This textbook invites the reader to develop a holistic grounding in
mathematical finance, where concepts and intuition play as important a
role as powerful mathematical tools. Financial interactions are
characterized by a vast amount of data and uncertainty; navigating the
inherent dangers and hidden opportunities requires a keen understanding
of what techniques to apply and when. By exploring the conceptual
foundations of options pricing, the author equips readers to choose
their tools with a critical eye and adapt to emerging challenges.
Introducing the basics of gambles through realistic scenarios, the text
goes on to build the core financial techniques of Puts, Calls, hedging,
and arbitrage. Chapters on modeling and probability lead into the
centerpiece: the Black-Scholes equation. Omitting the mechanics of
solving Black-Scholes itself, the presentation instead focuses on an
in-depth analysis of its derivation and solutions. Advanced topics that
follow include the Greeks, American options, and embellishments.
Throughout, the author presents topics in an engaging conversational
style. "Intuition breaks" frequently prompt students to set aside
mathematical details and think critically about the relevance of tools
in context.
Mathematics of Finance is ideal for undergraduates from a variety of
backgrounds, including mathematics, economics, statistics, data science,
and computer science. Students should have experience with the standard
calculus sequence, as well as a familiarity with differential equations
and probability. No financial expertise is assumed of student or
instructor; in fact, the text's deep connection to mathematical ideas
makes it suitable for a math capstone course. A complete set of the
author's lecture videos is available on YouTube, providing a
comprehensive supplementary resource for a course or independent study.
