An Undergraduate Introduction to Financial MathematicsAnyone 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 Black-Scholes 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 Cox-Ross-Rubinstein 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 InterestDiscrete ProbabilityThe Arbitrage TheoremOptimal Portfolio ChoiceForwards and FuturesOptionsApproximating Option Prices Using Binomial TreesNormal Random Variables of ProbabilityRandom Walks and Brownian MotionBlack-Scholes Equation and Option FormulasExtensions of the Black-Scholes ModelDerivatives of Black-Scholes Option PricesHedgingExotic OptionsAppendix A: Linear Algebra PrimerReadership: Undergraduate students in finance, economics, actuarial science, and applied mathematics; professionals in banking, insurance, actuarial careers, and finance.Reviews of the Third Edition:’This book provides an ideal introduction to basic topics in financial mathematics not only for undergraduates studying mathematical related subjects, but also graduates in finance. It strikes an excellent balance between exposition and mathematical technicality. The author has produced a first-rate textbook that will become a classic read.’ – John G O’HaraUniversity of Essex, UK’This is the most lucid and helpful mathematics book I have ever read, since the derivations and proofs are elegant, pertinent, and instructive; the exercises effectively reinforce and extend the lessons of the text; and the detailed answers to the exercises, which comprise about 20% of the book, should ensure that no gap is left in the foundation for understanding material in subsequent chapters.’ – James B f Cripps, C f A, R f P, CfPSenior Financial PlannerVancouver Financial Planning Consultants Inc.Review of the First Edition:’This text now covers adequately most material needed to be covered in an undergraduate course in financial mathematics. The level of material is easy to follow, understand and work out which makes it suitable for classroom adoption. Overall, it is a good introduction to financial mathematics at the undergraduate level providing enough useful information which encourages one to think.’ – Professor Man M ChawlaFellow of Indian National Science Academy andformer Professor of Mathematics, Indian Institute of Technology, New DelhiKey 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 Black-Scholes 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 titleISBN: 9789811260308, 9811260303
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