What follows is a brief review of the mathematical and statistical concepts with which the reader must be familiar in order to fully understand the material presented in this book. The assumption is that this material has already been encountered in elementary mathematics, statistics, or finance classes and that this presentation is simply a refresher. If this is not the case, I highly recommend picking up an introductory calculus or statistics text. These concepts are not only fundamental to an understanding of modern finance, but an essential part of the set of intellectual tools that should be available to any educated adult: innumeracy is no less a shortcoming than illiteracy.
In keeping with the “practical” objectives of the book, our presentation is deliberately informal and includes no derivations or proofs. Our goal is to make as clear as possible the meaning of the mathematical concepts so that the reader is able to see through the symbology to the underlying significance of the formulas and in doing so, better understand the characteristics of the products and markets discussed. The fact is that mathematics provides an incredibly concise and clear way to explain the structure of financial instruments, determine their value, and understand their risks. Unfortunately the teaching of mathematics too often focuses on the mechanical manipulation of formulas rather than on the underlying significance of the operations—like learning ...