141 lessons · 1342 questions · 4 study paths
Probability, mental arithmetic, market making, derivatives, statistics and systems — written as a textbook, drilled in the formats the firms actually use, and checked line by line against the arithmetic.
The first lesson of each path is free in full. The trial opens every lesson and the graded apparatus; nothing is charged for 7 days and you can cancel before then.
The three legs are drawn faintly and their sum in full. It is zero outside the wings, worth $10 at the middle strike, and never below zero anywhere — which is the entire reason being paid to put it on would be an arbitrage rather than a view.
Both highlighted paths end in a positive test. The test is doing its job on each branch; what decides the answer is how many people started down each one.
Value at risk is the edge of the shaded region: the loss you beat 99 days in 100. It says nothing whatever about the shape inside it. Expected shortfall is the average of that region — 2.67 sigma for a normal — and it is the number that changes when the tail gets fatter.
Newton squares the error each step, so the number of correct digits doubles: five iterations take you from one digit to sixteen. Bisection halves it, gaining a third of a digit a step — reliable, never fast, and the right fallback when the derivative misbehaves.
The exact distribution for a hundred people. The count itself is random — more than a third of the time nobody gets their own hat — but it averages exactly one, and linearity delivers that average without ever computing these probabilities. They are e−1/k! to four decimal places for any n above about ten.
The highlighted observation sits far from the others in both factor exposure and response. Including it pulls the fitted slope from about 0.50 to 0.75. Cook’s distance detects this combination of leverage and residual size; the honest report shows the fit with and without the point.
The curriculum
Pick the seat you are interviewing for. Each path is a complete sequence, from the arithmetic gate through to the material the final round actually turns on.
34 lessons · 373 questions
Speed, probability and judgement under uncertainty: the path to a quoting seat at a market maker.
26 lessons · 318 questions
From payoff diagrams to the volatility surface: what an options market maker has to know before they can quote.
56 lessons · 436 questions
Statistics, econometrics and signal research: finding an edge in data and proving it is not noise.
25 lessons · 215 questions
Algorithms, numerical methods and the systems knowledge that separates a quant developer from a general software engineer.
Inside a lesson
Follow an idea through the equations, figures and worked examples that make it useful. This unedited excerpt from the Greeks chapter scrolls on its own; take control whenever you like.
Proposition 1.2
Delta is the hedge ratio — how many shares to hold against the option. It is the sensitivity — how much the option moves for a one-point move in the underlying. And it is roughly the risk-neutral probability of finishing in the money, which is N(d2) exactly and N(d1) near enough for an at-the-money option.
Holds when
Equation 1.5
A second-order Taylor expansion of the option price. Every day on an options desk is an argument about which of these four terms explained the day.
Proposition 1.6
Gamma is paid for with theta. Long an option, you profit from movement in either direction but lose a little every day nothing happens; short an option, you collect that decay and are exposed to a large move. There is no position that is long gamma and long theta, and a candidate who proposes one has not understood the equation.
Holds when
Example 1.7
You are long 100 at-the-money calls, delta-hedged. Gamma is 0.04 per contract, theta is −$8 per contract per day, and each contract covers 100 shares. The stock moves $2 and implied volatility is unchanged. Roughly what is the day’s P&L?
Worked solution
Sanity check. A two-dollar move is exactly the break-even here. A larger move and the convexity pays; a quieter day and the decay wins.
| Question | Answer |
|---|---|
| Which has more vega, a one-month or a one-year at-the-money option? | The one-year — vega grows roughly with T. |
| Where is gamma largest? | At the money, and it grows without bound as expiry approaches. |
| You are long a straddle. What do you want? | Movement, in either direction, and quickly — you are long gamma and short theta. |
| Delta of a deep in-the-money call? | Close to one, with almost no gamma or vega left. |
| You are short gamma into an earnings announcement. What do you do? | Reduce, or buy convexity back. A single large move is exactly what you are exposed to. |
How you practise
Each mode gives feedback on the decisions that matter in that format, from arithmetic speed to risk and sizing.
16 generators · five levels each
FreeGenerated, never repeated: every item is derived from a seed, so a run is reproducible and the bank cannot be memorised. Pace, median time and the technique behind every miss come back at the end.
80 in 8 · number sequences · beat the odds
FreeThe timed online assessments trading firms use to decide who gets an interview. The same items and clock for everyone, marked on the server, and ranked against every other player.
1342 questions
Free sampleNumeric answers are parsed, not matched — 23/6, 2^-1, C(52,5) and √2/2 all read correctly — and a wrong answer that matches a known mistake is told which mistake it was.
Re-roll a fair die once. Fair price?
Correct. Re-roll 1–3.
One free tree · five-minute Premium runs
First free sampleInspect option quotes on a binomial tree, catch the prices that break replication, and name the locking trade.
4 scenarios
First free sampleQuote two-sided, get filled by counterparties who are sometimes informed, carry the inventory and requote. Width, skew and discipline are graded against a reference maker run on the same seed.
Five-level books · five-minute runs
Free sampleThe spread and the microprice, what a market order really pays as it walks the book, where you sit in the queue, which way the book leans, and when two venues cross.
Eight races · £1,000 bankroll
PremiumUse the form guide and two sets of odds to find edges and Dutch books. Sizing is graded against a disciplined bettor.
7 papers
PremiumTopic weights and a difficulty mix are declared rather than left to whatever the bank happens to hold. Feedback is withheld until you submit and the clock runs against the start time.
Everything you get wrong returns on a spaced interval in the review queue, alongside the answers you were confident about and still missed.
Timed runs post to the leaderboard, and your best scores collect on a profile you can make public and share.
Why you can trust it
A textbook with a wrong number in it teaches the wrong number. Every figure in every worked example is recomputed in a test, and the build fails if the content and the arithmetic disagree.
it('separates a GBM mean from its median', () => {
const S0 = 100;
expect(S0 * Math.exp(0.08)).toBeCloseTo(108.33, 2);
// Variance drag: the median lags the mean.
const median = (v) => S0 * Math.exp(0.08 - v ** 2 / 2);
expect(median(0.25)).toBeCloseTo(105.0, 2);
expect(median(0.45)).toBeLessThan(S0);
});npm run content:check
4 tracks · 24 topics · 141 lessons · 1342 questions
10,956 expressions compiled
0 errors, 0 warnings
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