The strike price Xbasket is usually set at the current value of the basket (at-the-money), and the payoff profile will be max(Sbasket − Xbasket, 0) where Sbasket is a weighted average of n asset prices at maturity, and each weight represents the percentage of total investment in that asset.
[5] Basket options are usually priced using an appropriate industry-standard model (such as Black–Scholes) for each individual basket component, and a matrix of correlation coefficients applied to the underlying stochastic drivers for the various models.
While there are some closed-form solutions for simpler cases (e.g. two-color European rainbows),[6] semi-analytic solutions,[7] analytical approximations,[8] and numerical quadrature integrations,[9] the general case must be approached with Monte Carlo or binomial lattice methods.
Problems in hedging basket options can be of some significance when dealing with markets that exhibit a strong skew.
[10] This problem arises in swaps and Eurodollar strips (baskets of Eurodollar options) but in equities and fixed income it is mitigated by the fact that when correlation between assets is high, the sum would come closer to a lognormally distributed asset.