Simulating Option Prices and Sensitivities by Higher Rank Lattice Rules

Y. Lai (Canada)

Keywords

Simulation of multivariate integrations; Monte Carlo and Quasi-Monte Carlo methods; Lattice rules; Option Pricing.

Abstract

In this paper we introduce the intermediate rank or higher rank lattice rule for the general case when the number of quadrature points is nt m, 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 lat tice rules are good candidates for applications to ļ¬nance based on the following reasons: the higher rank lattice rule has better asymptotic convergence rate than the conven tional good lattice rule does and searching higher rank lat tice points is much faster than that of good lattice points for the same number of quadrature points; furthermore, numer ical tests for application to option pricing problems showed that the higher rank lattice rules are not worse than the con ventional good lattice rule on average.

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