Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all the policies at the same time. We introduce here a probabilistic approach to examine the consequences of its...

Generally, in the financial literature, the notion of quadratic VaR is implicitly confused with the Delta-Gamma VaR, because more authors dealt with portfolios that contained derivatives instruments. In this paper, we postpone to estimate both the expected shortfall and Value-at-Risk of a...

Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticized for issues relating to backtesting. In particular, ES has been found not to be elicitable which means that backtesting for ES...

We analyze the impact of the estimation frequency - updating parameter estimates on a daily, weekly, monthly or quarterly basis - for commonly used GARCH models in a large-scale study, using more than twelve years (2000-2012) of daily returns for constituents of the S&P 500 index. We assess the...

Countless test statistics can be written as quadratic forms in certain random vectors, or ratios thereof. Consequently, their distribution has received considerable attention in the literature. Except for a few special cases, no closed-form expression for the cdf exists, and one resorts to...

Nous proposons dans cet article, à partir des approches de Taylor (2008) et de Gouriéroux et Jasiak (2008), d'agréger différents modèles de quantiles et d'expectiles afin d'obtenir une méthode plus robuste de calcul de la valeur-en-risque et de la perte conditionnelle maximale en...

This discussion paper resulted in a publication in the <I>International Journal of Forecasting</I> (2010). Vol. 26(2), 231-247.<P> An efficient and accurate approach is proposed for forecasting Value at Risk [VaR] and Expected Shortfall [ES] measures in a Bayesian framework. This consists of a new...</p></i>