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Financial derivatives or options represent a critical development in modern finance and are based upon the analysis of empirical data as well as rigorous developments in probability and stochastic processes. While there is overwhelming general acceptance of the famous Black-Scholes formula for pricing European options, there is no equivalent acceptance of a uniform method for evaluating American, path-dependent and exotic options, not to mention the many versions of interest rate options and credit derivatives. This article presents one of the simplest such models – the binomial model – which can be adapted to price any type of security based option. It is shown that Mathematica can provide procedural code for binomial models that is more straightforward and easier to understand than typical numerical programs like C and MATLAB. More importantly it will also be demonstrated that such binomial models are best described using functional programming, not only from the viewpoint of simplicity, but also for increased speed of execution. This is the first of a series of articles that aims to study a range of finance methodologies and techniques that are currently being used by educators and professional practitioners using the power of Mathematica’s programming style.
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