We propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model. The method is based on Taylor and Chebyshev expansions and involves mixed exponential-power moments of a Gaussian distribution. Our numerical results show that both approaches are comparable in accuracy to a standard Monte Carlo method, with a lesser computational effort.
Pablo Olivares. Alexander Alvarez. "Pricing Basket Options by Polynomial Approximations." J. Appl. Math. 2016 1 - 12, 2016. https://doi.org/10.1155/2016/9747394