A motivation for conditional moment matching

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One can find approaches galore in the literature for the valuation of Asian basket options. When the number of underlyings is large one has to resort to bounds or approximations to value these options. In this respect, Curran (1994) and Rogers and Shi (1995) very successfully applied a conditioning approach. Recently, Lord (2005) combined their approach with the traditional ad-hoc moment matching approaches, to obtain an approximation which is extremely accurate and has an analytical bound on its error. Here we review this approach and extend the results to multiple conditioning variables, along the lines of Vanmaele, Deelstra and Liinev (2004).