A Novel Sampling Approach to Combinatorial Optimization Under Uncertainty
Computational Optimization and Applications
On the Use of Quasi-Monte Carlo Methods in Computational Finance
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
New simulation methodology for finance: efficient simulation of gamma and variance-gamma processes
Proceedings of the 35th conference on Winter simulation: driving innovation
Randomized Quasi-Monte Carlo: a tool for improving the efficiency of simulations in finance
WSC '04 Proceedings of the 36th conference on Winter simulation
The delivery option in mortgage backed security valuation simulations
WSC '05 Proceedings of the 37th conference on Winter simulation
50th ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications
Management Science
New Brownian bridge construction in quasi-Monte Carlo methods for computational finance
Journal of Complexity
Dimension Reduction Techniques in Quasi-Monte Carlo Methods for Option Pricing
INFORMS Journal on Computing
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Monte Carlo simulation is playing an increasingly important role in the pricing and hedging of complex, path dependent financial instruments. Low discrepancy simulation methods offer the potential to provide faster rates of convergence than those of standard Monte Carlo methods; however, in high dimensional problems special methods are required to ensure that the faster convergence rates hold. Indeed, Ninomiya and Tezuka (1996) have shown highdimensional examples, in which low discrepancy methods perform worse than Monte Carlo methods. The principal component construction introduced by Acworth et al. (1998) provides one solution to this problem. However, the computational effort required to generate each path grows quadratically with the dimension of the problem. This article presents two new methods that offer accuracy equivalent, in terms of explained variability, to the principal components construction with computational requirements that are linearly related to the problem dimension. One method is to take into account knowledge about the payoff function, which makes it more flexible than the Brownian Bridge construction. Numerical results are presented that show the benefits of such adjustments. The different methods are compared for the case of pricing mortgage backed securities using the Hull-White term structure model.