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Ω-HMM. Enhanced Hidden Markov Model 3D probability surface. April 20, 2007. S&P closed +2.6% the red peak on that heatmap is where the model said probability was concentrated the x marks where price actually landed they matched Markov's math from 1906 predicting Wall Street 101 years later hidden markov...

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a quant at a prop firm showed me a 5x5 grid on a napkin said: > this is our entire edge. we don't predict price. we predict which box the market is in and where that box historically leads i didn't understand it for weeks. then it clicked never looked at a chart the same way since grid is called a Markov Chain transition matrix. the math is from 1906, it's in every probability textbook on earth and hedge funds use it because it asks a completely different question than retail traders ever ask retail: will this go up or down quant: what state is this market in, and where does this state typically go every market lives in one of maybe 5-6 states at any given moment tight range, volatility compression, trending with momentum, post-spike reversal, pre-breakout coil not random labels - clusters you identify from actual data using volatility, volume, and momentum readings stacked together once you have the states, you build the matrix: P(state 2 -> state 4) = 73% P(state 4 -> state 1) = 61% P(state 1 -> state 3) = 68% each cell is a historical probability. now when the market is in state 2, you're not guessing you're betting on 73% historical completion. you size it with Kelly. you take the trade when the math says to, not when it feels right i built this on BTC using 2 years of 4-hour data. identified 5 states one i labeled "volatility compression below 20-day mean for 6+ consecutive candles" transitioned to a directional move above 1.8 ATR in 71% of cases average reward/risk on those trades: 5.4 that's not prediction. that's reading a probability table the market keeps filling in for you every single day the part that should bother you: the data to build this is free. the framework is in any quant textbook python to implement it is maybe 200 lines what Renaissance Technologies has that you don't isn't secret data or proprietary signals it's this framework applied to higher-resolution data with more sophisticated state definitions you're not missing information you're asking the wrong question every single time you open a chart

Livsun

188,928 Aufrufe • vor 3 Monaten

this model doesn't predict where the S&P 500 will go it predicts when the market's own velocity is about to collapse Z(x,y) = F(β, α, τ, ∇τ; x, y, t) one equation. four parameters. a 3D surface that maps how price momentum evolves across time and space β is drift velocity: μ/σ, the ratio of expected return to volatility when β is high the market is moving with conviction when β decays toward zero the trend is losing energy before the chart shows any sign of it α measures how fast that velocity is changing τ is the time structure of the regime ∇τ is the gradient, the rate at which the regime itself is shifting the 3D surface on screen is not decoration the red peaks are where momentum is concentrated and unstable the blue basin is where the system is calm and mean-reverting the yellow marker is where the S&P sat at the moment of the snapshot the model's output: position sizing optimization not buy or sell. how much exposure to hold given the current position on that surface the bottom chart shows it: blue line is the model, white line is buy & hold same asset, same period, different sizing at every point based on where the dynamics equation said the market was > time dynamics models: rooted in physics, applied to finance since the 1990s > drift-to-volatility ratio: standard risk metric at Two Sigma, AQR, Man Group > this exact framework: free, public, 60 seconds in this video > what retail uses instead: lagging indicators that measure the past, not the velocity of the present retail asks "is the market going up or down?" this model asks "how fast is the market's own energy decaying and where on the surface are we right now?" completely different question. completely different result full breakdown in the video below

delost

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the entire math roadmap for quant trading fits on a single page and this video breaks it down in 60 seconds probability. linear algebra. calculus. statistics four subjects. every quant strategy ever built sits on top of these four probability comes first because everything else depends on it conditional probability, Bayes' theorem, expected value this is the actual language trading models are written in linear algebra is how you stop thinking about one stock and start thinking about 5,000 at once factor models, PCA, portfolio optimization Bridgewater, AQR, Two Sigma all run on matrix math calculus is derivatives pricing. Black-Scholes is a PDE if you trade options without understanding the equation underneath them, you're reading the answer key without knowing the question statistics is the filter regression, hypothesis testing, distribution fitting this is how Renaissance decides if a signal is real or if a backtest got lucky here's what nobody tells retail: every indicator you've ever used is a dumbed-down version of one of these four subjects RSI is momentum statistics. Bollinger Bands are standard deviation. MACD is signal processing they took the math, removed the part that makes it useful, and sold you the wrapper > this roadmap: free, 60 seconds, in this video > same four subjects tested at every quant interview since the 1990s > time to learn properly: 6-8 months with free resources > what they unlock: the actual language Wall Street runs on the information was never gated it was just never packaged for the people who needed it most full breakdown in the video below

delost

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robert engle won the nobel prize in economics for proving something hedge funds already knew they never bothered to mention it to retail price direction is mostly noise. but volatility? predictable. mathematically, provably, across every liquid market ever studied it clusters - that's not a pattern someone found, it's a structural law. high vol today predicts high vol tomorrow with 70%+ historical accuracy the model is called GARCH. published in every econometrics textbook on earth, chapter 4, about 60 lines of python to run quant desks at citadel and D.E. Shaw don't ask "will it go up?" - they ask "will the next move be large or small?" because sizing correctly inside a vol regime is worth more than being right on direction a trader right 48% of the time who sizes with vol awareness beats someone right 62% of the time sizing blindly - every time, over any long enough sample run it on 10 years of SPY data: > low vol state -> 74% chance next session stays low vol > vol spike -> 81% chance next session is also elevated now you're not predicting markets. you're reading a state machine the market keeps filling in for you every single session with real data the predictable part of markets was never price direction it was the distribution of price. the size of the moves. which regime you're currently inside math is free, data is free, implementation is free you were just told to stare at candlesticks instead Bookmark this before the feed buries it

Hrundel75 🐷

802,471 Aufrufe • vor 5 Tagen

In 1905, Russian Mathematician Andrey Andreyevich Markov asked a heretic question for the time: if randomness is allowed to remember something, do averages still behave or does probability theory fall apart? His answer was a very specific kind of memory. The next step only depends on the present, P(Xₙ₊₁=j | Xₙ=i, Xₙ₋₁, …) = Pᵢⱼ, and yet the law-of-large-numbers stability survives. The bead jitters forever, but long-run occupation settles. Time-averaged state frequencies converge to a fixed profile π satisfying π = πP. Fast-forward to 1931, another Russian Andrey Nikolaevich Kolmogorov, takes the same Markov mechanism and turns it into dynamics. Instead of only asking where does the chain spend its time?, you watch the whole distribution move in real time through the Kolmogorov forward (master) equation dp/dt = pQ, where Q is the generator of the continuous-time chain. That’s exactly what the render is showing as the same mechanism wearing two different lenses. The fog is p(t) spreading through the labyrinth, the flux layer is the net current pushed through corridors and the portal, and the particles are just sample paths driven by the same generator. One Markov engine...either you look at the evolving law, or you watch trajectories and let ergodic averages do the estimating. That’s also why Markov’s "memory without collapse" became a workhorse. MCMC engineers a chain whose stationary distribution is the target, then uses time-averages to estimate things you can’t integrate directly (posteriors, partition functions, constrained geometries). The same skeleton appears in hidden Markov models for time series, in biophysics as channels switching between states, and in control/RL through Markov decision processes. #ProbabilityTheory #MarkovChains #ContinuousTimeMarkovChains #KolmogorovForwardEquation #StochasticProcesses #Kolmogorov #Markov #MCMC

Mathelirium

96,415 Aufrufe • vor 7 Monaten

Wall Street doesn't predict prices - it prices the randomness in them. That is where the billions are, and it runs on one equation. The model trading desks actually use is Geometric Brownian Motion: dS = μS·dt + σS·dW μ (drift) is the slow expected trend. σ·dW is the random shock - a coin flip scaled by volatility. It is the engine under Black-Scholes, the formula that prices trillions in options. The idea is 125 years old. Louis Bachelier modeled prices as a random walk in 1900 - five years before Einstein used the same math for particles. His verdict: "the mathematical expectation of the speculator is zero." Sixty years later Eugene Fama won a Nobel for the same finding: prices are "no more predictable than the path of a series of cumulated random numbers." And the math is brutal. Drift grows with time (t); noise grows only with its square root (√t). Over one day the shock buries the trend - so daily direction is a coin flip, and traders invent reasons after the candle prints. The trap hides in one assumption: that returns are "normal." Real markets have fat tails. Black Monday 1987 (-22.6% in a day) was a 20-sigma event under the bell curve - impossible in billions of years. Nassim Taleb calls that bell curve "the great intellectual fraud." The equation that prices everything is blind to the one day it matters most. the edge was never the trend inside the wiggle. it is knowing how much of the wiggle is nothing. the full quant build is in the article below.

Di Krass

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a citadel options trader told me the one concept they test first in every quant interview and it's been sitting on a free website for years not a hedge fund textbook, not a $3,000 prep program. a free course syllabus - options greeks, volatility, quizzes - publicly available, almost nobody applying has ever opened it concept is expected value across a probability distribution retail looks at a chart and asks which direction. quant looks at expected payout across every possible outcome and asks if that number beats the cost of the trade - completely different question options pricing is just EV made rigorous fair value of any position = sum of (each outcome's probability x its payoff), discounted back. that formula is in every intro stats course and every free options curriculum these firms post publicly citadel's first round isn't a stock pitch or a DCF it's a market-making problem: "set me a bid and ask on a coin flip" if you can solve that fast and size it correctly, you can price any derivative on earth prep is documented in 6 categories: probability, greeks, volatility, mental math, coding, microstructure firms don't want you pattern-matching to old trades. they want raw EV instinct - and that's in free courses that have been online for years entry-level quant traders at these firms start at $300k. senior traders clear $650k+ most people never make it past round 1. not because they weren't smart - because nobody told them what the test was actually measuring Bookmark this they kept you reading charts while they were drilling expected value at 2am

Livsun

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a $40/month server beat a room full of analysts to the same trade by five and a half hours market opens at 9:30. his position was already in at 4am the system is a neural net trained on 11 years of tick data. it flagged the setup before the candle that "confirmed" it had even started forming this is the part retail misunderstands about ML in markets it isn't prediction in the mystical sense. it's pattern classification at a speed and scale human eyes physically cannot match the mechanics: 847,000 labeled historical setups as training data 4,200 data points per second ingested live each new state scored against every pattern the net has ever seen, in milliseconds the model isn't asking "where is price going" it's asking "how closely does the current microstructure match the conditions that preceded a move in my training set" that's a classification problem, and classification is what neural nets do better than anything else output: 3-4 candidate trades a day. he takes the top 2 by confidence score last 90 days: 71% win rate at 2.3 average risk-reward the edge isn't the architecture. the architecture is public pytorch is free, the papers are on arxiv, the network is a few hundred lines the edge is the labeling. what you feed it and how you tag the setups is the entire game retail feeds a model price and time and gets noise a desk feeds it order flow, volatility state, cross-asset context, each example hand-labeled by outcome same network. different training data. that's the whole difference retail watches the news at the open and reacts this system scored every pattern before sunrise and already decided you're not losing because your analysis is wrong you're losing to something that doesn't sleep, doesn't panic, and doesn't second-guess a probability it already computed the dataset was free. the framework was free. the compute was $40 a month the edge was never behind a paywall. it was sitting in a format almost nobody bothered to train on full breakdown in the article below

delost

20,942 Aufrufe • vor 1 Monat