Application of Range Searching to Fast Financial Risk Estimation

Value at Risk (VaR) is a popular measure of the financialrisk of a portfolio. For a specific class of problems, the mainbottleneck in VaR estimation is a matrix-vector multiplicationinvolved in the computation. In the decision version of the problem, weare interested not in the VaR itself, but in whether it exceeds agiven threshold. We demonstrate in this paper that we can use computationalgeometry techniques, in particular, range search, to eliminate rows ofthe matrix, to obtain significant increases in speed for a particularclass of VaR problems.