Monte Carlo simulation techniques that use function approximations have been successfully applied to approximately price multi-dimensional American options. However, for many pricing problems the time required to get accurate estimates can still be prohibitive, and this motivates the development of variance reduction techniques. In this paper, we describe a zero-variance or ‘perfect ’ control variate to price American options. We then discuss how function approximation may be used to approximate this perfect control variate. Empirically, we observe that on simple one dimensional examples, this approximately perfect control variate gives orders of magnitude of variance reduction compared to naive estimation.
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