Weighted Intermediate Rank Lattice Rules with Applications in Finance

Y. Lai and K.S. Tan (Canada)


Multivariate integrations; Weighted higher rank lattice rules; Option pricing; Monte Carlo and QuasiMonte Carlo simulation methods.


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 = lr n, 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 aver age 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.

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