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Options on baskets (linear combinations) of assets are notoriouslychallenging to price using even the simplest log-normal continuous-timestochastic models for the individual assets. The paper [5] gives a closed formapproximation formula for pricing basket options with potentially negativeportfolio weights under log-normal models by moment matching. Thisapproximation formula is conceptually simple, methodologically sound, and turnsout to be highly accurate. However it involves solving a system of nonlinearequations which usually produces multiple solutions and which is sensitive tothe selection of initial values in the numerical procedures, making the methodcomputationally challenging. In the current paper, we take the moment-matchingmethodology in [5] a step further by obtaining a closed form solution for thisnon-linear system of equations, by identifying a unary cubic equation basedsolely on the basket's skewness, which parametrizes all model parameters, andwe use it to express the approximation formula as an explicit function of themean, variance, and skewness of the basket. Numerical comparisons with thebaskets considered in [5] show a very high level of agreement, and thus ofaccuracy relative to the true basket option price.

Pricing basket options with the first three moments of the basket: log-normal models and beyond