Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
Journal of Complexity
Fast convergence of quasi-Monte Carlo for a class of isotropic integrals
Mathematics of Computation
The effective dimension and quasi-Monte Carlo integration
Journal of Complexity
On the tractability of the Brownian bridge algorithm
Journal of Complexity
Smoothness and dimension reduction in Quasi-Monte Carlo methods
Mathematical and Computer Modelling: An International Journal
Dimension Reduction Techniques in Quasi-Monte Carlo Methods for Option Pricing
INFORMS Journal on Computing
Pricing barrier and American options under the SABR model on the graphics processing unit
Concurrency and Computation: Practice & Experience
American option pricing with randomized quasi-Monte Carlo simulations
Proceedings of the Winter Simulation Conference
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Quasi-Monte Carlo (QMC) methods have been playing an important role for high-dimensional problems in computational finance. Several techniques, such as the Brownian bridge (BB) and the principal component analysis, are often used in QMC as possible ways to improve the performance of QMC. This paper proposes a new BB construction, which enjoys some interesting properties that appear useful in QMC methods. The basic idea is to choose the new step of a Brownian path in a certain criterion such that it maximizes the variance explained by the new variable while holding all previously chosen steps fixed. It turns out that using this new construction, the first few variables are more ''important'' (in the sense of explained variance) than those in the ordinary BB construction, while the cost of the generation is still linear in dimension. We present empirical studies of the proposed algorithm for pricing high-dimensional Asian options and American options, and demonstrate the usefulness of the new BB.