This is a short book on the fundamental concepts of the no-arbitrage theory of pricing financial derivatives. Its scope is limited to the general discrete setting of models for which the set of possible states is finite and so is the set of possible trading times–this includes the popular binomial tree model. This setting has the advantage of being fairly general while not requiring a sophisticated understanding of analysis at the graduate level. Topics include understanding the several variants of “arbitrage”, the fundamental theorems of asset pricing in terms of martingale measures, and applications to forwards and futures.
The authors’ motivation is to present the material in a way that clarifies as much as possible why the often confusing basic facts are true. Therefore the ideas are organized from a mathematical point of view with the emphasis on understanding exactly what is under the hood and how it works. Every effort is made to include complete explanations and proofs, and the reader is encouraged to work through the exercises throughout the book.
The intended audience is students and other readers who have an undergraduate background in mathematics, including exposure to linear algebra, some advanced calculus, and basic probability. The book has been used in earlier forms with students in the MS program in Financial Mathematics at Florida State University, and is a suitable text for students at that level. Students who seek a second look at these topics may also find this book useful.
Table of Contents
Overture: Single-Period Models
The General Discrete Model
The Fundamental Theorems of Asset Pricing
Forwards and Futures
Incomplete Markets
About the Author(s)
Greg Anderson, Bank of America Merrill Lynch
Greg Anderson is a director in the rates quant group at Bank of America Merrill Lynch. Previously, he was in the fixed income research group at MSCIBarra. He holds a PhD in mathematics from the University of California at Berkeley.
Alec Kercheval, Florida State University
Alec N. Kercheval is professor of mathematics at Florida State University, where he has been director of the financial mathematics graduate program. He earned a PhD in mathematics from the University of California, Berkeley, and has taught at Boston University, Indiana University, Bloomington and the University of Texas at Austin. Prior to arriving at Florida State University, he worked in the fixed income research group at MSCIBarra, a financial consulting firm in Berkeley, California.
