An Undergraduate Introduction to Financial Mathematics

Anyone with an interest in learning about the mathematical modeling of prices of financial derivatives such as bonds, futures, and options can start with this book, whereby the only mathematical prerequisite is multivariable calculus. The necessary theory of interest, statistical, stochastic, and differential equations are developed in their respective chapters, with the goal of making this introductory text as self-contained as possible.

In this edition, the chapters on hedging portfolios and extensions of the BlackScholes model have been expanded. The chapter on optimizing portfolios has been completely re-written to focus on the development of the Capital Asset Pricing Model. The binomial model due to CoxRossRubinstein has been enlarged into a standalone chapter illustrating the wide-ranging utility of the binomial model for numerically estimating option prices. There is a completely new chapter on the pricing of exotic options. The appendix now features linear algebra with sufficient background material to support a more rigorous development of the Arbitrage Theorem.

The new edition has more than doubled the number of exercises compared to the previous edition and now contains over 700 exercises. Thus, students completing the book will gain a deeper understanding of the development of modern financial mathematics.

Contents:

• The Theory of Interest
• Discrete Probability
• The Arbitrage Theorem
• Optimal Portfolio Choice
• Forwards and Futures
• Options
• Approximating Option Prices Using Binomial Trees
• Normal Random Variables of Probability
• Random Walks and Brownian Motion
• BlackScholes Equation and Option Formulas
• Extensions of the BlackScholes Model
• Derivatives of BlackScholes Option Prices
• Hedging
• Exotic Options
• Appendix A: Linear Algebra Primer

Readership: Undergraduate students in finance, economics, actuarial science, and applied mathematics; professionals in banking, insurance, actuarial careers, and finance.
Key Features:

• Self-contained introduction to financial mathematics with the relatively modest prerequisite of multivariable calculus
• Over 700 exercises more than doubled from previous edition
• The book begins at a basic enough level that the reader with no prior exposure to financial mathematics or statistics will find it accessible
• All the necessary statistics, theory of interest, stochastic processes, and differential equations knowledge is developed within the textbook, minimizing or eliminating the need for supplemental texts
• Contains enough material to support a two-semester sequence of courses on financial mathematics
• The latest edition provides a more comprehensive treatment of the application of the BlackScholes framework for pricing vanilla options on a wide variety of underlying assets than in previous editions
• This edition includes a completely new chapter on exotic options which derives and justifies pricing formulas for many types of exotic options, whereas many other books merely provide the formulas devoid of motivation and derivation
• More exercises added
• One of the few books on financial mathematics that is suitable both as a text for undergraduate courses and a self-study title

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