# ECS550NFB - Introduction to Numerical Methods using MATLAB

## Content

This is a more detailed and updated outline of the course and is subject to minor changes. The course is intended to introduce you to a broad range of numerical methods using MATLAB. Focus is on understanding the scope of usefulness and limitations of the presented methods.

• Monday - Essentials
• Lecture: Motivation, MATLAB essentials, Number Representation, Coding conventions, Solving system of linear equations, Function approximation, Integration - quadrature and Monte Carlo, Debugging
• Practice session: matrix multiplication, overfitting, Chebyshev nodes, MC integration
• Tuesday - Optimization
• Lecture: Root finding - Newton method, Secant method, Classification of optimization problems, Formulating problem in MATLAB, Line search and Trust region methods, Quasi-Newton methods, Linear programming, Integer programming - branch and bound, Quadratic programming, Global optimization methods
• Practice session: Simple Newton-Raphson algorithm, Linear programming example, Providing gradient information to solver
• Assignment 1: Include a specific constraint to Travelling Salesman Problem.
• Wednesday - Macroeconomics
• Lecture: Spectral frequency decomposition - representation, Band pass filter, Hoddrick-Prescott filter, Dynamic programming - math preliminaries, Bellman equation, Value function iteration, Interpolation of the value function, Policy function iteration, Stochastic dynamic programming, Dynare - introduction to solving DSGE models
• Practice session: Spectrum decomposition, Dynamic programming example, Dynare - impulse response functions
• Assignment 2: Implement policy function iteration for a given simple dynamic macroecononic model.
• Thursday - Econometrics
• Lecture: Econometrics essentials - overview on available methods (OLS, IV, Panel data, Time series), Bootstrap - math preliminaries, usefulness, practical side, Selected topics: Principal Components Analysis, Support Vector Machines, Non-parametric Estimation.
• Practice session:  Bootstrapping Confidence intervals, Empirical coverage probability of Bootstrap CI
• Assignment 3: Demonstrate that Bootstrap fails on a specific (simulated) example.
• Friday - Finance
• Lecture: Bond pricing, Derivatives pricing - Binomial and Trinomial Lattice, Monte Carlo method, Finite differences method,
• Practice session: Derivatives' pricing using binomial lattice, MC method and finite differences method.
• Assignment 4: Investment valuation using Monte Carlo simulation.

## Organisation

• Date: January 9-13
• Place: NHH – Norwegian School of Economics, Karl Borch Auditorium, (45min + 15min break)
• 10:00 – 11:00 Session 1
• 11:00 – 12:00 Session 2
• 14:00 – 15:00 Session 3
• 15:00 – 16:00 Practice session (with laptops)
• Software requirements: Participants must ensure to have MATLAB installed on their laptops prior to the beginning of the course, together with Optimization Toolbox. We will also make use of certain parts of Statistical and Machine Learning Toolbox and Financial Toolbox, but these are not essential for this course. You can find the list of toolboxes installed typing the command 'ver' in the Command Window.  Shareware 30days student version may be downloaded on Mathworks website. NHH PhD scholars may contact the IT administrator to get their copies of MATLAB.
• Credits: 5 ECTS will be awarded to participants with good performance in all four Assignments. Deadline for the submission is 30days after the end of the course. Candidates will be awarded PASS/FAIL grade.
• Literature: Various sources will be used, main references are listed here. These books supplement the course content along many directions, but are not necessary. A detailed reference list will be provided in the slides.
• Brandimarte, Paolo. Numerical methods in finance and economics: a MATLAB-based introduction. John Wiley & Sons, 2013. - (this is an all-round book that is both practical and accessible).
• Judd, Kenneth L. Numerical methods in economics. MIT press, 1998.
• Fackler, Paul L. Applied computational economics and finance. MIT press, 2002.