A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of finance
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.
Table of Contents
PART I. BACKGROUND.
1. Motivation.
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.
Index.
