Numerical Methods and Optimization in Finance

This book describes computational finance tools. It covers fundamental numerical analysis and computational techniques, such as option pricing, and gives special attention to simulation and optimization. Many chapters are organized as case studies around portfolio insurance and risk estimation problems.  In particular, several chapters explain optimization heuristics and how to use them for portfolio selection and in calibration of estimation and option pricing models. Such practical examples allow readers to learn the steps for solving specific problems and apply these steps to others. At the same time, the applications are relevant enough to make the book a useful reference. Matlab and R sample code is provided in the text and can be downloaded from the book's website.

Shows ways to build and implement tools that help test ideasFocuses on the application of heuristics; standard methods receive limited attentionPresents as separate chapters problems from portfolio optimization, estimation of econometric models, and calibration of option pricing models

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. Modelling 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. Portfolio Optimization

14. Econometric Models

15. Calibrating Option Pricing Models