© 2004

Derivative Securities and Difference Methods


  • Currently there are no other books covering this topic

  • There is a need for a book of this type in the rapidly developing area of Computational Finance


Part of the Springer Finance book series (FINANCE)

Table of contents

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

    1. Front Matter
      Pages 1-1
    2. You-lan Zhu, Xiaonan Wu, I-Liang Chern
      Pages 3-15
    3. You-lan Zhu, Xiaonan Wu, I-Liang Chern
      Pages 17-112
    4. You-lan Zhu, Xiaonan Wu, I-Liang Chern
      Pages 113-203
    5. You-lan Zhu, Xiaonan Wu, I-Liang Chern
      Pages 205-263
  3. Numerical Methods for Derivative Securities

    1. Front Matter
      Pages 205-205
    2. You-lan Zhu, Xiaonan Wu, I-Liang Chern
      Pages 267-329
    3. You-lan Zhu, Xiaonan Wu, I-Liang Chern
      Pages 331-404
    4. You-lan Zhu, Xiaonan Wu, I-Liang Chern
      Pages 405-471
    5. You-lan Zhu, Xiaonan Wu, I-Liang Chern
      Pages 473-502
  4. Back Matter
    Pages 503-513

About this book



This book is devoted to determining the prices of financial derivatives using a partial differential equation approach. In the first part the authors describe the formulation of the problems (including related free-boundary problems) and derive the closed form solutions if they have been found. The second part discusses how to obtain their numerical solutions efficiently for both European-style and American-style derivatives and for both stock options and interest rate derivatives. The numerical methods discussed are finite-difference methods. The book also discusses how to determine the coefficients in the partial differential equations.

The aim of the book is to provide readers who have some code writing experience for engineering computations with the skills to develop efficient derivative-pricing codes. The book includes exercises throughout and will appeal to students and researchers in quantitative finance as well as practitioners in the financial industry and code developers.


Derivative Securities Finance Futures Lookback options Options Swaps

Authors and affiliations

  1. 1.Department of MathematicsUniversity of North Carolina at CharlotteCharlotteUSA
  2. 2.Department of MathematicsHong Kong Baptist UniversityKowloon Tong, Hong KongChina
  3. 3.Department of MathematicsNational Taiwan UniversityTaipei, TaiwanChina

Bibliographic information

Industry Sectors
Finance, Business & Banking


From the reviews:

"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

"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)