Introduction to Quantitative Finance

What is quantitative finance? It applies mathematics, statistics and computing to financial markets. Quants price derivatives, design trading strategies, measure risk and build portfolios. The field is often described by its tools, which is misleading: the tools are shared, but the questions in a pricing team, a trading desk and a risk department are very different.

What is quantitative finance used for?

Banks use it to price and hedge the products they sell and to hold enough capital against their positions. Hedge funds and proprietary trading firms use it to find and trade statistical edges. Asset managers use it to build portfolios and measure what their managers add. Regulators use it to check that all of the above are not taking risks they cannot carry.

Who should take this course?

Anyone considering a quant career or a quant course who wants to know what the field involves before committing time or money. It is free, takes about six hours and ends with a recommendation of where to start.

What you will be able to do

• Explain how quantitative finance replaces discretionary judgment with a testable, rules-based pipeline spanning data collection, pattern identification, validation, and execution.
• Distinguish sell-side Q-measure roles from buy-side P-measure roles by probability measure, time horizon, and the mathematical tools each emphasizes.
• Describe how a central limit order book functions and identify the adverse selection and inventory costs embedded in every bid-ask spread.
• Explain why financial return distributions are leptokurtic and state the consequences for any risk model calibrated on the normal distribution.
• State the six structural assumptions of the Black-Scholes model and identify the empirical evidence that the constant-volatility assumption is violated.
• Interpret Value at Risk and Expected Shortfall figures and identify the three structural biases that inflate backtested performance relative to live results.
• Identify the four quant role archetypes by their skill emphasis and match an existing knowledge profile to the appropriate entry point into the field.

Syllabus, module by module

1. What Is Quantitative Finance?

   What quantitative finance is, where its core ideas came from, and how the field evolved from Bachelier's 1900 thesis through Black-Scholes to the arrival of physicists and computer scientists on Wall Street.

2. A Day in the Life of a Quant

   The four distinct roles operating simultaneously on a modern trading floor, how they divide between the Q and P probability measures, and what separates sell-side from buy-side quantitative work.

3. Markets 101: What Quants Are Actually Trading

   How financial markets match buyers with sellers, set prices, and guarantee settlement, including the order book mechanics and structural failures that quantitative models must account for.

4. The Language of Uncertainty: Probability and Statistics for Quants

   The probability and statistics that quantitative finance runs on, why the normal distribution systematically understates tail risk, and what fat-tailed distributions reveal about the true behavior of financial returns.

5. How Models Work: From Black-Scholes to Machine Learning

   How quantitative models are constructed and where they break down, from the Black-Scholes formula and its six structural assumptions through factor models to volatility clustering.

6. The Quant Toolkit: Python, Data, and the Workflow

   The Python-centered toolkit that powers modern quantitative research, including how NumPy handles matrix computation and how Pandas was designed to manage the structural problems specific to financial data.

7. Risk, Performance, and Why Strategies Die

   How professional risk managers measure downside exposure, evaluate strategy performance, and identify the structural biases in backtesting that inflate apparent returns before a strategy goes live.

8. Where to Go Next: Your Roadmap into the Field

   How the quantitative finance job market is organized into four role archetypes, what each demands in terms of skills and interview format, and how to identify the right entry point from any starting knowledge base.

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.

Assessment

Not assessed. Study notes, a cheat sheet and a workbook come with every lesson. Open courses are free, have no exam and award no certificate. Read how certification works.