Authors:
- New chapters and subsections added
- Exercises are included at the end of each chapter
- Covers a variety of topics in finance
- Includes supplementary material: sn.pub/extras
- Request lecturer material: sn.pub/lecturer-material
Part of the book series: Springer Finance (FINANCE)
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Table of contents (10 chapters)
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Front Matter
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Partial Differential Equations in Finance
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Front Matter
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Numerical Methods for Derivative Securities
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Front Matter
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Back Matter
About this book
This book is mainly devoted to finite difference numerical methods for solving partial differential equations (PDEs) models of pricing a wide variety of financial derivative securities. With this objective, the book is divided into two main parts.
In the first part, after an introduction concerning the basics on derivative securities, the authors explain how to establish the adequate PDE boundary value problems for different sets of derivative products (vanilla and exotic options, and interest rate derivatives). For many option problems, the analytic solutions are also derived with details. The second part is devoted to explaining and analyzing the application of finite differences techniques to the financial models stated in the first part of the book. For this, the authors recall some basics on finite difference methods, initial boundary value problems, and (having in view financial products with early exercise feature) linear complementarity and free boundary problems.In each chapter, the techniques related to these mathematical and numerical subjects are applied to a wide variety of financial products. This is a textbook for graduate students following a mathematical finance program as well as a valuable reference for those researchers working in numerical methods in financial derivatives. For this new edition, the book has been updated throughout with many new problems added. More details about numerical methods for some options, for example, Asian options with discrete sampling, are provided and the proof of solution-uniqueness of derivative security problems and the complete stability analysis of numerical methods for two-dimensional problems are added.
Review of first edition:
“…the book is highly well designed and structured as a textbook for graduate students following a mathematical finance program, which includes Black-Scholes dynamic hedging methodology to price financial derivatives. Also, it is a very valuable reference for those researchers working in numerical methods in financial derivatives, either with a more financial or mathematical background." -- MATHEMATICAL REVIEWS
Reviews
“It is mainly devoted to finite difference methods, and it is intended for researchers as well as graduate students. It is the most complete and useful book on the subject I have seen. … Derivative Securities and Difference Methods is a really good book that anyone studying or working in this field should own.” (Anita Mayo, SIAM Review, Vol. 57 (1), March, 2015)
"This book is devoted to pricing financial derivatives with a partial differential equation approach. It has two parts, each with four chapters. … The book covers a variety of topics in finance, such as forward and futures contracts, the Black-Scholes model, European and American type options, free boundary problems, barrier options, lookback options, multi-asset options, interest rate models, interest rate derivatives, swaps, swaptions, caps, floors, and collars. The treatment is mathematically rigorous. There are exercises at the end of each chapter." (Elias Shiu, Zentralblatt MATH, Vol. 1061 (12), 2005)
"This book is mainly devoted to finite difference numerical methods for solving partial differential equations (PDEs) models of pricing a wide variety of financial derivative securities... the book is highly well designed and structured as a textbook for graduate students following a mathematical finance program, which includes Black-Scholes dynamic hedging methodology to price financial derivatives. Also, it is a very valuable reference for those researchers working in numerical methods in financial derivatives, either with a more financial or mathematical background." -- MATHEMATICAL REVIEWS
Authors and Affiliations
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Dept. Mathematics & Statistics, University of North Carolina, Charlotte, Charlotte, USA
You-lan Zhu
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Dept. Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong SAR
Xiaonan Wu
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National Taiwan University, Taipei, Taiwan R.O.C.
I-Liang Chern
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Southeast University, Nanjing, China, People's Republic
Zhi-zhong Sun
About the authors
Bibliographic Information
Book Title: Derivative Securities and Difference Methods
Authors: You-lan Zhu, Xiaonan Wu, I-Liang Chern, Zhi-zhong Sun
Series Title: Springer Finance
DOI: https://doi.org/10.1007/978-1-4614-7306-0
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Hardcover ISBN: 978-1-4614-7305-3Published: 04 July 2013
Softcover ISBN: 978-1-4899-9093-8Published: 05 August 2015
eBook ISBN: 978-1-4614-7306-0Published: 04 July 2013
Series ISSN: 1616-0533
Series E-ISSN: 2195-0687
Edition Number: 2
Number of Pages: XXII, 647
Topics: Quantitative Finance, Partial Differential Equations, Computational Mathematics and Numerical Analysis, Numerical Analysis, Finance, general