A Simple Closed-Form Formula for Pricing Basket Options

Abstract

Options involving more than one underlying, often called basket options, are quite common, but valuation presents a mathematical problem. Although returns for a single stock can be assumed to follow a lognormal diffusion, leading to a variety of possible standard pricing models, sums, averages, or differences among lognormals are not lognormal. A number of approaches to approximating the returns distribution for an underlying basket have been proposed. Among the more successful is Levy’s technique of fitting an approximating lognormal for the basket by calculating and matching the first two moments of the basket’s return distribution. A problem arises, however, when the component assets have heterogeneous volatilities. Kan proposes a new technique that breaks the valuation formula into several pieces, each of which can be well approximated by moment matching. The accuracy of the Kan model over a wide range of parameter values is shown to be better than that of alternative models, and computation speed is nearly as good as the Levy model, which is much less accurate in general.