Mathematical Methods for Finance: Tools for Asset and Risk Management by Sergio M. Focardi, Frank J. Fabozzi, and Turan G. Bali (Wiley, 2013) may have chapter titles that sound like a math department’s course offerings, but this book is no substitute for actually taking the courses. The reader is not about to learn differential calculus in 30 pages or matrix algebra in 26 pages. And the two concluding chapters on stochastic calculus are definitely not for those who opted to round out their college schedules with the history of art instead of math. The authors may claim that “there is no prerequisite mathematical knowledge for reading this book,” but without some pretty extensive math background (or an extraordinary ability to grasp mathematical concepts intuitively) the reader’s understanding of the text will be minimal. Prospective readers looking for a crash course should understand that they won’t go from 0 to 60 in 300 pages.
Since the authors are trying to cast a wide net they explain key concepts in each field. For instance, the differential calculus chapter discusses the notion of limit, the essentials of limit theorems, the common definitions linking relevant conditions to limits of functions and sequences, the concept of continuity and total variation, differentiation and commonly used rules for computing first-order derivatives, computing second-order and higher-order derivatives, the chain rule, and the Taylor series expansion. The reader whose grasp of calculus is firm, or the reader who just needs a quick refresher course, will then learn a couple of applications of derivatives in bond portfolio management.
For many who would like to understand the quantitative side of modern finance this book serves as a daunting to-do list. Probability in finance, for example, is not the kind of probability used by poker players (and taught in beginning probability courses). Poker players don’t have to worry about fat tails and Hermite polynomials, quants do. Poker players can win big without ever having seen an integral, quants can lose millions/billions for their firms if they don’t understand integrals inside out.
Even though the book spends far more time on mathematical concepts than on applications, Mathematical Methods for Finance is still a good reference book for those who want to move from the math of the academy to the math of Wall Street. A primer, however, it’s not.