American Basket and Spread Option pricing by a Simple Binomial Tree

In this article we address the problem of valuing and hedging American options on baskets and spreads, i.e., on portfolios consisting of both long and short positions. We adopt the main ideas of the Generalized Lognormal (GLN) approach introduced in Borovkova et al. (2007) and extend them to the case of American options. We approximate the basket price process by a suitable Geometric Brownian motion, shifted by an arbitrary parameter and possibly reflected over the x-axis. These adjustments to the GBM are necessary for dealing with negative basket values and possible negative skewness of basket increments’ distribution. We construct a simple binomial tree for an arbitrary basket, by matching the basket’s volatility, and evaluate our approach by comparing the binomial tree option prices to those obtained by other methods, whenever possible. Moreover, we evaluate the delta-hedging performance of our method and show that it performs remarkably well, in terms of both option pricing and delta hedging. The main advantages of our method is that it is simple, computationally extremely fast and efficient, while providing accurate option prices and deltas.