Numerical Methods in Finance and Economics

Introduction

This is a course in the basic tools of numerical analysis that can be used to address analytically intractable problems in finance and economics. A large class of problems cannot be analyzed with analytical tools, and numerical methods are increasingly expanding the questions we can address.

Numerical methods are vital to all types of applied financial and economic research. The generality with which the techniques will be presented in this course will make them applicable to a wide range of fields, including finance, econometrics, corporate finance, asset pricing, resource economics, labor economics, economic theory, international trade, macroeconomics, game theory, public finance, contract theory and others.

In order to learn how to use computational tools in an informed and intelligent way, this course endeavors to explain not only when and how to use various numerical algorithms but also how and why they work; in other words, the course opens up the “black boxes” and provide the students with a versatile toolbox for their own research.

Course content

The course has four main parts:

1. Elementary numerical methods on R^n (differentiation, root finding, optimization, interpolation, integration)
2. Functional equation problems
3. Solving individual choice models, heterogeneity and aggregation.
4. Advanced topics (aggregate shocks, continuous time methods, default models,etc).