A note to enhance the BPW model for the pricing of basket and spread options

Borovkova, Pernuma, and Weide [2007, BPW] proposed an accurate and versatile method to price general basket options (including spread options). In implementing the BPW model, a nonlinear system of three equations with three unknowns must be solved to estimate parameters. If we directly compute the system of equations via a computer, it takes about 2.3 seconds, which is not significantly shorter than the computing time (about 5.7 seconds) based on Monte Carlo simulation for pricing basket options. To relieve this somewhat time-consuming problem, this note provides an analytical method to solve this equation system. With our method, it takes almost no time, about 0.015 seconds, to price a basket option. Therefore, our parameter estimation method enhances the efficiency and tractability of the BPW model for end-users in the marketplace.