Review: A Primer for the Mathematics of Financial Engineering

Joy Pathak

Swaptionz

Paperback: 302 pages
Publisher: FE Press (April 4, 2008)
Amazon review
This is my first review in a range of reviews I will be posting from the viewpoint of a student. The reviews will entail everything from books, to movies (if I have time to watch any), to that Café on 30th and 3rd. For me to make a review it will have to be exceptionally high-quality or unnaturally dreadful.

REVIEW
Dr. Stefanica in his first book on financial engineering makes a gallant and fervent attempt at providing a succinct primer for financial engineering aimed at technical students entering the financial engineering world without the knowledge of application. In my opinion, he has not only accomplished, but has done so in a heroic manner.
Developing a Primer for this field is an ambitious task. Dr. Stefanica with his extensive familiarity in the field has brought to us a primer, that in short, ‘sums-it-all and some’. The primer is the culmination of years of experience within the Baruch Masters in Financial Engineering program. Having taught the refreshers for the Advanced Calculus and Linear Algebra at Baruch over the years, Dr. Stefanica has in-short bought to us a Refresher Course within the confines of a 302 page book.
The exposition is not as rigorous as people might expect it to be but that is primarily his aim at it seems: to give the reader a quick summary of many of the basics of differential/integral calculus, differential equations, probability, taylor series, etc, with strong applications to the financial world.
The book is meant to build a solid mathematical foundation required to understand the intricate mathematical concepts that will be taught in financial engineering programs and future in the workplace.

What makes this book truly amazing?
As I said above, being able to visualize the applications of the mathematics to the financial world is key for students entering financial engineering programs from the plethora of technical programs like mechanical engineering, pure mathematics, computer science etc. As a Mechanical Engineering undergrad myself, I was craving for a book that would give me a good refresher on all the key mathematics that will be required during the upcoming semesters and how these concepts apply to finance. Dr. Stefanica in short has read the minds of millions and provided us with a financial engineering student’s bible.
The book surpasses any of its potential competitors in the fact that it not only provides you with a range of questions, which I might add as he puts it, are some of the most common quant interview questions; he also portrays the connection between the mathematics in the book to numerical coding. As everyone knows, majority of the mathematical problems are solved numerically as it is just too intensive to attempt by the human hand. Dr. Stefanica provides after every important mathematical concept that needs to be solved numerically an effective Pseudo-Code. One can utilise this pseudo-code to learn/code the numerical methods utilising C++ or any programming language of their picking.
The Pseudo-Code is something is found extremely useful, as I was not only trying to refresher/learn the mathematics and its application to financial theory but also trying to understand how these numerical methods actually play out in the computer science world. The book, aided me in all these matters.
One of the key reasons this book is truly marvellous is the Solutions Manual it comes with. One can attempt to solve the problems in the book and check their answers right away from the solutions manual where they are provided in a deeply detailed fashion.

Who should use this book?
This book is ideal if not a MUST for any student entering the world of financial engineering. I would recommend this book to all professors and directors of programs where ‘Refresher courses’ are taught before the beginning of their Masters in Financial engineering/Financial Mathematics/Computational Finance programs.
This book is not for the seasoned professional although for practitioners looking to refresh certain concepts might find it a good read.
In the book, there are a few paragraphs on ‘who should use this book’. I will let you read that by yourself. If you look at the PREVIEW on Amazon you can read the Preface and the chapter on the book’s audience to get a better feel if this book is for you.

How should you use this book?
I utilised the book in a certain way. Dr. Stefanica does go through the methods in which the book should be utilised. For my personal pleasure, I went through the mathematical concepts first; then coded the numerical methods as they came about in the book; and then solved the problems behind the book. The Solutions Manual for the book is quite a relief as coupled with the book it is a force to be reckoned with. I would utilise the solution manual to understand the questions and answers in a deeper fashion and they are very detailed. There are additional questions in the solution manual. Once finishing the code, questions and the chapter I would go back to the code and try to make it as general as possible so that I can utilise it with a range of different questions. There are several questions in the book where you HAVE to use you code to answer them, sometimes to the 8th decimal digit.
If I haven’t conveyed it above, I would like to say that I truly enjoyed this book and recommend it whole heartedly. My only suggestion as I look forward the next edition, is more pseudo-code (Bootstrap especially).
There are a few typographical errors in the book but a complete Errata is now available.
In short, the Primer along with its solution manual is a short course in financial engineering at your finger tips.
(I will post a second part to this review AFTER my refresher course at Baruch in Advanced Calculus is over in which I will be utilizing the book.)

Current Read: I am currently using Walter Savitch's "Problem Solving with C++ (7th Ed)" and will mostly likely make a review for it. It has been quite helpful to me in learning C++ from the ground up.
 
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