How to solve multiasset Black-Scholes with time-dependent volatility and correlation

It is shown that, just as in the single-asset case, one may solve the multiasset Black-Scholes equation by replacing time-varying volatilities and other parameters by their constant averages. This associated constant parameter problem may then be solved either by the usual integral formulas or by means of a recombining binary tree, neither of which would have been possible without using the transformation. The result extends what is already well known for single-asset single-factor models to the multidimensional case, for which the usual one-dimensional proof does not apply.