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It has long been the belief of the financial sector that high-dimensional integrals should be computed using Monte Carlo (MC) rather than Quasi-Monte Carlo (QMC). In 1992 our research group in the computer Science Department at Columbia University started testing QMC, using improved low discrepancy sequences (LDS), on a 360 dimensional CMO provided by Goldman Sachs. To our surprise QMC always beat MC. Test results were reported in a series of papers:
A related paper by S. Paskov, There has been much interest in a theoretical explanation of why QMC is superior to MC for finance computations. A posible explanation is that QMC algorithms automatically take advantage of the non-isotropic nature of finance problems. This is made precise in For a semi-popular account of this work see B. Cipra, FinDer is a software system for evaluating high-dimensional integrals. For related material see Quasi-Monte Carlo Algorithms. Columbia University has received a patent for an estimation method and system for complex securities using low-discrepancy deterministic sequences. |