ABSTRACT
T his chapter provides an introduction to computational methods used in derivative pricing from the factor model perspective. In particular, we explore the
popular binomial tree approach to the pricing of derivative securities [14, 43]. This method is explained by showing that it follows from a discretization of the
factor model approach and three step procedure that we used to derive absence of arbitrage equations in previous chapters. In particular, we rely upon the simple binary approximation to a Brownian factor given in Chapter 1. That binary approximation allows us to describe our factor dynamics on a tree that is created by binary up and down moves of the factor. Since underlying variables and tradables are ultimately also driven by the factors, they become representable on the same tree structure. In essence, discretization of the factors induces discretization of the underlying variables and tradables as it flows through the modeling paradigm. Finally, calibration and absence of arbitrage pricing can be performed numerically on the resulting trees, resulting in a systematic computational methodology.
