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is an associate professor at Vrije Universiteit Amsterdam in Amsterdam, The Netherlands. s.a.borovkova@vu.nl F.J. PERMANA is an associate professor at Universitas Katolik Parahyangan in Bandung, Indonesia, and a postdoc researcher at Universitas Gajah Mada in Yogyakarta, Indonesia. ferryjp@unpar.ac.id J.A.M VAN DER WEIDE is an associate professor at Delft University of Technology in Delft, The Netherlands. j.a.m.vanderweide@tudelft.nl In this article, we address the problem of valuing and hedging American options on baskets and spreadsthat is, on portfolios consisting of both long and short positions. The main challenge here is dealing with multiple underlying assets: a situation where traditional methods such as binomial trees or Monte Carlo simulations lead to prohibitive computational time or memory requirements.The key feature of our approach is constructing a simple two-dimensional binomial tree for the basket evolution. For that, we approximate the basket price process by a suitable geometric Brownian motion, shifted by an appropriate amount along the x-axis and potentially reflected over the y-axis. These adjustments to the GBM are necessary for dealing with negative basket values and possible negative skewness of basket distribution. This approximation is inspired by the generalized lognormal approach for European basket options introduced by Borovkova et al. [2007].We match the basket volatility and build a single binomial tree for the basket evolution, which we use for valuing American (or any other pathdependent) options on the basket, calculating deltas and deciding on an early exercise. We evaluate our approach by comparing binomial tree option prices to those obtained by other methods, where possible. We show that our method performs remarkably well: Option prices obtained by our method coincide up to the second decimal with those obtained by a much more time-consuming full binomial tree. Furthermore, we evaluate the delta-hedging performance of our method and show that our hedge errors are comparable with those obtained for a single-asset American option. The advantages of our method are that it is simple, computationally extremely fast, and efficient, while providing accurate option prices and deltas.

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