A Primer For The Mathematics Of Financial Engineering, Second Edition (Financial Engineering Advanced Background Series)

I bought this book before entering a top MFE program and found it is extremely helpful! It is not an undergraduate level calculus textbook as someone may think. This book emphasizes advanced calculus methods and math foundations with applications in the financial world. Thus, I would strongly recommend it to anyone who is interested in quantitative finance and needs to enhance their math knowledge towards that. Specifically, there are five main aspects that highlight the book's value: 1. It covers the most important calculus and math foundations for quantitative analysis in solving financial problems. It goes from basic calculus, numerical integration and probability concepts to Newton's method, Taylor's formula, finite difference & ODEs, multivariate calculus and Lagrange multipliers. All math theorems/proofs/formulas are very clear and easy to follow. 2. It provides plenty of examples of real-world financial applications, such as options, put-call parity, Greeks and hedging, Black-Scholes PDE, and interest rates, Bonds, portfolio optimization. These practical problems are very common in the financial industry, and many of them have been frequently asked as interview questions for quant finance jobs. 3. It also provides many straightforward pseudocodes for implementing some programming algorithms, such as Simpson's numerical integration, Black-Scholes's option pricing model, computing implied vol, Newton's method, etc. No matter what programming language you use, it is very easy to implement following the pseudocodes. You will find how efficient it is. 4. It provides extensive practice exercises. I almost finished all exercise problems, some of them are theoretical, requiring derivations and proofs, and some are practical, requiring computation and programming. Very challenging but intellectually stimulating. 5. The book is well-organized and very easy to follow. Every chapter covers a major math topic with financial applications/examples. No need to worry if you don't have a finance background since all finance terminologies are well explained. Math notations are consistent and easy to understand and remember. This book has been continuously ranked as one of the most famous quant finance books by QuantNet.com. If you ask about what math background is required for a Master in Financial Engineering/Mathematical Finance program, the answer is always: read this book. If you want to review/refine/enhance your math knowledge for entering a MFE program, read this book.

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!

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.

First, primer means you have to have the fundamental math out of the way before you dive into this book. If you are fuzzy about what integration means, or the basic form of differentation then start with Calculus first. Though I think the author does a great job of teaching Calculus in this book. This book bridges a very important gap between math and finance, and that is from the pure theoretical math to applied finance. People do not realize that financial engineering employs some of the most advanced theories in both theoretical math and probility. Which is why Wall Street is looking for physicists and engineering students for quantative finance. This is a great self study, or textbook which instructs the student how to apply their math background to finance. The author does an excellent job of teaching the math, while using financial engineering as the examples and problems. Which in the end takes you from basic Calculus to Taylor series and Lagrange. Actually it would be a great way to teach calculus in the future. Instead of using theoretical physics and the sciences for examples and problems, simply use finance. The psuedocode is just a bonus in my mind. This is an excellent math book for students, even if they are not planning on a future in financial engineering because it does illustrate applied math like no other textbook.

The title of the book says Primer but don't expect this book to be primer. You really need to have a good understanding of the concepts of Calculus, differentiation and probability in order to use this book. I am out of school for more than 10 years and I really had to tweak my brain in order to grasp the concepts explained in this book. But here is the good news. One can easily get hold of all the concepts and theories in this book using online resources. Once you do that it should be good ride and if one can successful master this book doing an MS in FE should be well within the reach.

It covers a broad range of topics (especially options) in math finance and the level of details is incomparable. It provides an alternative to stochastic calculus. I personally found the exposition about finance concept is very clear. The style is down-to-the-earth. It has quite a lot technique details which I couldn't find in many other math finance books. I hope author can write another book about portfolio optimization which I would purchase in no time.

I own this book for the last 5 years and it is one of the most popular in my library. I originally used it while I was a student and nowadays as practitioner, it is my go-to book to refresh my memory for most of the covered topics. Dan has a clean, easy to read, with full proof explanations and examples style, which helps the reader to quickly and rigorously understand the basic ideas and concepts. The book contains a plethora of topics that any quant in finance will come across at some point. The selection helps the reader to gain a robust foundation before moving to more advance constructions (from integrals -> continuous probabilities -> risk neutral estimation and properties of Black-Scholes as well as other topics e.g. Taylor expansion, numerical methods, bond mathematics, portfolio construction, etc.). I would highly recommend it.

This book is a great math refresher and to be more precise: it shows how advanced undergraduate calculus applied into quantitative finance. Chapters 1 to 4: cover the basic of calculus and probability and how those applied into option pricing with many exercises (I suggest to buy the solution manual too). Then, the rest of the book cover several numerical methods that widely used in financial engineering.