Abstract
Binomial trees provide an intuitive way to explain the logic that underlies option pricing models; at the same time they serve as a powerful and versatile computational technique. With tree models it is, for instance, straightforward to value options that allow early exercise or to introduce alternative payoffs. In this chapter we discuss the workings of such models; more specifically, we show how to implement a Cox–Ross–Rubinstein tree for European and American options in Matlab and R, including some extensions such as discrete dividends. Strategies to accelerate the computations are discussed, such as the replacement of loops by vectorized computations. We also explain how to compute the Greeks by finite differences and how to estimate them directly from the tree. Sample code is provided for all examples.
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