Options pricing: using simulation for option pricing
Proceedings of the 32nd conference on Winter simulation
The effective dimension and quasi-Monte Carlo integration
Journal of Complexity
On the tractability of the Brownian bridge algorithm
Journal of Complexity
Quasi-monte carlo methods in practice: quasi-monte carlo methods for simulation
Proceedings of the 35th conference on Winter simulation: driving innovation
Probabilistically induced domain decomposition methods for elliptic boundary-value problems
Journal of Computational Physics
Quasi-Monte Carlo methods in finance
WSC '04 Proceedings of the 36th conference on Winter simulation
Space-time adaptive finite difference method for European multi-asset options
Computers & Mathematics with Applications
New Brownian bridge construction in quasi-Monte Carlo methods for computational finance
Journal of Complexity
Comparison of Point Sets and Sequences for Quasi-Monte Carlo and for Random Number Generation
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Simulation of a Lévy process by PCA sampling to reduce the effective dimension
Proceedings of the 40th Conference on Winter Simulation
Dimension Reduction Techniques in Quasi-Monte Carlo Methods for Option Pricing
INFORMS Journal on Computing
A practical view of randomized quasi-Monte Carlo: invited presentation, extended abstract
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Quasi-random walks on balls using C.U.D. sequences
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
Enhancing Quasi-Monte Carlo Methods by Exploiting Additive Approximation for Problems in Finance
SIAM Journal on Scientific Computing
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The need to simulate stochastic processes numerically arises in many fields. Frequently this is done by discretizing the process into small time steps and applying pseudorandom sequences to simulate the randomness. This paper addresses the question of how to use quasi-Monte Carlo methods to improve this simulation. Special techniques must be applied to avoid the problem of high dimensionality which arises when a large number of time steps is required. Two such techniques, the generalized Brownian bridge and particle reordering, are described here. These methods are applied to a problem from finance, the valuation of a 30-year bond with monthly coupon payments assuming a mean reverting stochastic interest rate. When expressed as an integral, this problem is nominally 360 dimensional. The analysis of the integrand presented here explains the effectiveness of the quasi-random sequences on this high-dimensional problem and suggests methods of variance reduction which can be used in conjunction with the quasi-random sequences.