ECG790C  Computational
Methods in Economics and Finance Spring 2011
Nelson 2403  MW 1:30 2:45
Prof. Paul L. Fackler
4344 Nelson, 5154535
paul_fackler@ncsu.edu
Office Hours: by appointment via email
</span>Course web site: http://www4.ncsu.edu/~pfackler/ECG790C
Course
Description
Fundamental methods for formulating
and solving economic models will be developed. Emphasis will be on defining the
mathematical structure of problems and on practical computer methods for
obtaining model solutions. Major topics will include solution of systems of
equations, complementarity relationships and
optimization. Both finite and infinite dimensional problems will be addresses,
the latter through the use of finite dimensional approximation techniques.
Particular emphasis will be placed on solving dynamic optimization and
equilibrium problems. Applications will be drawn from finance, agricultural and
resource economics, macroeconomics and econometrics.
Prerequisites
Although there are not specific required courses, students registering for this course must have a reasonable background in mathematics, including college calculus, linear algebra and differential equations. In addition, some background in either computer programming or economic theory is necessary. Students who are not sure of their level of preparation for this course should consult the instructor.
Student Learning Outcomes
By the end of this course, students will
be able to:
.......identify and apply appropriate methods for solving
equations and optimization problems
.......compute numerical approximations to integrals and
derivatives
.......understand how to apply function approximation methods to solve
functional equations
.......model and solve basic financial derivatives models
.......model and solve discrete and continuous time dynamic
programming problems
.......design and document software to solve economic and/or
financial models
Required Textbook
Applied Computational Economics and Finance, Mario J. Miranda & Paul L. Fackler, MIT
Press, 2002.
Grading Policy
Grades will be based on a series
of homework sets (20%), 2 takehome and inclass exams that will count for 25%
of the grade each and a takehome and inclass final exam (30%). Grades will be
given on an A, B, C, D, F basis, to be interpreted as excellent, satisfactory,
unsatisfactory, unacceptable and failing. Homework and exams will be posted on
the course web site and you will have one week to complete them. Answers will
be posted one week later. Homework will be collected but not graded; you will
receive one point for satisfactory completion of a homework.
Homework & Exam Policies
You are encouraged to discuss homework problems with your classmates but should
develop your own answers. If you share computer code, you should understand and
be able to explain what the code does. I consider the homework to be an
essential part of the learning process; you cannot learn to formulate and solve
models without actively attempting to do so. If you wait until a quiz before
attempting to work problems you will be in for an unpleasant surprise.
READ CAREFULLY:
Takehome exams should not be discussed with any one
else (except me) and computer code for solving exam problems should not be
shared. Evidence of collaboration on quizzes will result in a grade of 0
for the exam, F for the course or even expulsion from the university (see
section below on academic integrity).
Multiple files should be sent as a single compressed (ZIP) file (not RAR
files please). If not already on your computer, utilities for zipping files
are available on the internet. Responses to quiz questions should include a
document with answers to homework questions and/or documentation of your code.
I prefer that this be typed and emailed along with any relevant code  MS Word
DOC, DVI or PDF formats are ok. If not typed, please strive to make your
answers legible and scan them to include with your zip file.
All computer code submitted should run without encountering error messages. If
you are having trouble debugging your code you should get help (from me) before
it is due. My answers will be posted to the web after the due date. Plan
accordingly; computer code generally takes at least twice as long to write as
you expect, even after you know what you want the code to do. If you wait until
the night before a homework is due, you will almost
certainly not complete it in time.
A document describing how homework and quizzes
should be prepared is available. An associated zip file
is also available. You should read this document carefully.
Important Dates
Feb. 14 first takehome posted
Feb. 21 first take home due at 1:00 PM
Feb. 21 first inclass exam
March 8 last day to drop without a grade
March 23 second takehome posted
March 30 second take home due at 1:00 PM
March 30 second inclass exam
April 29 Takehome final posted
May 6 Takehome final due at noon
May 6 Inclass final exam (14 PM)
Academic Integrity
You should be aware of University policy on academic integrity: see Code
of Student Conduct.
The university has also adopted the following Honor Pledge:
I have neither given nor received
unauthorized aid on this test or assignment.
It is assumed that students understand and agree with this pledge when
submitting exams.
Students with
Disabilities
Reasonable accommodations will be made for students with verifiable
disabilities.
In order to take advantage of available accommodations, students must register
with
Disability Services for Students at
1900
For more information on NC State's policy on working with students with
disabilities, please see http://www.ncsu.edu/provost/hat/current/appendix/appen_k.html
Online Course Evaluation
Online class
evaluations will be available for students to complete during the last 2 weeks
of spring term:
12 p.m. April 14 through 8 a.m. May 6
Students will receive an email message directing them to a website where they
can login using their Unity ID and complete evaluations. All evaluations
are confidential; instructors will not know how any one student responded to
any question, and students will not know the ratings for any instructors.
Evaluation website: https://classeval.ncsu.edu/
Student help desk: classeval@ncsu.edu
More information about ClassEval:
http://www.ncsu.edu/UPA/classeval/
Computer programming
The basic computing language
used in the course is MATLAB, which provides a highlevel interactive
programming and graphics environment. MATLAB is installed on machines in Economics
graduate student computing labs and on the UNITY system. Student versions of
MATLAB are also available for purchase. The booklet "Getting Started with
MATLAB" provides an introduction to the language. It is available in PDF
form on the MATLAB CD. You should work through this booklet and explore
MATLAB's demos as soon as possible. I have also written a MATLAB
Primer that can be downloaded. There is a ZIP file with the code files
discussed in the primer (Download
Primer Code Files). I will discuss the basics you will need in class. You
should also be aware that there are lots of resources for MATLAB user, the two
most important of which are the MathWorks
Web Site and the MATLAB discussion group (comp.softsys.matlab),
where people post questions and comments and hope for useful replies. The FAQ
(Frequently Asked Questions) page for the group is http://www.mit.edu/~pwb/cssm/. An
excellent reference is available at:
http://www.mathworks.com/access/helpdesk/help/pdf_doc/matlab/matlab_prog.pdf
Also see: http://www.mathworks.com/access/helpdesk/help/techdoc/matlab.html
CompEcon
Toolbox
You should install the CompEcon Toolbox as soon as possible (follow the
instructions in the README file) and make sure that the demonstration files run
correctly.
References
William F. Ames. Numerical Method for Partial Differential
Equations, 3rd ed.
K.E. Atkinson. An Introduction to
Numerical Analysis, 2nd ed.
A.T. BharuchaReid. Elements of the Theory of Markov Processes and Their
Applications.
Eric Briys, et al. Options, futures, and exotic derivatives :
theory, application and practice.
D.R. Cox and H.D. Miller. The Theory of Stochastic Processes.
J.E. Dennis, Jr. and R.B. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear
Equations.
Avinash K. Dixit and Robert S. Pindyck. Investment Under
Uncertainty.
Darrell Duffie. Dynamic Asset Pricing Theory, 2nd ed.
R. Fletcher. Practical
Methods of Optimization, 2nd ed. P.E. Gill, W. Murray, and M.H. Wright. Practical Optimization.
Gene H. Golub, and James M. Ortega.
Scientific Computing and Differential Equations: An Introduction to Numerical
Methods.
G.H. Golub and C.F.
van Loan. Matrix Calculations, 2nd ed.
John C. Hull. Options,
Futures and Other Derivative Securities.
D. R. Jones,
C. D. Perttunen, and B. E. Stuckman.
Lipschitzian optimization without
the Lipschitz constant. Journal of Optimization Theory and Applications, 79(1):157181,
October 1993.
Kenneth L. Judd. Numerical Methods in Economics.
M.I. Kamien and
N.L. Schwartz. Dynamic Optimization: The Calculus of
Variations and Optimal Control in Economics and Management, 2nd ed.
Samuel Karlin and
Howard M. Taylor. A Second Course in Stochastic Processes,
2nd ed.
William J. Kennedy and James E. Gentle. Statistical Computing.
David R. Kincaid and E. Ward Cheney.
Numerical Analysis: Mathematics of Scientific Computing.
Cleve Moler. Numerical Computing with MATLAB.
(http://www.mathworks.com/moler/chapters.html)
Salih N. Neftci. An Introduction to the Mathematics of
Financial Derivatives.
William H. Press, Saul A. Teukolsky,
William T. Vetterling and Brian P. Flannery. Numerical
Recipes, 2nd ed.
Domingo Tavella. Quantitative Methods in Derivatives Pricing: An Introduction to
Computational Finance.
Domingo Tavella and
Curt Randall. Pricing Financial
Instruments: The Finite Difference Method.
Paul Wilmott. Derivatives: The Theory and Practice of Financial Engineering.
Course Schedule (this is an approximation and may change
during the semester)
10Jan 
Class 1 
Introduction to Numerical
Computing 
C1, AB, Article 
12Jan 
Class 2 
Computer Arithmetic 
A2, Article 
17Jan 
Holiday 

19Jan 
Class 3 
Linear Equations 
C2, Notes 
24Jan 
Class 4 
NonLinear Equations 
C3.13.6 
26Jan 
Class 5 
Sparse Systems of Equations and Complementarity
Problems 
S3.63.8 
31Jan 
Class 6 
Unconstrained Optimization 
S4.14.4 
2Feb 
Class 7 
Statistical Computing 
S4.5 & Notes 
7Feb 
Class 8 
Constrained Optimization 
S4.6 
9Feb 
Class 9 
Global Optimization 
Jones, et al. & Notes 
14Feb 
Class 10 
Numerical Integration 
S5.1, 5.2, 5.5 
16Feb 
Class 11 
Numerical Differentiation 
5.6 
21Feb 
Class 12 
First InClass
Exam 

23Feb 
Class 13 
Evolutionary Methods for
Differential Equations 
S5.7, ODESuite, Using

28Feb 
Class 14 
Function Approximation 
S6.16.7 
2Mar 
Class 15 
Function Approximation (cont.) 

7Mar 
Spring Break 

9Mar 
Spring Break 

14Mar 
Class 16 
Functional Equations 
S6.86.9 
16Mar 
Class 17 
PDEs 

21Mar 
Class 18 
Derivatives Pricing 
S10.1 
23Mar 
Class 19 
PDE Methods for Derivative Pricing 
S11.1 
28Mar 
Class 20 
PDE Methods for Derivative Pricing (cont.) 

30Mar 
Class 21 
Second Inclass
Exam 

4Apr 
Class 22 
Dynamic Programming & Real Options Theory 
S8.18.4, 10.4 
6Apr 
Class 23 
DP in Continuous Time  Discrete Controls 
S10.4, S11.4 & Article 
11Apr 
Class 24 
DP in Continuous Time  Discrete Controls (cont.) 

13Apr 
Class 25 
DP in Continuous Time (Infinite Controls) 
S10.5 & S11.5 
18Apr 
Class 26 
DP in Continuous Time (Continuous Controls) 
S10.210.3, S11.211.3 
20Apr 
Class 27 
DP in Discrete Time (Solution Techniques) 
S9.19.7 
25Apr 
Class 28 
Rational Expectations Models 
S8.6, S9.9 & RESolve 
27Apr 
Class 29 
Wrap up and review 



6May 
Final Exam 
14PM (Friday) 
