In this paper, we characterize explicitly the first derivative of the Value at Risk and the Expected Shortfall with respect to portfolio allocation when netting between positions exists. As a particular case, we examine a simple Gaussian example in order to illustrate the impact of netting...

Economic cycles are the key credit portfolio risk driver and they are autocorrelated over time. We then show that it is economically meaningful to define risk for credit portfolios in a multi period setup. Since one period expected shortfall fails to measure risk adequately in a multi period...

We consider a nonparametric method to estimate copulas, i.e. functions linking joint distributions to their univariate margins. We derive the asymptotic properties of kernel estimators of copulas and their derivatives in the context of a multivariate stationary process satisfactory strong mixing...

The Basel Committee on Banking Supervision ("the Committee") released a consultative document that included a regulatory capital charge for operational risk. Since the release of the document, the complexity of the concept of "operational risk" has led to vigorous and recurring discussions. We...