Springer Finance

Derivative Securities and Difference Methods

Authors: Zhu, Y.-l., Wu, X., Chern, I.-L., Sun, Z.-z.

  • New chapters and subsections added
  •  Exercises are included at the end of each chapter
  •  Covers a variety of topics in finance
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Hardcover $149.00
price for USA
  • ISBN 978-1-4614-7305-3
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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

About the authors

You-Lan Zhu is a Professor of Mathematics at the University of North Carolina at Charlotte. Xiaonan Wu is a Professor of Mathematics at Hong Kong Baptist University. I-Liang Chern is a Professor of Mathematics at National Taiwan University. Zhi-zhong Sun is a Professor of Mathematics at Southeast University.

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


Table of contents (10 chapters)

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4614-7306-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-1-4614-7305-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover n/a
  • ISBN 978-1-4899-9093-8
  • Free shipping for individuals worldwide
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Derivative Securities and Difference Methods
Authors
Series Title
Springer Finance
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-7306-0
DOI
10.1007/978-1-4614-7306-0
Hardcover ISBN
978-1-4614-7305-3
Softcover ISBN
978-1-4899-9093-8
Series ISSN
1616-0533
Edition Number
2
Number of Pages
XXII, 647
Topics