Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
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In this paper we introduce the intermediate rank or higher rank lattice rule for the general case when the number of quadrature points is ntm, where m is a composite integer, t is the rank of the rule, n is an integer such that (n,m) = 1. Our emphasis is the applications of higher rank lattice rules to a class of option pricing problems. The higher rank lattice rules are good candidates for applications to finance based on the following reasons: the higher rank lattice rule has better asymptotic convergence rate than the conventional good lattice rule does and searching higher rank lattice points is much faster than that of good lattice points for the same number of quadrature points; furthermore, numerical tests for application to option pricing problems showed that the higher rank lattice rules are not worse than the conventional good lattice rule on average.