The practice of Delta-Gamma VaR: Implementing the quadratic portfolio model

This paper intends to critically evaluate state-of-the-art methodologies for calculating the VaR of non-linear portfolios from the point of view of computational accuracy and efficiency. We focus on the quadratic portfolio model, also known as “DeltaGamma,” and, as a working assumption, we model risk factor returns as multi-normal random variables. We present the main approaches to Delta-Gamma VaR weighing their merits and accuracy from an implementation-oriented standpoint. One of our main conclusions is that the Delta-Gamma normal VaR may be less accurate than even Delta VaR. On the other hand, we show that methods that essentially take into account the non-linearity (hence gammas and third or higher moments) of the portfolio values may present significant advantages over full Monte Carlo revaluations. The role of non-diagonal terms in the Gamma matrix as well as the sensitivity to correlation is considered both for accuracy and computational effort. We also qualitatively examine the robustness of Delta-Gamma methodologies by considering a highly non-quadratic portfolio value function.