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Derivative Securities and Difference Methods

  • You-lan Zhu
  • Xiaonan Wu
  • I-Liang Chern
  • Zhi-zhong Sun

Part of the Springer Finance book series (FINANCE)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Partial Differential Equations in Finance

    1. Front Matter
      Pages 1-1
    2. You-lan Zhu, Xiaonan Wu, I-Liang Chern, Zhi-zhong Sun
      Pages 3-15
    3. You-lan Zhu, Xiaonan Wu, I-Liang Chern, Zhi-zhong Sun
      Pages 17-103
    4. You-lan Zhu, Xiaonan Wu, I-Liang Chern, Zhi-zhong Sun
      Pages 105-157
    5. You-lan Zhu, Xiaonan Wu, I-Liang Chern, Zhi-zhong Sun
      Pages 159-275
    6. You-lan Zhu, Xiaonan Wu, I-Liang Chern, Zhi-zhong Sun
      Pages 277-345
  3. Numerical Methods for Derivative Securities

    1. Front Matter
      Pages 347-347
    2. You-lan Zhu, Xiaonan Wu, I-Liang Chern, Zhi-zhong Sun
      Pages 349-389
    3. You-lan Zhu, Xiaonan Wu, I-Liang Chern, Zhi-zhong Sun
      Pages 391-444
    4. You-lan Zhu, Xiaonan Wu, I-Liang Chern, Zhi-zhong Sun
      Pages 445-534
    5. You-lan Zhu, Xiaonan Wu, I-Liang Chern, Zhi-zhong Sun
      Pages 535-604
    6. You-lan Zhu, Xiaonan Wu, I-Liang Chern, Zhi-zhong Sun
      Pages 605-636
  4. Back Matter
    Pages 637-647

About this book

Introduction

This book is mainly devoted to finite difference numerical methods for solving partial differential equation (PDE) 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 initial/initial-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 of 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, 2005

 

Keywords

Asset Price Models Black-Scholes Equation Derivative Securities Free-Boundary Problems Jump Conditions

Authors and affiliations

  • You-lan Zhu
    • 1
  • Xiaonan Wu
    • 2
  • I-Liang Chern
    • 3
  • Zhi-zhong Sun
    • 4
  1. 1.Dept. Mathematics & StatisticsUniversity of North Carolina, CharlotteCharlotteUSA
  2. 2.Dept. MathematicsHong Kong Baptist UniversityKowloonHong Kong SAR
  3. 3.National Taiwan UniversityTaipeiTaiwan R.O.C.
  4. 4.Southeast UniversityNanjingChina, People's Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-7306-0
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-7305-3
  • Online ISBN 978-1-4614-7306-0
  • Series Print ISSN 1616-0533
  • Series Online ISSN 2195-0687
  • Buy this book on publisher's site
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