Skip to main content

Probability Theory

Learn fundamental concepts of probability to prepare for a career in Finance and Data Science

About This Course

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


Prior experience with Python, Linear Algebra and strong calculus background

Course Staff

Course Staff Image #1

Meet the Instructor

Niels O Nygaard is a Professor in the Department of Mathematics at the University of Chicago since 1982. Prior to joining the University of Chicago he taught at Princeton University. He holds a Ph.D. in Mathematics from MIT. Professor Nygaard was the Director of the Financial Mathematics Program since its inception in 1996 until April 2010. Besides his interest in Financial Mathematics he has done research in Arithmetic, Algebraic Geometry and Number Theory. Professor Nygaard was the founding director of both the Financial Mathematics Program and the Stevanovich Center for Financial Mathematics. Professor Nygaard is a recognized scientist in the field of financial mathematics and has a long list of publications