Extending quadrature methods to value multi-asset and complex path dependent options

The exposition of the quadrature (QUAD) method (Andricopoulos, Widdicks, Duck, and Newton, 2003. Universal option valuation using quadrature methods. Journal of Financial Economics 67, 447–471 (see also Corrigendum, Journal of Financial Economics 73, 603 (2004)) is significantly extended to cover notably more complex and difficult problems in option valuations involving one or more underlyings. Trials comparing several techniques in the literature, adapted from standard lattice, grid and Monte Carlo methods to tackle particular types of problem, show that QUAD offers far greater flexibility, superior convergence, and hence, increased accuracy and considerably reduced computational times. The speed advantage of QUAD means that, even under the curse of dimensionality, it is not necessary to resort to Monte Carlo methods (certainly for options involving up to five underlying assets). Given the universality and flexibility of the method, it should be the method of choice for pricing options involving multiple underlying assets, in the presence of many features, such as early exercise or path dependency.