The Computation of Risk Budgets under the Lévy Process Assumption

This paper revisits the computation of Value-at-Risk and other risk indicators based on the use of Lévy processes. We first provide a new presentation of Variance Gamma Pro- cesses with Drift: we reconstruct them in an original way, starting from the exponential distribution. Then, we derive general Fourier formulas that allows to compute VaR quickly and efficiently, but also other typical indicators like Tail Conditional Expectation (TCE), TailVaR or Expected Shortfall. Based on this formula, we conduct a study of the term structure of VaR, and provide a discussion of the Basle 2 and Solvency II agreements.