Abstract
For the approximation of multidimensional integrals, two types of methods are widely used. Monte Carlo (MC) methods are the best known and require the use of a pseudorandom generator. Quasi-Monte Carlo (QMC) methods use low discrepancy point sets and are deterministic. The idea is to use points that are more regularly distributed over the integration space than random points. The best known methods to achieve this are the lattice rules and (t,s) sequences (or (t,m,s) nets) (A.B. Owen, 1998; H. Niederreiter; 1992; I.H. Sloan and S. Joe, 1994). The paper compares Monte Carlo methods, lattice rules, and other low discrepancy point sets on the problem of evaluating Asian options. The combination of these methods with variance reduction techniques is also explored.
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