Numerical Methods in Finance and Economics: A MATLAB-Based Introduction, 2nd Edition
October 2006, ©2006
The use of mathematical models and numerical techniques is a practice employed by a growing number of applied mathematicians working on applications in finance. Reflecting this development, Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition bridges the gap between financial theory and computational practice while showing readers how to utilize MATLAB?--the powerful numerical computing environment--for financial applications.
The author provides an essential foundation in finance and numerical analysis in addition to background material for students from both engineering and economics perspectives. A wide range of topics is covered, including standard numerical analysis methods, Monte Carlo methods to simulate systems affected by significant uncertainty, and optimization methods to find an optimal set of decisions.
Among this book's most outstanding features is the integration of MATLAB?, which helps students and practitioners solve relevant problems in finance, such as portfolio management and derivatives pricing. This tutorial is useful in connecting theory with practice in the application of classical numerical methods and advanced methods, while illustrating underlying algorithmic concepts in concrete terms.
Newly featured in the Second Edition:
* In-depth treatment of Monte Carlo methods with due attention paid to variance reduction strategies
* New appendix on AMPL in order to better illustrate the optimization models in Chapters 11 and 12
* New chapter on binomial and trinomial lattices
* Additional treatment of partial differential equations with two space dimensions
* Expanded treatment within the chapter on financial theory to provide a more thorough background for engineers not familiar with finance
* New coverage of advanced optimization methods and applications later in the text
Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition presents basic treatments and more specialized literature, and it also uses algebraic languages, such as AMPL, to connect the pencil-and-paper statement of an optimization model with its solution by a software library. Offering computational practice in both financial engineering and economics fields, this book equips practitioners with the necessary techniques to measure and manage risk.
From the Preface to the First Edition.
PART I. BACKGROUND.
2. Financial Theory.
PART II. NUMERICAL METHODS.
3. Basics of Numerical Analysis.
4. Numerical Integration: Deterministic and Monte Carlo Methods.
5. Finite Difference Methods for Partial Differential Equations.
6. Convex Optimization.
PART III. PRICING EQUITY OPTIONS.
7. Option Pricing by Binomial and Trinomial Lattices.
8. Option Pricing by Monte Carlo Methods.
9. Option Pricing by Finite Difference Methods.
PART IV. ADVANCED OPTMIZATION MODELS AND METHODS.
10. Dynamic Programming.
11. Linear Stochastic Programming Models with Recourse.
12. Non-Convex Optimization.
PART V. APPENDICES.
Appendix A. Introduction to MATLAB Programming.
Appendix B. Refresher on Probability theory and Statistics.
Appendix C. Introduction to AMPL.
- reorganization in order to make adoption in financial engineering courses easier.
- advanced optimization methods are illustrated in later chapter (10, 11, 12), together with applications.
- first chapter to provide motivation and chapter 2 on financial theory has been enlarged and improved to provide better background for engineers (not familiar with finance) and to appeal a little more to economists.
- chapter on numerical integration (which was part of the old chapter on numerical analysis) which also includes the old chapter on Monte Carlo.
- new chapter on binomial and trinomial lattices, which were dealt with superficially in the first edition.
- new appendix on AMPL (an algebraic language to describe optimization models) in order to better illustrate the optimization models in chapters 11 and 12.
- The text is primarily focused on MATLAB-based application, but it also includes descriptions of other readily available toolboxes to finance.
- Helpful appendices on the basics of MATLAB and probability and statistics theory (now greatly enhanced) round out the balanced coverage.
- In the new edition, techniques and applications have now been integrated throughout the book rather than presented in a layered fashion.
- There is now more discussion of economics, optimization, and MATLAB code.
- There are three new chapters on Asian options, pricing American options by Monte Carlo simulation, and (on an optional basis) numerical dynamic programming. There is added coverage of interest-rate derivatives.
- Extensive enhancements have been made in the new edition to topics such as partial differential equations, multi-asset options, and binomial and trinomial lattices.
"In summary, this book is a "must have" for professionals and researchers who employ numerical methods in economic and financial modeling. The amount and quality of the material that the author offers is so generous that readers are likely to benefit from it even if they are not interested in some of the specific applications presented." (Interfaces, June 2008)
"…a broad and enjoyable introduction to computational finance." (Journal of the American Statistical Association, December 2007)
"...written in such a lucid way that it provides great pleasure in reading...excellent for students...of great value to practitioners who are new to the field." (MAA Reviews, November 23, 2006)