A Note to Enhance the BPW Model for the Pricing of Basket and Spread Options

Abstract

The standard assumption for an underlying asset’s returns process is the lognormal diffusion. This works quite well for individual assets. Portfolios and indexes present a problem, however, because a weighted sum of lognormally distributed stock prices is not lognormal. But a lognormal approximation can typically still be used as long as all of the weights are positive. That condition fails for options on a spread, which generally involves approximately equally sized long and short positions. In the Summer 2007 issue of this journal, Borovkova, Permana, and Weide (BPW) presented a solution based on matching the moments of the returns distribution to a generalized lognormal. Here, Wu, Chang and Chen show how to speed up the BPW procedure considerably by using closed-form expressions for the relevant moments.