  Contrary to the common view that exact pricing is prohibitive owing to the
curse of dimensionality, this study proposes an efficient and unified method
for pricing options under multivariate Black-Scholes-Merton (BSM) models, such
as the basket, spread, and Asian options. The option price is expressed as a
quadrature integration of analytic multi-asset BSM prices under a single
Brownian motion. Then the state space is rotated in such a way that the
quadrature requires much coarser nodes than it would otherwise or low varying
dimensions are reduced. The accuracy and efficiency of the method is
illustrated through various numerical experiments.
