A state-of-the-art introduction to the powerful mathematical andstatistical tools used in the field of financeThe use of mathematical models and numerical techniques is apractice employed by a growing number of applied mathematiciansworking on applications in finance. Reflecting this development,Numerical Methods in Finance and Economics: A MATLAB-BasedIntroduction, Second Edition bridges the gap between financialtheory and computational practice while showing readers how toutilize MATLAB?the powerful numerical computing environmentforfinancial applications.The author provides an essential foundation in finance andnumerical analysis in addition to background material for studentsfrom both engineering and economics perspectives. A wide range oftopics is covered, including standard numerical analysis methods,Monte Carlo methods to simulate systems affected by significantuncertainty, and optimization methods to find an optimal set ofdecisions.Among this book's most outstanding features is the integration ofMATLAB?, which helps students and practitioners solve relevantproblems in finance, such as portfolio management and derivativespricing. This tutorial is useful in connecting theory with practicein the application of classical numerical methods and advancedmethods, while illustrating underlying algorithmic concepts inconcrete terms.Newly featured in the Second Edition:* In-depth treatment of Monte Carlo methods with due attention paidto variance reduction strategies* New appendix on AMPL in order to better illustrate theoptimization models in Chapters 11 and 12* New chapter on binomial and trinomial lattices* Additional treatment of partial differential equations with twospace dimensions* Expanded treatment within the chapter on financial theory toprovide a more thorough background for engineers not familiar withfinance* New coverage of advanced optimization methods and applicationslater in the textNumerical Methods in Finance and Economics: A MATLAB-BasedIntroduction, Second Edition presents basic treatments and morespecialized literature, and it also uses algebraic languages, suchas AMPL, to connect the pencil-and-paper statement of anoptimization model with its solution by a software library.Offering computational practice in both financial engineering andeconomics fields, this book equips practitioners with the necessarytechniques to measure and manage risk.
About the Author
PAOLO BRANDIMARTE is Professor of Quantitative Methods for Finance and Logistics at Politecnico di Torino in Italy. He is the author of several publications, including five books, on the application of optimization and simulation to diverse areas such as production management, telecommunications, and finance. Dr. Brandimarte has extensive teaching experience in engineering and economics faculties, including master's and PhD-level courses.
Table of Contents
Preface to the Second Edition.
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 CarloMethods.
5. Finite Difference Methods for Partial DifferentialEquations.
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.
What People are Saying About This
"Inquisitive statisticians may find this book an interesting read in which to put their theories and epistemology to the test." (Journal of American Statistics, 2008)
"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)