Derivative Securities and Difference Methods, 2nd Edition

  • Published By:
  • ISBN-10: 1461473063
  • ISBN-13: 9781461473060
  • DDC: 332.645
  • Grade Level Range: College Freshman - College Senior
  • 647 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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Presented in two parts, this book is mainly devoted to finite difference numerical methods for solving partial differential equations (PDEs) models of pricing a variety of financial derivative securities. 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. The authors recall some basics on finite difference methods, initial boundary value problems, and linear complementarity and free boundary problems. Techniques related to mathematical and numerical subjects are applied to financial products. This is a textbook for graduate students and a valuable reference for researchers working in numerical methods in financial derivatives. This edition has been updated throughout. 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 2-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

Table of Contents

Front Cover.
Editorial Board.
Other Frontmatter.
Title Page.
Copyright Page.
Preface to the Second Edition.
Preface to the First Edition.
1: Partial Differential Equations in Finance.
2: Introduction.
3: European Style Derivatives.
4: American Style Derivatives.
5: Exotic Options.
6: Interest Rate Derivative Securities.
7: Numerical Methods for Derivative Securities.
8: Basic Numerical Methods.
9: Finite-Difference Methods.
10: Initial-Boundary Value and LC Problems.
11: Free-Boundary Problems.
12: Interest Rate Modeling.