Lectures on financial mathematics : discrete asset pricing /
By: Anderson, Greg.
Contributor(s): Kercheval, Alec N.
Material type:
BookSeries: Synthesis digital library of engineering and computer science: ; Synthesis lectures on mathematics and statistics: # 7.Publisher: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool, c2010Description: 1 electronic text (xi, 51 p.) : digital file.ISBN: 9781608454969 (electronic bk.).Subject(s): Derivative securities -- Prices -- Mathematical models | arbitrage | martingale | incomplete markets | forward measure | forward contract | futures | tree modelsDDC classification: 332.645 Online resources: Abstract with links to resource Also available in print.| Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
E books
|
PK Kelkar Library, IIT Kanpur | Available | EBKE273 |
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Part of: Synthesis digital library of engineering and computer science.
Series from website.
Includes bibliographical references (p. 49-50).
Preface --
1. Overture: single-period models -- What is a model -- Warm-up: a forward contract -- A single time period -- The pricing formula -- Risky bond -- General case of one time step --
2. The general discrete model -- The tree -- The stock process -- Trading strategies and attainable claims -- Arbitrage --
3. The fundamental theorems of asset pricing --
4. Forwards and futures -- Forwards and the forward measure -- Futures -- The convexity correction -- Computational matters --
5. Incomplete markets --
A. Probability refreshner -- Before probability -- Probability introduced; independence -- Conditional expectation, the finite case -- Change of measure; the Radon-Nikodym derivative -- Martingales --
B. Orthogonal vectors in the positive cone -- Authors' biographies.
Abstract freely available; full-text restricted to subscribers or individual document purchasers.
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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.
Also available in print.
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