Numerical Methods with Matlab for Financial Mathematics
MA 591

Prof. Scroggs
Home Getting Started Lessons Assignments Syllabus (policies)

Syllabus for MA  591 , Fall 2011

Instructor: Jeffrey S. Scroggs

Office Hours: Posted at http://www4.ncsu.edu/~scroggs/mywebsite/OfficeVisits.html.
E-mail address: scroggs@math.ncsu.edu (use MA591 in the Subject line).
Office: 2108 SAS
Phone Number: 919.515.7817
Home page: http://www4.ncsu.edu/~scroggs/mywebsite
Class Meets: Harrelson Hall, rm G100,
-----Tu 1:30 - 4:00pm
-----Th 1:30 - 2:45pm

Course Pre-requisites

Knowledge of Statistics, Calculus, Linear Algebra, Differential Equations.

Learning Outcomes

Goal: This is an introduction to elementary programming concepts with Monte Carlo techniques for options pricing.  Starting with a problem suitable for mathematical analysis, students will be able to analyze the problem, and either identify appropriate Matlab tools to solve the problem, or create new tools.  Scientific visualization is included . 

Topics

The particular topics covered will likely be somewhat different than these, but here is the plan at the start of the semester

Book   Section(s) Topic
Brandimarte   3.1 Nature of numerical computation
Brandimarte   3.2 Solving Systems of linear equations
Brandimarte   3.3 Function Approximation and interpolation
Brandimarte   3.4 Solving Nonlinear Equations
Brandimarte   4.1 Deterministic Quadrature
Korn, et. al.   2.1 Random Number Generators
Korn, et. al.   2.3 Quality Measures of RNGs
Korn, et. al.   3.1 Monte Caro Methods, Introduction
Korn, et. al.   3.2 Strong Law of Large Numbers
Korn, et. al.   3.3 Improving Convergence
Korn, et. al.   4.1 Continuous-Time Stochastic Processes
Korn, et. al.   4.2 Stochastic Processes: Basic Definitions
Korn, et. al.   4.3 Stochastic Processes: Monte Carlo Method
Korn, et. al.   4.4 Stochastic Processes: Brownian Motion, Brownian Bridge
Korn, et. al.   4.5 Stochastic Processes: Ito calculus
Korn, et. al.   4.6 Stochastic Processes: Differential Equations
Korn, et. al.   4.7 Stochastic Processes: Simulating Solutions of DEs
Korn, et. al.   5.1 Financial Models
Korn, et. al.   5.2 Basics of stock price modeling
Korn, et. al.   5.3 Black-Scholes framework
Korn, et. al.   5.4 Basic Definitions
Korn, et. al.   5.5 Introduction to option pricing
Korn, et. al.   5.6 Option pricing and the Monte Carlo method in the BS setting
Korn, et. al.   5.7 Weakneses of the BS model
Korn, et. al.   5.8 Local volatility
Korn, et. al.   5.9 Calibrating
Korn, et. al.   5.12 Variance Reduction

 

Textbook Information

Required: Monte Carlo Methods and Models in Finance and Insurance, Ralf Korn, Elke Korn, Gerald Kroisandtt. Available from Amazon.com.

Required: Matlab 7 or later (software). This software is available on the computers in the NCSU-operated labs. You may wish to purchase the Student Edition at the NCSU bookstore. You can also use the software via the Virtual Computer Lab (VCL).

Required: USB drive

Required: NUMERICAL COMPUT.W/MATHLAB-REV.REPRINT Ed: 1ST Yr: 2004, Cleve Moler, ISBN: 97808987166
Availble for free online

Required: Two "blue books", available from local bookstores.

Recommended: Numerical Methods in Finance and Economics: A MATLAB-Based Introduction, Paolo Brandimart. Available from Amazon.com.

Good book: Monte Carlo Methods in Financial Engineering, Paul Glasserman.

Projected Schedule of Homework, Quizzes, and Exams

Except for Quiz 0, quizzes will not be announced in advance.

Quiz 0 will cover this syllabus. Specifically, you are required to know the material found in the Academic Integrity Statement. This quiz will be given the first day of class.

Homework will be assigned throughout the course.

There will be one mid-term exam and one final exam. Each exam will have a take-home portion and an in-class portion.

The take-home portion of the final exam will be assigned during the last week of class.

How Grades are Determined

Weight Category of Assignment
10 %
Homework
30 % Pop Quizzes
30 % Mid-term Exam
30 % Final Exam

 

Homework

Homework is graded on a 3-point scale using the guidlines at this link. It is also covered by the quizzes and exams. Homework will be submitted electronically.

Grades

Total Grade = (Quiz 0 score)*(Homework + Quizzes + Mid-term + Final)

Range Grade
97.6 <= X <= 100    A+ 
92.3 <= X < 97.6    A 
90.0  <= X < 92.3    A- 
87.6 <= X < 90.0    B+ 
82.3 <= X < 87.6    B 
80.0 <= X < 82.3    B- 
77.6 <= X < 80.0    C+ 
72.3 <= X < 77.6    C 
70.0 <= X < 72.3    C- 
67.6 <= X < 70.0    D+ 
62.3 <= X < 67.6    D 
60.0 <= X < 62.3    D- 
X < 60    F 

Policy on Incomplete Grades and Late Assignments

Incomplete grades will not be given. You must complete the assignments for the course as the semester progresses.

Policy on Attendance, Excused Absences, Missed Work

NCSU policy, including what constitutes an 'Excused Absence,' is covered in REG 02.20.3.

No late assignments will be accepted. The penalty for submitting an assignment late is a zero on the assignment.

Academic Integrity Statement

Students are required to follow NCSU policy available at www.ncsu.edu/provost/academic_regulations/integrity/reg.htm.  "Academic dishonesty is the giving, taking, or presenting of information or material by a student that unethically or fraudulently aids oneself or another on any work which is to be considered in the determination of a grade or the completion of academic requirements or the enhancement of that student's record or academic career." (NCSU Code of Student Conduct)

Much of the code you will be generating has probably already been written as a Matlab Demo or Matlab Function. If you are instructed to generate the code, use of predefined Matlab demos, or code from another source, will be considered a violation.

Homework. I encourage a free exchange of information regarding 'how to' accomplish the tasks in the homework. You can give and receive verbal assistance, write things down, point at the computer screen, nearly anything. If you do

Quizzes. You must work completely independently on quizzes.

Mid-term and final exam. You must work completely independently on exams. Do not talk with anybody except Dr. Scroggs regarding the content of the exam. You are suggested to not even talk about how the level of difficulty with other people.

Penalties for a violation: For the first violation, you will receive a zero on the assignment and be put on academic integrity probation for the remainder of your stay at NCSU. The second violation may result in your suspension from NCSU. Both situations will involve the Office of Student Conduct.

The Student Affairs web site has more information (http://www.ncsu.edu/student_affairs/osc/AIpage/acaintegrity.html).

Utilization implication of the Honor Pledge

The pledge, that you "have neither given nor received unauthorized aid on this test or assignment", is implicit in everything you turn in for this course. The penalty for non-compliance is mentioned above.

Further Information

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