Abstract: 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. the first is based on Monte Carlo simulations, applies to general portfolios and risk factor distributions. 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.

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