Abstract
In this chapter, we derive several mathematical models of financial derivatives, such as futures and options. The methodology used is commonly known as risk-neutral pricing, and was first presented by Merton, Black and Scholes in the 1970s. We start by presenting the basics of the Black-Scholes analysis, which leads to the Black-Scholes equation. Several option contracts such as plain European and American option contracts are derived. We also give an overview of some exotic option contracts. At last, we present mathematical models of the so-called Greeks, i.e., the partial derivatives of the value of the option contracts with respect to important model parameters.
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