Sensitivities of VaR with respect to trades that alter the delta and the gamma of a portfolio is interesting to practitioners as this information can be used to find optimal hedge ratios for complex portfolios. Computing sensitivities is a challenging numerical problem. We discuss two methodologies for its solution.
Importance sampling and quasi-random number generators are very useful to speed up convergence.
The second method is analytic, is based on the moment generating functions for delta-gamma portfolios, is limited to multivariate normal distributions and makes use of adaptive quadrature methods to compute Fourier integrals.