Numerical Methods and Optimization in Finance

Computationally-intensive tools play an increasingly important role in financial decisions. Many financial problems—ranging from asset allocation to risk management and from option pricing to model calibration—can be efficiently handled using modern computational techniques. Numerical Methods and Optimization in Finance presents such computational techniques, with an emphasis on simulation and optimization, particularly so-called heuristics. This book treats quantitative analysis as an essentially computational discipline in which applications are put into software form and tested empirically.

This revised edition includes two new chapters, a self-contained tutorial on implementing and using heuristics, and an explanation of software used for testing portfolio-selection models. Postgraduate students, researchers in programs on quantitative and computational finance, and practitioners in banks and other financial companies can benefit from this second edition of Numerical Methods and Optimization in Finance.

• Introduces numerical methods to readers with economics backgrounds
• Emphasizes core simulation and optimization problems
• Includes MATLAB and R code for all applications, with sample code in the text and freely available for download

Students (Master or PhD level) and researchers in programs on quantitative and computational finance, and also practitioners in banks and other financial companies

1. Introduction

I. Fundamentals
2. Numerical Analysis in a Nutshell
3. Linear Equations and Least Squares Problems
4. Finite Difference Methods
5. Binomial Trees

II. Simulation
6. Generating Random Numbers
7. Modeling Dependencies
8. A Gentle Introduction to Financial Simulation
9. Financial Simulation at Work: Some Case Studies

III. Optimization
10. Optimization Problems in Finance
11. Basic Methods
12. Heuristic Methods in a Nutshell
13.: Heuristic Methods: A Tutorial
14. Portfolio Optimization
15. Backtesting Investment Strategies
16. Econometric Models
17. Calibrating Option Pricing Models