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Complex option pricing problems often require some form of high-dimensional
numerical integration. Monte Carlo (MC) methods are often used in these cases
to avoid problems of dimensionality but the relatively slow rates of convergence
can make MC ineffective in practice. Quasi-Monte Carlo (QMC) methods, based on
low-discrepancy sequences, have some theoretical advantages over standard MC
and have been observed to perform well in many option pricing examples. The
traditional theoretical basis for QMC error bounds, however, generally breaks
down in these cases. In this talk, we will present some resolution of this
practice and theory disparity by showing how QMC error bounds can extend to
common option pricing examples. We will also discuss various forms of
low-discrepancy sequences in QMC and present computational results for
a variety of examples.
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