{"id":"2028904166895112617","url":"https://x.com/gemchange_ltd/status/2028904166895112617","text":"","author":{"name":"gemchanger","username":"gemchange_ltd","avatarUrl":"https://pbs.twimg.com/profile_images/1975113774680920064/-dpcubqz_200x200.jpg"},"createdAt":"Tue Mar 03 18:43:43 +0000 2026","engagement":{"replies":180,"retweets":1287,"likes":11881,"views":7435155},"article":{"title":"How I'd Become a Quant If I Had to Start Over Tomorrow","previewText":"In 2025, entry-level quants at top firms pulled $300K-$500K total comp.\nAI/ML hiring in finance grew 88% year-over-year.\nThis article is everything I wish someone had handed me when i started my path","coverImageUrl":"https://pbs.twimg.com/media/HCgcPCZXkAA4osL.jpg","content":"In 2025, entry-level quants at top firms pulled $300K-$500K total comp.\n\nAI/ML hiring in finance grew 88% year-over-year.\n\nThis article is everything I wish someone had handed me when i started my path laid out in the exact order you should learn it.\n\nThe path is like layers of a video game, where you can't skip levels.\n\nEvery concept builds on the last. But if you put in real work, not watching some lame ahh YouTube videos about finance, that's just wasting your time, actual problem-solving work - you can go from knowing nothing to being something in about 18 months.\n\nDisclaimer:\nNot Financial Advice & Do Your Own Research & Markets involve risk.\nMy own project  - [@coldvisionXYZ](https://x.com/@coldvisionXYZ)\n\n## Forget everything you think you know about trading\n\nMost people think quantitative trading is about picking stocks. Having opinions on Tesla. Predicting earnings.\n\nQuant trading is about math.\n\nYou are mostly working with statistical relationships, pricing inefficiencies, and structural edges that exist because markets are complex systems run by humans who make systematic errors.\n\n## Part I: Probability is the Language of Uncertainty\n\nEverything in quantitative finance reduces kinda to 1 question:\n\nWhat are the odds, and are the odds in my favor?\n\nThat's probability. If you don't understand probability at a deep level, nothing else in this article matters.\n\nConditional thinking\n\nMost people think in absolutes. Something is true or it isn't.\nQuants think in conditionals. Given what I know, how likely is this?\n\n![](https://pbs.twimg.com/media/HCei_w7XcAAjMwU.png)\n\nThe probability of A given B equals the probability of both happening divided by the probability of B. Profound implications.\n\nA stock goes up 60% of days - that's the base rate. But on days when volume is above average, it goes up 75% of the time.\n\nThat conditional probability is a NOT BS. The raw 60% is NOISY BS.\n\nBayes' theorem\n\n![](https://pbs.twimg.com/media/HCejMkSbgAAeuXv.png)\n\nYour updated belief equals\n\n(how likely you'd see this data if your hypothesis were true) * (your prior belief) / (the total probability of seeing this data under any hypothesis).\n\nThe denominator sums over all hypotheses.\n\nIn practice, you compute this with Monte Carlo sampling.\n\nBut the logic is the same. Bayes is how you update your conviction in real time.\n\nA model says a stock should be worth $50. Earnings come out, revenue is 3% above estimate. The Bayesian posterior shifts upward. The traders who update fastest and most accurately win bread.\n\nExpected value and variance your two best friends\n\n![](https://pbs.twimg.com/media/HCejtL7XsAA5vQ7.png)\n\n![](https://pbs.twimg.com/media/HCejv0UXIAACqgx.png)\n\nExpected value is your conviction.\nVariance is your risk.\n\nIf your strategy has positive expected value and you can survive the variance, you likely will make money.\n\nLevel 1 homework (3-4 weeks at 2 hours/day):\n1. Read\nBlitzstein & Hwang, Introduction to Probability (free PDF from Harvard). Every problem in Chapters 1-6.\n2. Code\nSimulate 10,000 coin flips, verify the law of large numbers visually.\n3. Code 2\nImplement a Bayesian updater takes a prior and likelihood, returns a posterior.\n\n## Part II: Statistics\n\nOnce you speak probability, you need to learn to listen to data.\n\n![](https://pbs.twimg.com/media/HCgQBaXXYAEaXBx.png)\n\nThat's statistics and the #1 lesson statistics teaches is \"most of what looks like NOT A BS is actually NOISY BS\"\n\nHypothesis testing is the BS detector\n\nYou build a model. It backtests at 15% annual return. Is it real?\n\nSet up H_0: \"this strategy has zero expected return.\"\nCompute a test statistic.\nCalculate a p-value - the probability of seeing results this good if H_0 were true.\n\nBUT If you test 1,000 random strategies, 50 of them will show p-values below 0.05 purely by chance.\n\nThat's the multiple comparisons problem.\n\nUr fix is Bonferroni correction divide your significance threshold by the number of tests\nOr use Benjamini-Hochberg for false discovery rate control.\n\nEvery single beginner massively overestimates how much NOT A BS they've found. Your first 10 strategies will all be NOISY BS. Accept this now and save yourself a lot of money.\n\nRegression decomposing returns\n\nLinear regression y=Xβ+ϵ is the workhorse.\nIn finance, you regress your strategy's returns against known risk factors:\n\n![](https://pbs.twimg.com/media/HCgDDAkaEAEvrzK.png)\n\nThe intercept α is your alpha\nthe return that can't be explained by known factors. If α is zero after accounting for factors, your \"edge\" is just disguised market exposure.\n\nThe OLS estimator:\n\n![](https://pbs.twimg.com/media/HCgDMxxXIAA4zDW.png)\n\nThe most important number is α.\nUse Newey-West standard errors financial data has autocorrelation and heteroskedasticity, so default OLS standard errors are wrong. Using them is like driving with a cracked windshield.\n\nMaximum Likelihood Estimation\n\nGiven data x_1,…,x_n,​ from a model with parameter θ:\n\n![](https://pbs.twimg.com/media/HCgQ6rLXUAAaw9F.png)\n\nSet the derivative to zero and solve. (or it's over gng)\n\nMLE is how you calibrate every model in finance fit a GARCH model to volatility, estimate jump-diffusion parameters, calibrate option pricing to market quotes.\n\nIt's asymptotically efficient no other consistent estimator has lower variance for large samples (the Cramér-Rao lower bound).\n\nWhen someone at a firm says they're \"calibrating\" a model, they almost, like  always mean MLE.\n\nLevel 2 homework (4-5 weeks):\n1. Read\nWasserman, All of Statistics, Chapters 1-13.\n2. Code\nDownload real stock returns with yfinance. Test normality (they'll fail). Fit a t-distribution via MLE. Compare.\n3. Code\nRun a Fama-French 3-factor regression on a stock portfolio using statsmodels.\n4. Code\nImplement a permutation test shuffle dates 10,000 times, compare shuffled performance to actual.\n\n## Part III: Linear Algebra\n\nLinear algebra sounds boring. It's the machinery that runs everything: portfolio construction, PCA, neural networks, covariance estimation, factor models. You cannot be a quant without being fluent in matrices.\n\n![(if u skipped Algebra in school school doing that, it's over)](https://pbs.twimg.com/media/HCgSDNfawAUriXT.jpg)\n\nThinking in matrices\n\nA covariance matrix Σ captures how every asset moves relative to every other asset. For 500 stocks, Σ is 500×500 with 125,250 unique entries. Portfolio variance collapses to a single expression\n\n![](https://pbs.twimg.com/media/HCgEBHmWkAIWTsh.png)\n\nThis quadratic form is the core of Markowitz portfolio theory, of risk management, of everything.\n\nEigenvalues is what actually matters in a universe of stocks\n\nLook at a 500-stock universe and the first 5 eigenvectors explain 70% of all variance. Everything else is NOISY BS.\n\nThe first time eigendecomposition u use it the whole world changes. Look at a 500-stock universe and the first 5 eigenvectors explain 70% of all variance. Dimensionality reduction, and it's the foundation of factor investing.\n\nLevel 3 homework (4-6 weeks):\n1. Watch\nGilbert Strang's MIT 18.06 lectures all of them. Non-negotiable.\n2. Read\nStrang, Introduction to Linear Algebra. Do the problems.\n3. Code\nPCA decomposition of S&P 500 returns. Plot eigenvalue spectrum. Identify top 3 components.\n4. Code\nMarkowitz mean-variance optimization from scratch.\n\n## Part IV: Calculus & Optimization\n\nCalculus is the language of change. In finance, everything changes: prices, volatilities, correlations, the entire probability distribution shifts second by second. Calculus describes and exploits those changes.\n\nDerivatives (the math kind): appears in every neural network backpropagation and every Greek calculation.\n\nTaylor expansion:\n\n![](https://pbs.twimg.com/media/HCgE6k4boAA07fr.png)\n\nDelta hedging is the first-order approximation.\nGamma hedging adds the second-order correction.\nAnd the reason Itô calculus differs from ordinary calculus is precisely because the second-order Taylor term doesn't vanish for random processes. Just Remember it\n\nLevel 4 homework (4-5 weeks):\n1. Read\nBoyd & Vandenberghe, Convex Optimization (free PDF from Stanford), Chapters 1-5.\n2. Code\nImplement gradient descent from scratch. Minimize the Rosenbrock function.\n3. Code\nSolve a portfolio optimization problem with cvxpy including transaction cost constraints.\n\n## Part V: Stochastic Calculus\n\nBefore stochastic calculus, you're a data scientist who likes finance.\n\nAfter it, you're a quant. QUANTATIVE FINANCE EXPERT, you heard?\n\n![that's you](https://pbs.twimg.com/media/HCgU9xXW8AAmAc_.png)\n\nThis is where you learn to model randomness in continuous time, derive the Black-Scholes equation from first principles, and understand why the trillion-dollar derivatives market works the way it does.\n\nBrownian motion pure randomness, formalized\n\nA Brownian motion (Wiener process) W_t is a continuous-time random walk:\n\n- W_0 = 0\n\n- Increments W_t - W_s ~ N(0, t - s) for t > s\n\n- Non-overlapping increments are independent\n\n- Paths are continuous but nowhere differentiable\n\nThe critical insight that everything else depends on: dW_t has \"size\" dt, which means (dW_t)^2 = dt. This sounds like a technicality, but its the single most important fact in quantitative finance.\n\nGeometric Brownian Motion models stock prices:\n\n![](https://pbs.twimg.com/media/HCgHgzZWIAAmud7.png)\n\nItô's lemma\n\nIn normal calculus, df = f'(x)dx. You Taylor-expand, and the (dx)^2 term is infinitesimally small you drop it.\n\nBut when x is a stochastic process, (dW_t)^2 = dt is first order. You can't drop it.\n\nItô's lemma:\n\n![](https://pbs.twimg.com/media/HCgHxPzawAE8TWR.png)\n\nApply it to an option price and you get Black-Scholes. Formula is the engine behind the entire derivatives industry.\n\nDeriving Black-Scholes from scratch\n\nFollow along with pen and paper.\n\nStep 1: Let V(S,t) be an option price. Apply Itô's lemma:\n\n![](https://pbs.twimg.com/media/HCgH4u8W8AAi9NX.png)\n\nStep 2: Construct a delta-hedged portfolio Π=V−∂S/∂V​⋅S. Compute dΠ:\n\n![](https://pbs.twimg.com/media/HCgIDXgXoAA_PP_.png)\n\nThe dW_t​ terms cancel perfectly. The portfolio is locally riskless.\n\nStep 3: A riskless portfolio must earn the risk-free rate: dΠ=rΠ dtd\\Pi = r\\Pi \\, dt dΠ=rΠdt.\n\nStep 4: Substitute and rearrange:\n\n![](https://pbs.twimg.com/media/HCgIfdGWYAEfPl8.png)\n\nThis is the Black-Scholes PDE.\n\nNotice what happened - the drift μ vanished. The option price doesn't depend on the expected return of the stock. Risk preferences don't matter. You can price options as if everyone is risk-neutral. The first time this sinks in genuinely mind-bending.\n\nSolving this PDE for a European call with strike K and expiry T gives:\n\n![](https://pbs.twimg.com/media/HCgIq17boAAZdI7.png)\n\n![where d_1=](https://pbs.twimg.com/media/HCgIyuuawAAEWtg.png)\n\n![d_2 =](https://pbs.twimg.com/media/HCgI4E5WoAAzATN.png)\n\nThe Greeks\n\n- Delta Δ is How much the option moves per $1 stock move. Your hedge ratio.\n\n- Gamma Γ​: How fast delta changes. Your convexity exposure.\n\n- Theta Θ: Time decay. Typically negative for long options.\n\n- Vega V: Sensitivity to volatility. Where most derivatives money is made.\n\n- Rho ρ: Sensitivity to interest rates.\n\nDelta tells you your hedge ratio. Gamma tells you how often to re-hedge. Theta is the cost of holding. Vega is the bread and butter of vol trading desks.\n\nLevel 5 homework (6-8 weeks - the hardest level):\n1. Read\nShreve, Stochastic Calculus for Finance II. The gold standard.\n2. Alternative\nArguin, A First Course in Stochastic Calculus (newer, more accessible).\n3. Derive\nApply Itô's lemma to f(S)=ln⁡(S) where S follows GBM. Get the −σ^2/2.\n4. Derive\nThe full Black-Scholes equation from the delta-hedging argument.\n5. Code\nBlack-Scholes from scratch. Compare to Monte Carlo. Verify convergence.\n\n## Polymarket\n\nThis is the most interesting market in the world right now and the math behind it connects everything in this article: probability, information theory, convex optimization, integer programming\n\nHow LMSR prices beliefs\n\nThe Logarithmic Market Scoring Rule (LMSR), invented by Robin Hanson, powers automated prediction markets. The cost function for n outcomes:\n\n![](https://pbs.twimg.com/media/HCgK1C4X0AAdWZK.png)\n\nwhere q_i​ tracks outstanding shares of outcome i and b is the liquidity parameter. The price of outcome i:\n\n![](https://pbs.twimg.com/media/HCgK60sXYAEqP3I.png)\n\nThat's the softmax function - function powering every neural network classifier.\n\nPrices always sum to 1, always lie in (0,1), and always exist providing infinite liquidity. The market maker's maximum loss is bounded at b * ln(n)\n\n## The Quant Career Landscape\n\n4 archetypes:\nQuant Researcher\nThe most-cracked guy who finds patterns in petabytes, builds predictive models, designs strategies. Needs PhD-level math/stats/ML, or exceptional undergraduate achievement. At firms like Jane Street, QRs work with tens of thousands of GPUs.\n\nQuant Developer/Engineer\nThe mid-cracked guy, mostly the builder. Trading platforms, execution engines, real-time data pipelines. Makes the researcher's model actually trade. Needs production C++/Rust/Python, low-latency systems.\n\nQuant Trader\nEither the biggest degen or the most-cracked guy, mostly the decision-maker. Runs capital, manages risk, makes real-time calls. Highest compensation variance - eight figures in exceptional years.\n\nRisk Quant\nThe most-cracked guy or just insanely experienced corporate guy, mostly the guardian. Model validation, VaR, stress testing, regulatory compliance. Steadier career, lower ceiling. The emerging AI/ML Quant role signal generation with deep learning is the fastest-growing, with hiring up 88% year-over-year in 2025.\n\nWhat it pays:\n\nLevel Top Tier (Jane Street, Citadel, HRT)\nNew grad $300K-$500K+ total comp\nMid career (3-7yr)$550K-$950K\nSenior (8+yr)$1M-$3M+\nStar trader/PM $3M-$30M+\n\nMid Tier (Two Sigma, DE Shaw)\nNew grad $250K–$350K\nMid career (3-7yr) $350K–$625K\nSenior (8+yr) $575K–$1.2M\nStar trader/PM  idk\n\nJane Street's average employee compensation was reported at $1.4 million/year in H1 2025. That's the average though\n\nThe interview gauntlet\n\nResume screen ->\nOnline assessment (mental math via Zetamac - target 50+, logic puzzles)  ->\nPhone screen (probability problems, betting games) ->\nSuperday (3-5 back-to-back interviews, mock trading, coding, whiteboard derivations).\n\nJane Street gives problems intentionally too hard to solve alone - they test how you use hints and collaborate.\n\nOver two-thirds of their recent intern class studied CS; over a third studied math. Finance knowledge generally not required.\n\nThe #1 prep resource\nXinfeng Zhou's Green Book (A Practical Guide to Quantitative Finance Interviews) - 200+ real problems.\nSupplement with QuantGuide.io (\"LeetCode for quants\")\nBrainstellar\nJane Street's Figgie card game\n\n## The Complete Toolbox\n\nPython stack\nData: pandas, polars (Polars is 10-50x faster on large datasets)\nNumerics: numpy, scipy\nML (tabular): xgboost, lightgbm, catboost\nML (deep): pytorch\nOptimization: cvxpy\nDerivatives: QuantLib (Industry-grade, C++ backend)\nStats: statsmodels\nBacktesting: NautilusTrader\nBacktesting (simpler): backtrader, vectorbt (Easier starting point)\nQuant research: Microsoft Qlib (17K+ stars, AI-oriented)\nRL for trading: FinRL (10K+ stars)\n\nC++ and Rust\nTbh i don't know anything about this. This is what I've found:\nC++ libraries: QuantLib, Eigen, Boost.\nRust: RustQuant for option pricing, NautilusTrader as the Rust+Python paradigm (Rust core for speed, Python API for research).\n\nData sources\nFree: yfinance, Finnhub (60 calls/min), Alpha Vantage.\nMid-range: Polygon.io ($199/mo, sub-20ms latency), Tiingo.\nEnterprise: Bloomberg Terminal (~$32K/yr), Refinitiv, FactSet.\nBlockchain: Alchemy (free tier with archive access).\n\nSolvers\nGurobi: Fastest commercial MIP solver, free academic license. Essential for combinatorial arbitrage.\nGoogle OR-Tools: Strongest free solver.\nPuLP/Pyomo: Python modeling interfaces.\n\n## The Reading List (In Order)\n\nMathematics\n\n1. Blitzstein & Hwang - Introduction to Probability (free PDF from Harvard)\n\n1. Strang - Introduction to Linear Algebra + MIT 18.06 lectures\n\n1. Wasserman - All of Statistics\n\n1. Boyd & Vandenberghe - Convex Optimization (free PDF from Stanford)\n\n1. Shreve - Stochastic Calculus for Finance I & II\n\nQuant finance\n\n1. Hull - Options, Futures, and Other Derivatives\n\n1. Natenberg - Option Volatility and Pricing\n\n1. López de Prado - Advances in Financial Machine Learning\n\n1. Ernest Chan - Quantitative Trading\n\n1. Zuckerman - The Man Who Solved the Market\n\nInterview prep\n\n1. Zhou - Practical Guide to Quantitative Finance Interviews (Green Book #1)\n\n1. Crack -Heard on the Street\n\n1. Joshi - Quant Job Interview Questions\n\nCompetitions\n\n- Jane Street Kaggle ($100K prize)\n\n- WorldQuant BRAIN (100K+ users, pays for alpha signals)\n\n- Citadel Datathon (fast-track to employment)\n\n- Jane Street monthly puzzles (above interview difficulty)\n\n## Three things I wish I'd known earlier\n\nEstimation error is the real enemy.\nFull Kelly betting, unconstrained Markowitz, ML models with too many features - they all fail for the same reason: overfitting NOISY BS in parameter estimates.\n\nThe math works perfectly with true parameters. You never have true parameters. The gap between theory and practice is always estimation error, and the best quants are the ones who respect it.\n\nTools have democratized. Conviction hasn't.\nAnyone can access QuantLib, Polygon.io, and PyTorch. Technology is necessary but not sufficient. Edge lives in unique data, unique models, or unique execution - not better pip installs.\n\nThe math is the moat\nAI can write code and suggest strategies. But the ability to derive why Itô's lemma has an extra term, to prove that discounted prices are martingales under the risk-neutral measure, to know when a convex relaxation is tight versus loose in a combinatorial market that mathematical fluency separates quants who build edge from quants who borrow it. And borrowed edge expires.\n\n## What comes in Part 2\n\nPart 2 covers: exotic derivatives (barriers, Asians, lookbacks), stochastic volatility (Heston model calibration), jump-diffusion (Merton), advanced measure theory (martingale representation, optional stopping), stochastic control for optimal execution (Almgren-Chriss), reinforcement learning for market making, transformer architectures for financial time series, FPGA trading infrastructure, WebSocket feeds, parallel execution, Frank-Wolfe with Gurobi for combinatorial arbitrage across thousands of conditions.\n\nThe math gets harder. The paycheck gets longer"},"adhxContext":{"savedByCount":1,"publicTags":[],"previewUrl":"https://adhx.com/gemchange_ltd/status/2028904166895112617"}}