In this paper, we characterize explicitly the first derivative of the Value at Risk and theExpected 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 theimpact of netting...

This paper defines two distribution free goodness-of-fit test statistics for copulas and statestheir asymptotic distributions under some composite parametric assumptions. The results arestated formally in an independent identically distributed framework, and partially in timedependentframeworks....

We provide conditions for the existence and the unicity of strictly stationary solutions of the usual Dynamic Conditional Correlation GARCH models (DCC-GARCH). The proof is based on Tweedie's (1988) criteria, after having rewritten DCC-GARCH models as nonlinear Markov chains. Moreover, we study...

We propose a new goodness-of-fit test for copulas, based on empirical copula processes and nonparametric bootstrap counterparts. The standard Kolmogorov-Smirnov type test for copulas that takes the supremum of the empirical copula process indexed by orthants is extended by test statistics based...

We provide a rigorous proof of granularity adjustment (GA) formulas to evaluate loss distributions and risk measures (value-at-risk) in the case of heterogenous portfolios, multiple systematic factors and random recoveries. As a significant improvement with respect to the literature, we detail...