Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Latin supercube sampling for very high-dimensional simulations
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
A generalized discrepancy and quadrature error bound
Mathematics of Computation
On selection criteria for lattice rules and other quasi-Monte Carlo point sets
Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
Algorithm 823: Implementing scrambled digital sequences
ACM Transactions on Mathematical Software (TOMS)
Variance with alternative scramblings of digital nets
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Optimal quadrature for Haar wavelet spaces
Mathematics of Computation
Variance Reduction via Lattice Rules
Management Science
Derivatives and credit risk: enhanced quasi-monte carlo methods with dimension reduction
Proceedings of the 34th conference on Winter simulation: exploring new frontiers
New simulation methodology for finance: efficient simulation of gamma and variance-gamma processes
Proceedings of the 35th conference on Winter simulation: driving innovation
Mathematical and Computer Modelling: An International Journal
Smoothness and dimension reduction in Quasi-Monte Carlo methods
Mathematical and Computer Modelling: An International Journal
WSC '05 Proceedings of the 37th conference on Winter simulation
A study of variance reduction techniques for American option pricing
WSC '05 Proceedings of the 37th conference on Winter simulation
Inverting the symmetrical beta distribution
ACM Transactions on Mathematical Software (TOMS)
Dimension Reduction Techniques in Quasi-Monte Carlo Methods for Option Pricing
INFORMS Journal on Computing
Simulating Lévy Processes from Their Characteristic Functions and Financial Applications
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Inverse transform method for simulating Levy processes and discrete Asian options pricing
Proceedings of the Winter Simulation Conference
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We review the basic principles of Quasi-Monte Carlo (QMC) methods, the randomizations that turn them into variance-reduction techniques, and the main classes of constructions underlying their implementations: lattice rules, digital nets, and permutations in different bases. QMC methods are designed to estimate integrals over the s-dimensional unit hypercube, for moderate or large (perhaps infinite) values of s. In principle, any stochastic simulation whose purpose is to estimate an integral fits this framework, but the methods work better for certain types of integrals than others (e.g., if the integrand can be well approximated by a sum of low-dimensional smooth functions). Such QMC-friendly integrals are encountered frequently in computational finance and risk analysis. We give examples and provide computational results that illustrate the efficiency improvement achieved.