Analytic Approximations For Multi-Asset Option Pricing

The authors derive a general analytic approximation for pricing basket options on N assets, which is extended to analytic approximations for pricing general rainbow options, including best-of and worst-of N asset options. The key idea is to express the option's price as a sum of prices of various compound exchange options, each with different pairs of sub-ordinate multi- or single-asset options. For some multi-asset options a strong condition holds, whereby each compound exchange option is equivalent to a standard single-asset option under a modified measure, and in such cases an almost exact analytic price exists for the multi-asset option. The underlying asset prices are assumed to follow log-normal processes, although the strong condition can be extended to certain other price processes for the underlying.