More information on each title can be found at

• A Primer for the Mathematics of Financial Engineering, Second Edition
• Solutions Manual – A Primer for the Mathematics of Financial Engineering, Second Edition

The Solutions Manual to the Second Edition of A Primer for the Mathematics of Financial Engineering offers the reader the opportunity to undertake a rigorous self-study of the mathematical topics presented in the Math Primer, with the goal of achieving a deeper understanding of the financial applications therein.

It contains detailed solutions to every one of the 175 exercises from the Second Edition of  the Primer. A section on arbitraging the convexity of options value is also included in the Solutions Manual.

The First Edition of the Solutions Manual proved to be an important resource for prospective financial engineering graduate students. The Supplemental Exercises from the First Edition are included in the Second Edition of the Math Primer, and their solutions appear in this Solutions Manual.  New exercises were added to the Second Edition of the Math Primer, including exercises on the new topics covered therein.

Studying the material from the Math Primer and using the Solutions Manual as a companion is an efficient way to ensure that the reader can solve every exercise, therefore achieving a deeper understanding of the financial applications therein.

About the Author

Dan Stefanica has been the Director of the Financial Engineering Masters Program at Baruch College, City University of New York, since its inception in 2002. He teaches graduate courses on numerical methods for financial engineering, as well as pre-program courses on advanced calculus and numerical 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.

Sample Sections:

• 1.1. Chapter 1 Exercises (Download)
• 1.2. Complete Solutions to Chapter 1 Exercises (Download)

• Softcover: 280 pages
• Publisher: Financial Engineering Press
• List Price: $40
• ISBN-13: 978-0979757617
• ISBN-10: 0979757614

A Primer for the Mathematics of Financial Engineering is the first book in the Financial Engineering Advanced Background Series, and is meant to build the solid mathematical foundation required to understand the quantitative models used financial engineering and can be used as a reference book or as a self-study book.

The Second Edition of A Primer for the Mathematics of Financial Engineering was published in March 2011. A Solutions Manual including detailed solutions to every exercise was published concurrently and is available here.

The First Edition, published in 2008, was warmly received by a large audience, including students and prospective students of financial engineering programs, academics teaching in such programs or in finance departments, and many practitioners from the financial industry, and was the top QuantNet bestselling book of 2010.

Reviews for “A Primer for the Mathematics of Financial Engineering”, First Edition:

One of the hottest degrees on today’s campus is a Masters in Financial Engineering. Whether you need to retrieve hallowed memories or just want to familiarize yourself with the mathematics underlying this degree, this unique book offers a terrific return on investment.

Peter Carr, PhD

Global Head of Modeling, Morgan Stanley; Director of the Masters Program in Mathematical Finance, Courant Institute, NYU

This is the book I always recommend to people who ask about their mathematics before doing an MFE, and a few people could do with reading it after as well.

Dominic Connor

Director, P&D Quantitative Recruitment

Important financial applications were added to the Second Edition, and sections on selected topics were expanded, including:

• New sections on dollar duration, dollar convexity, DV01, bond portfolios immunization
• New sections on log return and arithmetic return
• New section on the effect of parallel shifts in the yield curve to changes in bond yields
• Separate chapter on numerical methods for solving nonlinear equations, computing bond yields and implied volatilities, and bootstrapping yield curves
• Streamlined: Lagrange multipliers sections include a step-by-step example following the general theory
• New section on finding maximal return portfolios
• New section on the numerical precision of finite difference approximations of the Greeks
• Streamlined: sections on Taylor approximations and Taylor series
• New: Mathematical Appendix
• New section, Solutions Manual: Arbitrage and the convexity of option values

NEW TOPICS: Dollar duration, Dollar convexity, DV01; the effect of parallel shifts in the yield curve to changes in bond yields; bond portfolio immunization; arbitraging the Put-Call parity; percentage vs. log returns for individual assets and portfolios; optimum investment portfolios: maximum return portfolios and minimum variance portfolios; the numerical precision of finite difference approximations of the Greeks.

New or expanded sections: new chapter on solving nonlinear problems; expanded Lagrange multipliers sections; streamlined Taylor series and Taylor expansion sections; Mathematical Appendix at the end of the book.

Financial applications (selected): Put-Call parity, bond mathematics, numerical computation of bond yields, Black-Scholes model, numerical estimation for Greeks, implied volatility, yield curves bootstrapping

Mathematical topics (selected): numerical approximation of definite integrals; Taylor approximations and Taylor series expansions; finite difference approximations; Stirling’s formula, polar coordinates; numerical methods for solving one dimensional problems; Newton’s method for higher dimensional problems

About the Author

Dan Stefanica has been the Director of the Financial Engineering Masters Program at Baruch College, City University of New York, since its inception in 2002. He teaches graduate courses on numerical methods for financial engineering, as well as pre-program courses on advanced calculus and numerical 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.

Sample Sections:

• Table of Contents (Download)
• 3.6.1. Explaining the magic of Greeks computations (Download)
• 5.2.1. The N-dimensional Newton’s Method (Download)
• 6.5. Parallel shifts in the yield curve (Download)
• 6.7. Dollar duration and dollar convexity; bond portfolio immunization (Download)
• 8.6. Integrating the density function of the standard normal variable (Download)
• 9.1. Lagrange multipliers (Download)
• Exercises – Chapter 1 (Download)
• Exercises – Chapter 6 (Download)

Book Details:

• Softcover: 352 pages
• Publisher: Financial Engineering Press
• List Price: $62
• ISBN-13: 978-0979757624
• ISBN-10: 0979757622

OUT OF PRINT: The Solutions Manual to the First Edition of  A Primer for the Mathematics of Financial Engineering was published in 2008.

• Softcover: 216 pages
• Publisher: Financial Engineering Press
• ISBN-13: 978-0979757631
• ISBN-10: 0979757630

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OUT OF PRINT: The First Edition of A Primer for the Mathematics of Financial Engineering was published in 2008.

Errata (August 2010 version)

• Softcover: 304 pages
• Publisher: Financial Engineering Press
• ISBN-13: 978-0979757600
• ISBN-10: 0979757606