Financial mathematics (also known as mathematical finance, quantitative finance, computational finance, and financial engineering) is a field of applied mathematics that applies mathematical methods to financial problems.
Probability, stochastic processes, statistics, and economic theory are common terms used in financial mathematics books, helping analysts gain detailed insights into business performance, the industrial market, profitability, and growth potential.
However, quality investment in time, dedication, and effort is required to excel in this subject. You would want to grasp the best knowledge to outsmart the competition.
So, in the following guide, we have covered the top 7 best financial mathematics books to help you work with numbers, understand the problems related to financial management, reduce mathematical errors, and increase profit.
- Other names for financial mathematics are mathematical finance, quantitative finance, computational finance, and financial engineering.
- The best books relating to financial mathematics cover in detail probability, stochastic processes, statistics, economic theory, multivariable calculus, risk management, etc.
- An Introduction to Mathematical Finance with Applications: Understanding and Building Financial Intuition by Arlie O. Petters is one of the best introductory books for beginners. It addresses important concepts related to financial mathematics and helps readers grasp the knowledge by providing exercises classified into conceptual, application-based, and theoretical problems.
- MATHEMATICAL FINANCE: A Very Short Introduction by Mark H. A. Davis is an excellent book for those looking for a brief introduction to mathematical finance. However, the book covers everything in concise language, so it’s the best option for those with a basic understanding of the subject.
- The Concepts and Practice of Mathematical Finance by Mark S. Joshi is a fantastic book to understand everything about financial mathematics in a detailed yet simple and conversational style. However, the particular conversational, lengthy style also makes this book a little bland if you want all the information arranged logically.
- Problems and Solutions in Mathematical Finance: Stochastic Calculus by Eric Chin is a theory-focused book on financial mathematics. It is best suited to those looking for more depth and detail in financial mathematics and significant problems related to stochastic calculus. However, it can also confuse those habitual to learning theory and practice side by side.
- Probability for Finance by Ekkehard Kopp, Jan Malczak & Tomasz Zastawniak is an excellent book for beginners focusing on problems and solutions for mathematical finances. Yet, it can be confusing for some due to its rigorous, unfussy text.
- Methods of Mathematical Finance by Ioannis Karatzas & Steven Shreve is a sequel to Brownian Motion and Stochastic Calculus and provides an advanced understanding of mathematical finance. It is not suitable for beginners as it requires a good grasp of probability and random processes.
- The Model Thinker: What You Need to Know to Make Data Work for You by Scott E. Page is an advanced-level book on financial mathematics featuring a simple style. It covers theory and practical examples with many graphs to better understand the concepts.
1. An Introduction to Mathematical Finance with Applications: Understanding and Building Financial Intuition by Arlie O. Petters
Arlie Petters is a Belizean-American mathematical physicist and a Professor of Physics and Economics at Duke University, North Carolina. He is famously well-known for his contributions to the mathematical theory of gravitational lensing and his work in quantitative finance.
An Introduction to Mathematical Finance with Applications: Understanding and Building Financial Intuition by Arlie O. Petters is an excellent book for anyone getting started on financial mathematics without any background understanding.
The book covers various quantitative finance terminologies, including multivariable calculus, probability, and linear algebra. The author has provided theoretical treatments and their applications and carefully explained formulas with their appropriate derivations.
The book also offers a comprehensive approach toward a deeper understanding of the subject by providing exercises classified into conceptual, application-based, and theoretical problems.
Mark H. A. Davis served as a professor of mathematics at Imperial College London and is widely regarded as one of the most influential and memorable figures in financial mathematics. He made significant contributions to mathematical finance, including his fundamental work for stochastic control and process theories.
MATHEMATICAL FINANCE: A Very Short Introduction by Mark H. A. Davis is a book written for quantitative analysts to help them master the mathematical and computational skills required in the financial mathematical industry. The subject matter focuses on solving complex problems and challenges regarding asset valuation and risk management.
It is one of the best materials on financial mathematics, covering a brief but detailed overview of various terms, including the theory of arbitrage. The author has provided an in-depth analysis of the working of arbitrage theory, pricing theory, and its applications to interest rates, credit trading, risk management, and fund management.
However, note that the book is “a very short introduction” to mathematical finance, so it is most suitable for those who already have a basic understanding of the subject. It is written in simple yet concise language, so you might need to reread a topic several times to understand it.
Mark S. Joshi was a researcher and consultant in mathematical finance and served as a professor at the University of Melbourne. He is regarded as a leading expert in analysis and financial mathematics and has authored more than sixty mathematical research papers and well-received textbooks.
The Concepts and Practice of Mathematical Finance by Mark S. Joshi is best known for its simple and conversational style. The book explains technical topics related to financial mathematics, including derivatives pricing, models implementation, and their practical adaptation.
However, the book might not be a great option if you are unfamiliar with Joshi’s style and level of presentation, as the author explains everything in long, detailed paragraphs with little attention to a logical sequence.
You would have to find and highlight important terms and definitions through the topic as the information is scattered throughout the book.
Eric Chin graduated from the University of Oxford with an MSc in Applied Statistics and Mathematical Finance. Eric is a skilled and experienced entrepreneur and venture capitalist with over 30 years of expertise.
Problems and Solutions in Mathematical Finance: Stochastic Calculus by Eric Chin is best-suited for those looking for more depth and detail in financial mathematics. It covers all the major problems in stochastic calculus and offers various presumed solutions to let the reader learn the best possible method to tackle challenges.
However, note that the problems are more theoretical, and the book provides more theorems than problems. It can easily confuse those who prefer learning theory and practice side by side in quantitative finance. If not, the solved examples, figures, and formulas are an ideal start in mathematical finance.
Ekkehard Kopp is a professor of mathematics at the University of Hull, UK. He is famous for his more than 50 research publications and five books.
Jan Malczak is a mathematician widely known for his 20 published research papers and extensive knowledge in analysis, differential equations, measure and probability, and the theory of stochastic differential processes.
Tomasz Zastawniak serves as Chair of Mathematical Finance at the University of York and is known for his 50 research publications, six books, supervised four Ph.D. dissertations, and around 80 MSc dissertations in mathematical finance.
The Methods of Mathematical Finance is a collaborative work of three of the most well-known figures in the world of financial mathematics.
The book focuses on fundamental probabilistic concepts to make the reader understand financial market models, including independence and conditioning. It also provides extensive exercises and worked examples within the text to help students test their understanding of the test.
Overall, it’s an excellent book for getting started on problems and solutions for mathematical finances, yet it can be confusing for some due to its rigorous, unfussy text.
Ioannis Karatzas is a professor of mathematics at Columbia University. Steven Eugene Shreve is a mathematician, currently serving as an Orion Hoch Professor of Mathematical Sciences at Carnegie Mellon University.
The Methods of Mathematical Finance is written by authors known for their in-depth understanding of financial mathematics and related fields, such as stochastic analysis and stochastic control.
It is a sequel to Brownian Motion and Stochastic Calculus (by the same authors) and is aimed at those having a strong aptitude for financial mathematics. The book provides an advanced understanding of mathematical finance and requires a good grasp of probability and random processes.
It is definitely not for beginners and covers the fundamental topics in asset pricing, financial markets, consumption, investment, hedging, contingent claims, etc.
Scott E Page is the Leonid Hurwicz Collegiate Professor of Political Science, Complex Systems, and Economics at the University of Michigan. He also directs the Center for the Study of Complex Systems and is known for his contributions to quantitative finances.
The Model Thinker: What You Need to Know to Make Data Work for You by Scott E. Page is an advanced-level book on financial mathematics. However, it features a simple style that doesn’t confuse the reader.
The book is divided into chapters, and each chapter doesn’t cover more than 10-12 pages. This way, the author has made sure the reader will grasp the in-depth knowledge without getting distracted or confused. You’ll also find theory and practical examples in the book, with many graphs to better understand the concepts.
Financial mathematics careers are demanding, dynamic, and competitive. Though the study requires arithmetic expertise as well as knowledge and abilities in accounting and economics, it is not as complex as any other subject, especially for those with a strong aptitude for math.
With the help of books mentioned above, you can use your advanced skills to approach top professions like high-frequency trading, technical analysis, algorithmic trading, quantum finance, and quantitative investing.