Probability for Quantitative Finance

Probability for quantitative finance starts from one fact: every model in the field is a statement about probability. An option price is an expectation, a value-at-risk figure is a quantile, a trading signal is a conditional forecast. If the probability underneath is shaky, every later course is harder than it needs to be.

What makes probability for finance different?

Financial returns break the assumptions of most textbook examples. They have fat tails, their volatility changes over time and their dependence rises in a crisis. The course teaches standard probability and then shows, on market data, where each standard assumption holds and where it fails.

Who is this course for?

Engineers and scientists whose probability is rusty, finance graduates who want firmer foundations, and anyone heading for the researcher path. It is the first course of the Foundation Certificate in Computational Finance.

What you will be able to do

• Work with discrete and continuous random variables, their moments and their transformations.
• Use conditional probability and expectation to reason about information arriving over time.
• Explain the law of large numbers and the central limit theorem, and when they fail for fat-tailed data.
• Fit and compare normal, Student t and other distributions to asset returns.
• Simulate from the distributions you fit and check the simulation against the data.

Syllabus, module by module

1. Events, probability and counting

   Sample spaces, the axioms, independence and Bayes' rule, with examples from default and market events.

2. Random variables and distributions

   Discrete and continuous random variables, distribution and density functions, and the families used in finance.

3. Expectation and moments

   Mean, variance, skewness and kurtosis; why the fourth moment matters for returns.

4. Joint distributions and dependence

   Covariance, correlation and its limits, and a first look at copulas.

5. Conditioning

   Conditional distributions and conditional expectation as the best forecast given information.

6. Limit theorems

   The law of large numbers and the central limit theorem, and what changes when variance is infinite.

7. Fat tails in practice

   Fitting distributions to returns, tail plots and the cost of assuming normality.

8. Simulation

   Sampling from fitted distributions and checking simulated against observed behaviour.

How the certificate is earned

Each module ends with a graded quiz, and the course ends with a graded problem set mixing derivations and short Python exercises. On a pass you receive the Course certificate in Probability for Quantitative Finance, issued by the Institute with a verification code. Read how certification works.

Before you start

Single-variable calculus and high-school algebra. Some Python helps for the exercises, but none is required to start.

• Introduction to Quantitative Finance