Weighted intermediate rank lattice rules with applications in finance

Authors:
Yongzeng Lai;Ken Seng Tan
Affiliations:
Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada;Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada and China Institute for Actuarial Science, Central University Finance and Economics, Beijing, China
Venue:
MOAS'07 Proceedings of the 18th conference on Proceedings of the 18th IASTED International Conference: modelling and simulation
Year:
2007

Citing 3
Cited 1

Component-by-component construction of good lattice rules with a composite number of points

Journal of Complexity
On the step-by-step construction of quasi: Monte Carlo integration rules that achieve strong tractability error bounds in weighted Sobolev spaces

Mathematics of Computation
Component-By-Component Construction of Good Intermediate-Rank Lattice Rules

SIAM Journal on Numerical Analysis

Intermediate rank lattice rules and applications to finance

Applied Numerical Mathematics

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Abstract

This paper considers the intermediate-rank lattice rules or higher rank lattice rules under the weighted Korobov space by extending the weighted higher rank lattice rule (WHRLR) to the general case with composite integer n so that the number of quadrature points is N = lrn, where r is the rank of the rule and l is a positive integer such that gcd(n, l) = 1. We obtain a general expression for the average of Mn,d,copy(l,r) over a subset of Zd, and give an upper bound and strong tractability for WHRLR. These results extend the work of Kuo & Joe ([1] and [2]). By applying to option pricing, our numerical results indicate that WHRLR has some advantages over the weighted rank-1 good lattice rule and is competitively more efficient than the standard Monte Carlo method and the Sobol' sequence based quasi-Monte Carlo method.