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.


Readership

Graduate students studying quantitative or computational finance, as well as finance professionals, especially in banking and insurance.
Quotes

"With as much rigor as can be mastered by anyone in the still-developing field of computational finance and a sense of humor, the authors unravel its mysteries. The presentations are clear and the models are practical --- these are the two ingredients that make for a valuable book in this field. The book is both practical in scope and rigorous on its theoretical foundations. It is a must for anyone who needs to apply quantitative methods for financial planning --- and who doesn’t need to in our days?"

Stavros A. Zenios, University of Cyprus and the Wharton Financial Institutions Center



"'Numerical Methods and Optimization in Finance' is an excellent introduction to computational science. The combination of methodology, software, and examples allows the reader to quickly grasp and apply serious computational ideas."

Kenneth L. Judd, Hoover Institution, Stanford University

Table of Contents

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

Author Information

By Manfred Gilli, University of Geneva, Switzerland; and Swiss Finance Institute; Dietmar Maringer, University of Basel and University of Geneva, Switzerland and Enrico Schumann, VIP Value Investment Professionals AG, Switzerland