Heston Model and the Volatility Smile
A single volatility number cannot price a whole option chain. See how the Heston model lets variance wander, and what each parameter does to the smile.
Deep Dives
Forensic, single-subject investigations into individual stocks, events, and market-structure quirks.
ETF Relative Strength and Alpha Attribution
ETF relative strength ranks funds by 20-session return versus SPY. See what alpha attribution does to the intercept once the benchmark actually fits.
PCAP Market Data: How Market Replay Works
PCAP market data is the raw exchange packets with a capture timestamp per packet. How the file format works, and when a capture beats a normalized feed.
How to Estimate Queue Position From L2 Data
Queue position decides whether a passive order earns the spread. Here is how to estimate it from aggregated book data, and when to buy MBO instead.
MBO vs MBP Order Book Data Explained
MBO vs MBP order book data: message-by-order event streams versus aggregated depth per price level, what each can answer, and what each costs to run.
OTC Markets Tiers and SEC Rule 15c2-11
OTC markets tiers explained, and how amended SEC Rule 15c2-11 moved non-reporting stocks onto the Expert Market, where retail buyers often cannot buy at all.
How to De-Vig Betting Odds Into Probabilities
Bookmaker odds sum to more than 100 percent. Learn how to de-vig betting odds into fair probabilities with four methods, in one runnable Python script.
The January Effect: Does It Still Work?
The January effect claims small caps rally after year end. Here is the mechanism behind it, and why a documented anomaly usually shrinks after publication.
Why Odd Lots Don't Set the NBBO
A fill better than the quoted price is normal. The NBBO is computed from round lot quotes only, and odd lot quotes are ancillary data, not protected.
Contango and Roll Yield in Commodity ETFs
Contango explains why a commodity ETF can lose money while spot stays flat. See the roll trade, the arithmetic over twelve rolls, and real fund data.
How Continuous Futures Contracts Are Built
No single futures contract has a long history. Every futures chart is stitched. How continuous futures contracts get rolled, spliced and back adjusted.
Why Ticker Symbols Break Your Dataset
Ticker symbols break datasets in four ways: renames, reuse, share class punctuation, and mergers. See why each corrupts a join, and what to key on.
Why Trading Volume Dies at Midday: U-Shape
Trading volume dies at midday in a U shaped curve: heavy at the open and close, thin from 11:30 to 14:00 ET. See the intraday profile and what it costs.
Survivorship Bias in Stock Data, Explained
Survivorship bias hides delisted and acquired tickers from most stock datasets. See the gap it opens in a backtest, and how to measure a full universe.
Volatility Targeting for Position Sizing
Volatility targeting sizes a position to a fixed risk budget instead of an edge estimate. The formula, the lookback, the leverage cap, and the failure mode.
How Companies Execute Buybacks: Rule 10b-18
How companies execute buybacks: the Rule 10b-18 safe harbor and its four conditions, accelerated repurchases, tender offers, and the filings that prove it.
Reg T Margin vs Portfolio Margin Explained
Reg T margin vs portfolio margin: 50% initial and 25% maintenance versus TIMS risk scenarios and the $125,000 minimum, worked through one hedged spread.
Maker-Taker Fees and Rebates Explained
Maker-taker fees explained with arithmetic: what a venue keeps between the taker fee and the maker rebate, and how that gap steers where brokers route orders.
How to Read the COT Report: Columns Explained
How to read the COT report: what every column means across the legacy, disaggregated and TFF tables, plus the net position math and its two real limits.
SIP Feeds vs Direct Exchange Feeds
Why two screens show different prices for the same stock: what the SIP consolidated tape carries, and where direct exchange feeds gain speed and depth.
How Options Adjust After Mergers & Spinoffs
Your option now shows a strange symbol and a deliverable that is no longer 100 shares. See how options adjust after a merger or a spinoff, and what breaks.
Open-Source GEX Dashboard: How It Works
How an open-source GEX dashboard computes gamma exposure: the per strike formula, the dealer sign convention it assumes, and the limits of the output.
Price-Time Priority vs Pro-Rata Fills
Why two orders at the same price get different fills: price-time priority, pro-rata and parity allocation, worked through one book with real market data.
How OHLCV Bars Are Built From Ticks
How OHLCV bars are built from raw trades: the half open minute interval, which condition coded prints count, empty minutes, and the backtest fallout.
SPX vs SPY Options: Which One to Trade
SPX vs SPY options compared on contract size, settlement, early assignment and the 60/40 tax split, with the notional and tax math computed from data.
How split-adjusted price history works
Split-adjusted price history explained: the 1/N factor charts apply to old prices, the N they apply to old volumes, and the three ways it breaks a backtest.
Rule 605 vs 606: Execution Quality Reports
Rule 605 and 606 reports show execution quality and where your broker routes orders. Here is how to read effective spread and payment per hundred shares.
Probability of Touch vs Probability ITM
Probability of touch is roughly double the probability of expiring ITM. Here is why, with a seeded random walk argument and real SPY data to check it.
Trade Condition Codes Explained
Three platforms, three different daily highs for the same stock. Trade condition codes decide which prints update the high, the low, the close, and volume.
Why Index Options Are Taxed 60/40: Section 1256
Index options are taxed 60/40 under Section 1256 no matter how long you hold them. See which products qualify, the year end mark to market, and SPX vs SPY.
When Short Options Get Assigned Early
What makes a short option get assigned early: the dividend case, the interest case, the borrow case, and the margin call a short spread leg can produce.
Box Spread Options and the Implied Loan Rate
A box spread is a synthetic zero coupon loan built from four options. See how the payoff locks to the strike width and how to solve for the implied loan rate.
Do Stock Gaps Always Get Filled? The Data
Do stock gaps always get filled? Not on any fixed horizon. See same session, 5, 20 and 60 session fill rates for large caps, with the SQL behind them.
Reproducible Backtest in Python, No API Key
Run a reproducible backtest in Python with no API key: a pinned install plus deterministic sample data, and an honest read of what one equity curve hides.
Do Stocks Fall When a Lockup Expires?
Do stocks fall when a lockup expires? What the event studies actually find, and why a date printed in the prospectus is usually priced in ahead of time.
SPY Dividend Yield: Why It Trails the Index
SPY's dividend yield sits a few basis points under VOO and IVV. Here is the unit investment trust mechanism behind the gap, measured on live fund data.
Local A-Share Data Lake for AI Agents
ashare-lake builds a local A-share data lake on your own disk: 39 datasets, delisting records, point-in-time queries, and an MCP server for agents.
IV Term Structure: What the Curve Tells You
The IV term structure is implied volatility plotted by expiration. See what upward sloping and inverted curves mean, with real option data on the shape.
Dividend Yield Traps: How to Spot One
A dividend yield trap is a high yield produced by a falling price. See what the top yield decile did next, and the four checks that flag one early.
Expected Move From Implied Volatility
Expected move is price times IV times the square root of days over 365. See the formula, the straddle shortcut that matches it, and what realized moves did.
Does Sell in May and Go Away Work?
Sell in May and Go Away, tested on two decades of S&P 500 seasons. See the size of the summer gap and what the seasonal switch actually costs in practice.
How Markets Price Fed Rate Odds
Fed rate odds come from futures that settle on a month's average rate. See the day count arithmetic and a full worked example from a 2025 Fed meeting.
When Companies Announce Dividend Raises
Dividend raises cluster in the same fiscal month year after year. See which month each dividend grower declares, how tightly that month holds, and why.
Is a High Put/Call Ratio Bullish?
Contrarians call a high put/call ratio bullish. See the percentile bands for equity and index options, and what actually followed the extreme readings.
AM vs PM Settled Index Options Explained
AM settled index options settle off Friday's opening quotation and stop trading Thursday. PM settled options run to the close. The gap between them, measured.
Is 30% IV High? It Depends on the Ticker
Is 30% implied volatility high? It depends entirely on the ticker. See where 30% IV sits in each name's own percentile, and the daily move it implies.
Can an LLM Find Alpha Factors?
An LLM can write a hundred alpha factors in an hour. See what 240 coin flip factors score on ten years of real prices, and how to test the survivors.
Verizon's Dividend Increase History
Verizon's dividend increase history: a long streak of raises, and why it is not a dividend king. See the per share record and the size of each raise.
AI Daily Market Research Reports: What Breaks
An AI daily market research report pulls data on a watchlist and writes it up. See the five stages, what breaks at each one, and the numbers behind it.
Market Data Skills for AI Agents
A market data skill tells an AI agent which symbols, which calendar, what to cache, and what to do when a series comes back short. Here is the spec.
Covered Call ETFs: the Real Tradeoff
Covered call ETFs sell index calls and pay the premium out monthly. See where that distribution really comes from, and how total return behaves by year.
Does Dividend Capture Actually Work?
Dividend capture buys before the ex dividend date and sells after. See how far prices really open down, and what stacks up against the dividend collected.
Look-Ahead Bias: The Backtest Killer
Look-ahead bias is future data leaking into a backtest. See how same bar decisions, survivorship, and revised figures inflate results, and how to test for it.
Multi-Agent AI Trading Systems: What Is Real
Multi-agent AI trading systems run LLM committees on a trade. See the architecture, the market costs a signal clears, and the backtest traps involved.
Kelly Criterion Position Sizing, Measured
The Kelly criterion sets bet size from your edge. See what ten years of daily stock returns imply about full Kelly, drawdown, and half Kelly in practice.
Grid Trading Bots, Examined Honestly
A grid trading bot buys each step down and sells each step up inside a fixed range. See the market shape that pays for the mechanism and the one that breaks it.
What Is Gamma Exposure (GEX)? Dealer Hedging
Gamma exposure, or GEX, estimates the hedging dealers do as prices move. See the calculation, the assumptions it rests on, and why free GEX numbers differ.
How Earnings Move Option Greeks
Pin one real Tesla call through its Q1 earnings 8-K and watch implied volatility, price and delta move as the result lands and the IV crush follows.
Why Some Options Cost So Much More
Two nearly identical options can carry wildly different prices. Implied volatility is why: the market's priced-in expected move, mapped across six names.
Does Dollar-Cost Averaging Work?
Does dollar-cost averaging work? A data study of $500 a month into SPY versus one lump sum from 2016 to 2026, and what averaging in is really for.
How Markets Recover From Crashes
Every S&P 500 crash since 2016 recovered. We charted the market's underwater history: how deep the drawdowns ran, how often, and where it stands now.
What Missing the Best Days Costs
Time in the market beats timing it: missing the best days since 2016 turned a big SPY gain into a small one, and the best days hide inside the worst selloffs.
Buy When Others Are Fearful: The Data
Warren Buffett said be greedy when others are fearful. We built a fear gauge from real news sentiment and tested whether fearful days beat the market.
The Options Collar: A Cheap Hedge
A collar hedges a concentrated stock cheaply: own the shares, buy a put for a floor, sell a call for a cap. We trace a real SPY collar through June's selloff.
Covered Calls: Income on Your Shares
A covered call sells a call against stock you own for premium income. We trace one real SPY call to show the income and the capped-upside tradeoff.
Protective Puts: Portfolio Insurance
A protective put is insurance for stock you already own. Watch one real SPY put hold a floor under a $75,000 position when the market fell in June 2026.
Deep ITM LEAPS: Stock Replacement
A deep-ITM LEAPS call stands in for 100 shares at a fraction of the cash. We trace one real SPY LEAPS through its deep in-the-money life to show the trade.
What Are LEAPS? Long-Dated Options
LEAPS are options that expire more than a year out. Follow one real SPY call across two full years as its delta climbs toward 1 and its price rises tenfold.
How Option Greeks Change Over Time
A SPY call and put at the same $740 strike trace mirror-image greeks. Watch delta, gamma, theta and vega move day by day across one contract's life.
Buying and Selling Put Options
Buying and selling put options, traced through one real SPY put: what you pay, your max loss, the breakeven, and why selling to close beats decay.
Buying and Selling Call Options
Buying a call option pays a premium for leverage on a stock. We trace one real SPY call through a triple-digit gain and a hard crush to show every exit.
What Are Put Options?
A put option is the right to sell 100 shares at a set strike price. Watch one real SPY put move as the stock falls, and see what its price is built from.
What Are Call Options?
A call option is the right to buy 100 shares at a set strike before expiry. Follow one real SPY call through its whole life to watch leverage and decay work.
The 2011 US Downgrade: Black Monday's Tape
August 8, 2011: the first trading day after S&P stripped the US of its AAA rating. The tape fell all day and closed near the low, with the receipts inside.
Feb 24, 2022: War at the Open, Green by Close
February 24, 2022: Russia invaded Ukraine and US stocks gapped down, then closed green. The full reversal, plus oil, gold, defense, bonds and the aftermath.
Tesla's Bitcoin 10-K: Feb 8, 2021 on the Tape
Tesla's $1.5B bitcoin purchase, receipted: the Feb 8, 2021 filing and session tape, the sympathy rally in bitcoin stocks, the options shrug, and the 2022 exit.
SK Hynix's Nasdaq Debut, Measured
SK Hynix's Nasdaq debut, measured: a $28B raise (2026's second-largest), an $18B first tape, day-one short volume, and the memory trade re-ranked.
NVDA's May 2023 Earnings: The AI Gap
May 25, 2023: NVIDIA's guidance shocked Wall Street after the close and the stock opened 26% higher. The overnight gap that started the AI supercycle trade.
March 9, 2009: The Bottom, On the Tape
March 9, 2009 was the exact bottom of the financial crisis, and the tape shows a quiet, unremarkable Monday. What generational lows actually look like up close.
Lehman's Collapse: The 2008 Tape, Replayed
September 15, 2008: Lehman filed and SPY closed on its low. LEH's eighteen-month death spiral, the whipsaw week, and the full crash, panel by panel.
GameStop, Jan 28, 2021: $483 to $112 by Noon
Jan 28, 2021: GME printed $483 and $112 in one morning, Robinhood went position-close-only, and 76 minutes vanished into trading halts. The tape, receipted.
The 2010 Flash Crash, Minute by Minute
May 6, 2010: about a trillion dollars of market value vanished and mostly returned inside 36 minutes. The minute tape of the flash crash, receipted.
March 24, 2020: The Day the Market Turned
March 24, 2020, replayed from the minute tape: the crash and the dash for cash, the Fed package that differed, sector breadth, and the retest that never came.
COVID Crash 2020: Four Halts, Peak to Trough
The COVID crash of 2020, receipted: the March 9 halt minutes missing from the tape, four circuit breakers in eight days, and the peak-to-trough map on SPY.
SPCX: The Week It Went Underwater
SPCX's week of July 6, 2026: the index-add flow left, three of five closes printed under the June first-trade price, and Friday set a new post-listing low.
NVDA: Sit-Out, Then Surge, Week of July 6
NVDA's week of July 6, 2026: green through the rout, red on the rally, then the tape's heaviest name by Friday. Five sessions, with every number receipted.
SPCX: SpaceX Stock Price Decline From Peak
How far SpaceX stock (SPCX) sits below its June 16, 2026 peak, measured to the latest close: the session path, spreads, options flow, and SEC filings.
SpaceX Joins the Nasdaq-100: The Index-Add Trade
SpaceX's fast-tracked Nasdaq-100 add and the giant closing auction that priced it: Matt Levine's account, verified and extended on our own tick tape.
Macro Picture Entering H2 2026, With Receipts
The macro picture entering H2 2026: hot headline CPI over a quiet core, anchored expectations, a flattening curve, and the H2 prints that could change it.
Treasury Yield Curve, H1 2026: Twist, Not Shift
H1 2026 Treasury yield curve review: a twist that lifted the belly while both ends held, a 2s10s spread that never inverted, and the 30-year's brush with 5%.
SEC EDGAR Index Gap: the Missing Month-Ends
Three 2026 month-ends are near-empty in the SEC EDGAR filing index: the receipts, the ingest evidence that bounds the fault, the 2025 precedent, what breaks.
The Best and Worst Thousand Dollars of June 2026
June's best options contract returned 495x; selling that same contract lost 494,000 dollars on a thousand of premium. The full hindsight ledger. Not advice.
Sector Scorecard H1 2026: Winners and Losers
All eleven S&P 500 sector ETFs ranked for H1 2026: the winners and losers, the Q1-to-Q2 rotation, breadth inside each sector, and what each costs to trade.
NVDA: NVIDIA's Full June 2026, Tick by Tick
NVIDIA's June 2026 in full: a $235 pre-market peak, a 7.4% slide across 21 sessions, and the fourth-biggest dollar volume on the US tape.
MU: The Biggest Tape of June 2026
Micron's June 2026: 995.7 billion dollars of regular-hours turnover, the first-ranked tape in the market, while June's repricing cooled to 14 percent.
SPCX: SpaceX's First Month on the Public Market
SpaceX's June 2026 debut as SPCX, receipt by receipt: a delayed opening cross, a top-of-tape dollar-volume run, spread seasoning, day-three options, and shorts.
Microstructure Deep-Dive: June 29, 2026
Under the hood of June 29, 2026: the full trade and quote tape, a dictionary-derived volume correction, nanosecond receipts, and a truncated FINRA file.