Bounds and comparisons of quasi-Monte Carlo methods in option pricing

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.