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Probability Theory

Title Probability Theory
Quarter Summer 2017
Instructor Niels Nygaard (
Syllabus Course Description

This is a fast paced 10 week course in Probability theory for individuals with some background in Linear Algebra and Calculus. The course will introduce probability concepts for discrete and continuous random variables. We will apply these concepts to models of financial markets and prove the existence of Risk Neutral Probabilities and compute prices of derivatives. This course will use Python for all programming assignments

Course Contents

  • Probability Spaces and Random Variables.
  • Distribution and Density functions
  • Law of large numbers
  • Univariate and multivariate distributions
  • Expected Values and Higher Order Moments
  • Multivariate Theory (Covariance, Independence, Conditional Expectation)
  • Market Models and simple Portfolio Optimization
  • Discrete Market Models and Derivatives Pricing using Risk Neutral Probability measures
  • Stochastic Processes and martingales

Course Objectives:
At the completion of the course, students will be able to do the following:

  • Compute mean, variance and higher order moments for discrete and continuous random variables.
  • Compute covariance and correlations between random variables
  • Apply the theory to compute optimal portfolios
  • Use Risk Neutral Probability Measures to compute derivatives prices
Instruction Format Coursework will have following four important components:
  • Weekly tasks
    • The course instructor will provide reading material, short videos explaining key concepts and lecture notes to be completed at home
    • ¬†Instructor will hold regular video conferences to go over concepts where the students need help
  • Weekly Sessions with Teaching Assistants. The purpose of these sessions will be:
    • Discussion on topics from the week
    • Working in small groups on a problem and presenting solution to the class. Other groups will be required to challenge the concepts and methodology used for problem solving
    • Working on group and individual projects
    • Assignment discussions
    • Quizzes and Exams

The classrooms will be wi-fi enabled and students are required to bring their laptops for the lab sessions

  • Reading Assignment and homework for the week
  • Virtual office hour with TA/Instructor via video conferencing
Assessment A letter grade A,B,C,D or F for the course will be decided based on

Projects: 40% of the final grade

  • 2 group projects and 2 individual projects

Mid Term Exam: 10% of the final grade

  • 30 minutes duration which will include both multiple choice and subjective problems

Final Exam: 15% of the final grade

  • 30 minutes duration which will include both multiple choice and subjective problems

Homework: 20% of the final grade

  • There will be 6-8 homework which will be manually graded and feedback will be provided

Quizzes: 10% of the final grade

  • There will be 4 quizzes which will have multiple choice format

Class Participation:10% of the final grade

  • Your participation will be evaluated based on lab discussion, questions/comments, replies on the discussion forum and teamwork on the group projects
Textbook No Textbook required
Pre-Requisite Prior experience with Python, strong calculus background
Time Lecture Time: 8:30 pm to 10 pm EST, Tuesday
Lab Time: 8:00 pm to 9:00 pm EST Sunday
Virtual Office Hour time: TBA
TA Information  
Effort Required 6-10 hours per week
Certification Participants who complete the course will receive an instructor-signed certificate with a letter grade
Computer Requirements Prior programming experience in Python.