We suggest all four start on the same probability, statistics and code. After that, the trader learns how a price forms in the next second, the researcher learns to test whether a pattern is real, the developer learns to make a model run fast and give the same number twice, and the analyst learns what can be lost on a bad day. The roadmap is one trunk and four branches, and the trunk comes first.
A quant is a person who uses maths, statistics and code to make decisions about prices and risk in financial markets. The field is called quantitative finance. (It is not the "quant" aptitude section of the CAT or GMAT, which are entrance tests for business school.)
This page uses four role names: trader, researcher, developer and analyst. It gives the order to learn things in for each one. It does not describe a day at the desk. For that, read The four quant jobs first. Nothing here promises a job, and job titles mean different things at different firms. Read the job description of the role you want.
The trunk every role shares
We suggest every branch start from the same four subjects. This trunk and these role descriptions are our summary, not an industry standard.
- Probability. Probability is the maths of chance: how likely each outcome is, and what happens on average. Everything below builds on it.
- Statistics. How to learn from data, and how sure you can be of what it shows.
- Linear algebra and calculus. Linear algebra is the maths of tables of numbers. Calculus is the maths of change.
- Python. A programming language: a way to write instructions a computer follows. It is widely used for research code, often with a library, which is a ready-made set of tools.
On Thuztra Learn, this trunk is Levels 0 and 1 of the Core quant curriculum. Its eight Level 0 (beginner) modules start from school maths and a first notebook. Its Level 1 modules, one level up, cover probability, linear algebra, estimates and optimisation (finding the best choice under limits). If you would rather start with free material, the free quant learning path puts four steps in order: two university courses and two free books.
Branch 1: quant trader
A quant trader decides what to buy and sell, at what price, and how much risk to hold. The work is close to the market.
- How a price forms. An order book is the list of every price at which people wait to buy or sell. Start with the limit order book as a mechanism.
- Options and volatility. An Option is a contract that gives the right, but not the duty, to buy or sell at a set price later. Volatility is how much a price moves around. The Greeks are numbers that say how an option's price changes when one input moves. Then read the Greeks as a trading desk uses them.
- Market making. A market maker quotes a price to buy and a price to sell at the same time, and earns the gap when both fill.
- Position sizing. How much to hold, so that one bad day does not end the game.
On Learn, this is the Quant trader path: six modules, from how prices form to position sizing.
Branch 2: quant researcher
A quant researcher looks for patterns in data that might predict prices, and tests whether they are real or luck.
- Statistical inference. How to tell a real pattern from noise. A Backtest runs a fixed rule on past prices to see how it would have done, and the hard part is not fooling yourself with one.
- Stochastic calculus. The maths of prices that move at random over time. It starts with Brownian motion, a model of a path that wanders by chance.
- No-arbitrage pricing. Arbitrage is a profit with no risk. Pricing starts from the rule that a fair price allows none: read No arbitrage, and what it actually forbids.
- Factor models and machine learning. Ways to explain many prices with a few shared causes, and where machine learning (methods that let a computer find patterns in data) helps and where it does not.
On Learn, this is the Quant researcher path: seven modules, from Brownian motion to machine learning.
Branch 3: quant developer
A quant developer builds the code that prices, tests and runs the models. The work is close to the computer.
- Python, then C++. C++ is a faster, stricter language. Read when a pricing engine belongs in C++, and when it does not.
- Numerical methods. Monte Carlo prices a contract by running many random paths and taking the average. Start with the Monte Carlo pricing estimator.
- Performance. Why the same sum can take very different times. Read The complexity that bites, and the complexity we quote.
- Market data. Clean prices, as they were known on each day, so a test cannot see the future.
On Learn, this is the Quant developer path (six modules) plus the coding path, "Code a quant actually writes" (six modules: Python, C++, SQL, performance and AI-assisted work).
Branch 4: quant analyst
"Quant analyst" means different work at different firms, so read the job description. This branch follows the closest Learn path, the Risk quant path.
- Risk measures. What a single risk number claims, and what it hides. VaR (value at risk) is one such number: a loss size that daily losses stay below on most days. Read what a VaR number actually says.
- Tails. The rare, very large losses at the edges of the range of outcomes.
- Credit. The risk that someone who owes money does not pay it back.
- Rates. How a bond's price moves when interest rates move. This sits in the Core curriculum, not the Risk path. Read Duration, DV01 and convexity.
On Learn, the Risk quant path has five modules: risk measures, tails, credit, regulation (the rules banks must follow) and liquidity (how easily something can be sold without moving its price).
What Learn teaches, and what it does not
| Step | Taught on Thuztra Learn | Not taught on Thuztra Learn |
|---|---|---|
| Trunk | Probability, statistics, linear algebra, calculus, first Python | A full university degree |
| Trader | Order books, options, market making, sizing | Trading with real money, or a desk's own systems |
| Researcher | Inference, stochastic calculus, pricing, factor models | A firm's private data |
| Developer | C++ inside pricing code, numerical methods, SQL (a language for asking a database questions), profiling (measuring where code spends its time) | Low-latency trading systems, built to send orders as fast as possible: network code, exchange connections, FPGA chips (hardware set up for one task). Also general coding interview drills such as data structures (ways to arrange data in memory) |
| Analyst | Risk measures, tails, credit, regulation, plus rates from the Core curriculum | A bank's own model rules |
For the gaps, the firm's own pages and the job description are the place to look.
Choosing a branch
Pick the branch whose first step reads most like a question you would enjoy. Read the free page linked in that step. Then try one free interview question: quoting into a lopsided book or twenty vol, and what it says about tomorrow ("vol" is short for volatility).
You know it worked if you can say the main idea of the page out loud in two sentences. Two things go wrong most often. The page uses a word you do not know: go back to the trunk and the first Core page. Or every branch looks equally good: start with the trunk, which is the same for all four.
The whole order, with every module, is in the Core quant curriculum on Thuztra Learn. Membership is a paid subscription: see what Thuztra Learn is and what it costs.
In short
We suggest every role start with probability, statistics and code. The branch decides the next year of study: markets and options for a trader, inference and stochastic calculus for a researcher, numerical methods and C++ for a developer, risk measures for an analyst. Learn covers the maths and the pricing code, not low-latency trading systems.
Terms used here
Related
The four quant jobs
Researcher, trader, developer and risk, described by what each actually does all day. One rule followed through all four desks, and the places where the four of them disagree.
How to become a quant in India, in quantitative finance
The subjects to learn, the Indian degrees and entrance tests that teach the maths, free courses from Indian institutes, and Indian market data to practise on. Every link goes to the official page.
The best books for quantitative finance interviews
Nine books for quant interviews, grouped by the stage they help with, plus what the Green Book and Heard on the Street each are, from the author and catalogue records. No book problems copied.
What quantitative finance actually is
Money decisions made by measurement rather than by feel. One worked example on a made-up saver's arithmetic, what the field is not, and what this library will and will not do.
More on these topics
- How to become a quant in the UK and Europe, in quantitative finance
- Getting into quant from any college
- Quant vs data scientist, in quantitative finance
- Quant vs software engineer, and the quant developer in between
- Quantitative finance courses compared, and how to choose one
- Quantitative finance projects you can build, check and explain
Topics
- careers
- getting started
- quant roles
- roadmap