Probability for Quantitative Finance, with Statistics

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.

What is quantitative analysis in finance?

Most trading ideas that fail in live trading did not fail because the market changed. They failed because the statistics that supported them were wrong: a standard error that ignored autocorrelation, a result that was the best of fifty tries, a regression driven by three days in a crisis. This course teaches statistics for finance: the methods that catch those mistakes.

It is the use of data and statistical models to support financial decisions: whether a strategy has an edge, how much a stock moves with the market, how volatile a portfolio is. The methods are standard statistics. The difficulty is financial data, which is noisy, dependent and short relative to the effects being measured.

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.

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.
• Estimate means, volatilities and correlations with honest standard errors.

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. Describing returns

   Simple and log returns, summary statistics and the stylized facts of financial data.

6. Estimation

   Estimators, bias, variance and standard errors; why expected returns are so hard to estimate.

What every course contains

Every paid course comes with the first seven and the certificate, whichever level it sits at. The proctored exam and the credential come when the course is taken as part of a Certificate, Diploma or Fellowship. Everything is self-paced: the material is yours to study in any order, at any hour, for the whole of the license.

1. Workbooks. Written to train the thinking patterns and the important concepts of the course, with worked problems and the reasoning behind each answer, so that you learn to think the way the subject is thought.
2. Audio edition. Focused, well-presented recordings with explainers and examples of the material, made to be interesting, relevant and entertaining, so that the general subject can be learned away from the desk.
3. Notes. Pre-produced notes with every fact the course relies on, written out in full, so that nothing has to be transcribed from the films or the audio.
4. Cheat sheet. One sheet with every important learning concept of the course on it, to keep beside you during the work and to revise from before the exam.
5. Named sources. Every fact in the notes names its source, the paper, the book or the dataset, for anyone who wants to dig in further.
6. Explainer films. Focused films, in the style of the sample films on the catalog page, that walk through the most difficult concepts of the course with visual explanations of a high standard.
7. Transcript. A full transcript of every film and every audio recording, searchable and quotable.
8. Proctored exam. Taken as part of a Certificate, Diploma or Fellowship, the course ends in a proctored multiple-choice questionnaire, with a pass mark of 60% and three retakes included. A course taken on its own is assessed by its coursework and has no exam.
9. Verifiable certificate. A certificate of completion that a third party can verify: an employer sends the code on it to the credentials office and receives written confirmation of the course, the date and the result.
10. Credential of the program. The Certificate, Diploma or Fellowship of the program, track or path the course belongs to, awarded when every course in it is passed. Which one depends on the program you choose.

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, with Statistics, issued by the Institute with a verification code. A course taken as part of a Certificate, Diploma or Fellowship ends in a proctored online exam with a pass mark of 60%. The fee includes three retakes; each attempt after that carries a reduced proctored exam fee. A course taken on its own is assessed by its coursework and has no exam. 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