iolinked
iolinked · quantitative finance — the mathematics of markets

Put a number on
an uncertain future.

Quantitative finance is the mathematics of markets — probability, statistics, options pricing, risk and trading. It is what "quant" is short for, and it has nothing to do with quantum physics.

Every quant course you can buy hands you the same pile: a stochastic-calculus formula, a table of Greeks, a Sharpe ratio, and no idea why any of them exist. This one is built the other way round. It starts from one sentenceput a number on an uncertain future, using only finite noisy data, then size your bet against the risk of being wrong — and that sentence has exactly four verbs, which turn out to be the whole subject: you model the uncertainty, estimate it from data you don't fully trust, price a claim on it, and then act under it. Underneath sits the mathematics every other course assumes you already have and never teaches — so we teach it, from sets and counting up, with no gaps. This is not interview prep and it is not a formula sheet. It is for the pleasure of understanding the thing properly: you'll leave able to re-derive any result and reason about a case you have never seen. Every idea opens with a hook and lands on something you can drag, break, or predict.

01

Browse the course

24 of 45 chapters live · eight parts · 45 chapters · ~20 playable interactives each
Part 0 · 8 chapters

Foundations

The maths every quant course assumes and never teaches — sets, series, calculus, logs, linear algebra.

Start here
Part 1 · 7 chapters

Model the uncertainty

Probability from the axioms up: random variables, the distribution family tree, Markov chains, paradoxes.

Open
Part 2 · 6 chapters

Estimate from data

Every statistic is itself random. Sampling, p-values done honestly, regression, and the one sin: in-sample.

Open
Part 3 · 3 chapters

Learn from data

The bias–variance dial, regularization, trees and boosting, and scoring a classifier honestly.

Open
Part 4 · 5 chapters

Price the future

No-arbitrage, Brownian motion and Itô, the one pricing engine, the Greeks, and the volatility smile.

Open
Part 5 · 8 chapters

Act under risk

Sizing the bet: Sharpe and Kelly, VaR and the tail, factors, pairs, carry — and the spread that eats it.

Open
Part 6 · 4 chapters

Compute it

Big-O, the core data structures, dynamic programming and the order book, then a real vectorized stack.

Open
Part 7 · 4 chapters

The craft

Reason from nothing, build all ten projects — theory you can run is theory you own — and see the field.

Open
02

Part 0 · Foundations

8 chapters · all live · the maths everyone assumes you have
quant — part 0 · foundations
03

Part 1 · Model the uncertainty

7 chapters · all live · probability from the axioms up
quant — part 1 · model
04

Part 2 · Estimate from data

6 chapters · all live · every statistic is itself random
quant — part 2 · estimate
05

Part 3 · Learn from data

3 chapters · all live · machine learning, honestly scored
quant — part 3 · learn
06

Part 4 · Price the future

5 chapters · one engine: a discounted expected payoff
quant — part 4 · price
>>>
ch 25No-Arbitrage & Static ReplicationIf two portfolios pay the same, they cost the same — that alone gives put-call parity.soon ch 26Brownian Motion, GBM & Itô's LemmaThe chain rule keeps a second-order term — which is exactly why log-price drifts at μ−σ²/2.soon ch 27Risk-Neutral Pricing & Black–ScholesOne engine, evaluated under GBM. Black–Scholes is not a formula to memorize; it is that integral.soon ch 28The Greeks & Delta-HedgingThe Greeks are the Taylor expansion of the price; gamma is the cost of holding the hedge together.soon ch 29Volatility: Implied, Smile & Fat TailsImplied vol is Black–Scholes run backwards; the smile is the market pricing the tails it assumed away.soon
07

Part 5 · Act under risk

8 chapters · size the bet, then survive the spread
quant — part 5 · act
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ch 30Performance, Drawdown & Mean-VarianceSharpe is reward per unit risk; diversification adds Sharpes in quadrature, which feels like a free lunch.soon ch 31Value-at-Risk & Expected ShortfallVaR is a quantile of the loss distribution — and it is silent about exactly the days that ruin you.soon ch 32GARCH, MLE, Copulas & the TailVolatility clusters; the crisis is joint tail dependence, and Gaussian VaR never sees it coming.soon ch 33State-Space Models: HMM & KalmanWhen the state is hidden and moving, filter it — recursive Bayes with a linear-Gaussian shortcut.soon ch 34Factor Investing & Signal ResearchRank, go long-short, measure the Information Coefficient — and watch it decay.soon ch 35Cointegration, Pairs & Stat ArbCorrelation is co-movement; cointegration is a stationary spread you can actually bet on.soon ch 36Futures Carry & Term StructureCarry is the return if nothing happens — decomposed into roll yield, spot and basis.soon ch 37Microstructure & Market-MakingThe spread is compensation for adverse selection — where every theoretical edge goes to die.soon
08

Part 6 · Compute it

4 chapters · the number has to actually be computed
quant — part 6 · compute
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ch 38Complexity & the Problem-Solving FrameBig-O is how cost scales; O(log n) is always something being halved.soon ch 39The Core Data StructuresPick the structure whose invariant matches your query — hash, heap, deque, sorted container.soon ch 40Recursion, DP, Graphs & the Order BookRecursion plus memory is dynamic programming; an order book is a hash and a heap wearing a suit.soon ch 41Vectorization & the Quant-Dev StackArray ops instead of loops, then a backtester that does not lie to you about fills.soon
09

Part 7 · The craft

4 chapters · reason from nothing, then build it
quant — part 7 · the craft
>>>
ch 42Fermi Estimation & Mental MathPut a number on almost anything from almost nothing — decompose, assume, multiply, sanity-check.soon ch 43The Project LadderTen projects in dependency order — VaR, Black-Scholes, pairs, GARCH, factors, PCA risk.soon ch 44The Lay of the FieldWhat a researcher, a trader, a developer and a risk quant actually do all day — and which is you.soon ch 45Your Own Pace & an Honest MirrorA rhythm you set yourself, and a scorecard that tells you the truth about where you actually are.soon