A Primer for the Mathematics of Financial Engineering [Paperback]

Dan Stefanica (Author)

Book Description

Publication Date: April 4, 2008

This book is meant to build the solid mathematical foundation required to understand the quantitative models used financial engineering. The financial applications range from the Put-Call parity, bond duration and convexity, and the Black-Scholes model, to the numerical estimation of the Greeks, implied volatility, and bootstrapping for finding interest rate curves. On the mathematical side, useful but sometimes overlooked topics are presented in detail: differentiating integrals with respect to nonconstant integral limits, numerical approximation of definite integrals, convergence of Taylor series expansions, finite difference approximations, Stirling's formula, Lagrange multipliers, polar coordinates, Newton's method for higher dimensional problems. A Solutions Manual containing complete solutions to every exercise, as well as to over 50 supplemental exercises, is available on amazon.com. International shipping and the Errata are available at www.fepress.org

Editorial Reviews

About the Author

Dan Stefanica has been the Director of the Masters Program in Financial Engineering at Baruch College, City University of New York, since its inception in 2002. He is teaching courses on numerical methods for finance, as well as pre-program courses in advanced calculus and linear algebra with financial applications. He has a PhD in Applied Mathematics from New York University and taught previously at the Massachusetts Institute of Technology.

Product Details

• Paperback: 302 pages
• Publisher: FE Press (April 4, 2008)
• Language: English
• ISBN-10: 0979757606
• ISBN-13: 978-0979757600
• Product Dimensions: 8.8 x 6 x 0.9 inches
• Shipping Weight: 1.1 pounds
• Average Customer Review: 4.9 out of 5 stars  See all reviews (11 customer reviews)
• Amazon Best Sellers Rank: #683,486 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

18 of 23 people found the following review helpful:

5.0 out of 5 stars Highly recommended, May 7, 2008

By 

J. Bautista "IT Proj Mgr / Financial Eng'g Gr... (Manhattan, NYC) - See all my reviews

This review is from: A Primer for the Mathematics of Financial Engineering (Paperback)

I've been away from school for a while, and I needed to review a lot of advanced mathematical concepts as well as financial topics in a matter of few months in preparation for my graduate study in Financial Engineering. This book is very concise and compact, yet easy to follow. You could cover substantial amount of materials (math concepts and financial applications) even by just reading a few chapters. It has been very useful for my preparation, and I feel like I'm really building a solid foundation to start my advanced study this coming fall, and hopefully, be very successful as well. I can see that it would be equally useful as a reference for the entire duration of my study, as well as my current job and envisioned career direction at a major financial services company.

9 of 11 people found the following review helpful:

5.0 out of 5 stars A MUST for financial engineering students!, July 5, 2010

By 

Joy Pathak - See all my reviews

Amazon Verified Purchase

This review is from: A Primer for the Mathematics of Financial Engineering (Paperback)

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.

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.

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.

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.

In short, the Primer along with its solution manual is a short course in financial engineering at your finger tips.

6 of 7 people found the following review helpful:

5.0 out of 5 stars A Unique Blend of Finance Concepts and Mathematical Foundation: A Must Read for Students contemplating an MFE Degree, April 27, 2011

By 

Devdeep Sarkar "Devdeep Sarkar" (Ann Arbor, MI, USA) - See all my reviews
(REAL NAME)   

Amazon Verified Purchase

This review is from: A Primer for the Mathematics of Financial Engineering (Paperback)

Are you contemplating an MFE and/or MS in Math/Computational Finance Degree and asking yourself whether you have the right background?

I strongly believe that "A Primer for the Mathematics of Financial Engineering" by Prof. Dan Stefanica will take you through every step toward finding the Best answer. It will also help you start your journey as an MFE student with utmost confidence. This book is a must for all prospective students for an MFE (or equivalent) degree.

What I like the most about this book is the way the chapters are structured. Every chapter consists of two main parts. The first part deals with the basic mathematical foundation and/or numerical techniques required to understand a given subtopic of quantitative finance. Once the mathematical/numerical basis is set up, Prof. Stefanica moves on to describing how it can be applied to comprehend a specific set of topics in quantitative finance in the second part of each chapter.

Even if your math is not super strong to begin with, or you have not had much exposure to numerical techniques, you can easily master your skills while you are studying the first part of every chapter. And immediately following that, you see the application of the abstract mathematical concepts in the finance world. And then you can sharpen your skills much further by actually solving the stimulating questions/problems found at the end of each chapter.

Another thing I love about this book is the set of pseudo-codes. After describing the numerical techniques, be it Simpson's rules for numerical integration or Secant method for solving 1-D nonlinear problems, the author provides pseudo-codes showing practical examples of their implementation. You can easily translate these pseudo-codes to your favorite language (C++, Matlab, etc.) and start producing results immediately.

I hope you will enjoy studying the topics presented in this book... like I did.

Good Luck!