

In this talk we propose several nonparametric estimators of quantiles based on Beta kernel and applied to transformed data by the generalized Champernowne distribution initially fitted to the data. A Monte-Carlo based study will show that those estimators improve the efficiency, not only for light tailed distributions, but mainly for heavy tailed, when the probability level is close to 1. Another application will be seen, on portfolio optimization in the mean-VaR context.

Advances in copula density estimation

Exposé aux Gemeinsame Jahrestagung der Deutschen Mathematiker-Vereinigung und der Gesellschaft für Didaktik der Mathematik, dans la session Multivariate Dependence Modelling using Copulas – Applications in Finance, Humboldt-Universität zu Berlin, Mars 2007, à partir du chapitre écrit avec Jean David Fermanian et Olivier Scaillet sur The estimation of copulas : theory and pratice.

Copulas are a way of formalising dependence structures of random vectors. Although they have been known about for a long time (Sklar (1959)), they have been rediscovered relatively recently in applied sciences (biostatistics, reliability, biology, etc). In finance, they have become a standard tool with broad applications: multiasset pricing (especially complex credit derivatives), credit portfolio modelling, risk management, etc. For example, see Li (1999), Patton (2001) and Longin and Solnik (1995). […] In this chapter, we focus on the practical issues practitioners are faced with, in particular concerning estimation and visualisation. In the first section, we give a general setting for the estimation of copulas. Such a framework embraces most of the available techniques. In the second section, we deal with the estimation of the copula density itself, with a particular focus on estimation near the boundaries of the unit square.