# options.wiki

> options.wiki is a reference corpus for listed equity and index options: payoff algebra for every standard structure, closed-form Greeks, volatility and probability arithmetic, exercise and assignment mechanics, contract conventions, and baseline margin treatment. Every arithmetic entry carries an explicit formula and a recomputed worked example.

This is a reference corpus, not a tutorial and not commentary. Every strategy carries its exact maximum profit, maximum loss, breakeven and payoff expression as formulas rather than descriptions, and every figure labelled Worked has been recomputed from those formulas. Every convention states the rule and, where one exists, the authority that sets it. Notation is uniform across the whole site. Underlying and prices: S is the underlying price, S0 the entry price, K a strike, and K1 < K2 < K3 < K4 the strikes of a multi-leg structure in ascending order. Premiums and cash flows: P a single option premium, C a net credit, D a net debit, N a net credit that may be negative, and W a strike width. Model inputs: r the risk-free rate, q the continuous dividend yield, sigma implied volatility, T time to expiration in years, tau a remaining interval in years, and M the contract multiplier. Distribution functions: N() is the standard normal cumulative distribution and phi() its density; d1 and d2 are the standard Black-Scholes-Merton arguments. Volatility and probability: J is the standard deviation of a one-off event move, p a probability of profit, b a payoff ratio of maximum profit to maximum loss, and f* the Kelly fraction. All figures assume a standard 100-share multiplier and ignore commissions. Numeric inputs in worked examples are chosen so the arithmetic is checkable; they are not observations of any market and no figure on this site is a quote, a forecast, or a statistic.

Published and maintained by Wall Street Wiki, https://wallstreet.wiki. Contact: wallstreetwiki@agentmail.to. A reference published by the wallstreet.wiki network. Every figure is stated as a formula and recomputed from it, every convention names the authority that sets it, and corrections are versioned and dated.

Corpus: 150 defined terms and 51 reference tables across 10 sections. Reviewed 2026-08-27. Licensed CC BY 4.0.

Each section has a JSON endpoint carrying the same facts without markup or navigation. Measured on this corpus a section's JSON is 36 to 60 percent of the bytes of the equivalent HTML page. The full corpus is available in one request.

Content dates reflect editorial review, not build time. Use the change feed below to decide what to re-crawl rather than re-fetching the whole corpus; every JSON endpoint carries a reviewed field and sitemap.xml lastmod carries the per-section review date.

Calculator pages take their inputs as URL query parameters and compute in the browser. There is no API and no key.

## Data endpoints

- [Full corpus](https://options.wiki/llms-full.txt): every section inlined as Markdown, one request
- [Full corpus, JSON](https://options.wiki/index.json): the same content as structured JSON
- [Strategies, JSON](https://options.wiki/strategies.json): 28 terms, 10 tables
- [Pricing models, JSON](https://options.wiki/models.json): 16 terms, 4 tables
- [Greeks, JSON](https://options.wiki/greeks.json): 22 terms, 8 tables
- [Volatility, JSON](https://options.wiki/volatility.json): 20 terms, 7 tables
- [Exotics, JSON](https://options.wiki/exotics.json): 14 terms, 3 tables
- [Exercise and assignment, JSON](https://options.wiki/mechanics.json): 17 terms, 5 tables
- [Contract conventions, JSON](https://options.wiki/conventions.json): 2 terms, 3 tables
- [Market microstructure, JSON](https://options.wiki/microstructure.json): 11 terms, 3 tables
- [Margin treatment, JSON](https://options.wiki/margin.json): 13 terms, 5 tables
- [Probability and expectancy, JSON](https://options.wiki/probability.json): 7 terms, 3 tables

## Freshness

- [Change feed](https://options.wiki/changes.json): dated record of what changed and when, spec wiki-changes/1
- [Change feed, Atom](https://options.wiki/feed.xml): the same feed as Atom
- [Sitemap](https://options.wiki/sitemap.xml): lastmod carries the per-section review date

## Reference pages

- [Strategies](https://options.wiki/strategies/): Every standard structure with exact maximum profit, maximum loss, and breakeven formulas.
- [Pricing models](https://options.wiki/models/): Closed forms, lattices and numerical schemes, with measured convergence and stability arithmetic.
- [Greeks](https://options.wiki/greeks/): First and second-order sensitivities, with closed-form Black-Scholes-Merton expressions.
- [Volatility](https://options.wiki/volatility/): Implied, realised and historical volatility, and the arithmetic that converts between them.
- [Exotics](https://options.wiki/exotics/): Barriers, digitals, Asians, lookbacks and the rest: the payoff, the closed form where one exists, and the hedging problem.
- [Exercise and assignment](https://options.wiki/mechanics/): What actually happens at and before expiration, and who decides.
- [Contract conventions](https://options.wiki/conventions/): Symbology, multipliers, expiration schedules, and quoting rules.
- [Market microstructure](https://options.wiki/microstructure/): How a listed option is quoted, ticked, cleared and filled, and the arithmetic of each.
- [Margin treatment](https://options.wiki/margin/): Baseline Regulation T and FINRA requirements by structure.
- [Probability and expectancy](https://options.wiki/probability/): Probability of touch, probability in the money, probability of profit, and the expectancy algebra that connects them.

## Calculators

- [Payoff calculator](https://options.wiki/calc/): Expiration payoff for any combination of option and stock legs. Computes maximum profit, maximum loss, breakeven prices, net debit or credit, payoff diagram. Parameters: legs, spot, mult, range.
- [Decay viewer](https://options.wiki/decay/): The same position animated from purchase to expiration, with theoretical value recomputed from Black-Scholes-Merton at every step. Computes theoretical value at any day, position delta, gamma, vega, theta and rho, convergence of theoretical value onto the expiration payoff. Parameters: legs, iv, dte, spot.
- [Multi-leg strategy payoff builder](https://options.wiki/calc/payoff/): Builds the expiration payoff of an arbitrary multi-leg position from user-entered legs and returns maximum profit, maximum loss, every breakeven, and a payoff table across a price range. Computes maximum profit, maximum loss, all breakeven prices, net debit or credit, payoff table across a price range, payoff at each strike. Parameters: legs, from, to, step, mult.

## Calculator examples

- [Payoff calculator](https://options.wiki/calc/?legs=+1c100@3.20,-1c110@1.10&spot=100): bull call spread, long the 100 at 3.20 and short the 110 at 1.10. Max profit 790.00, max loss 210.00, breakeven 102.10
- [Payoff calculator](https://options.wiki/calc/?legs=-1p95@2.10,+1p90@0.95,-1c105@2.30,+1c110@1.10&spot=100): iron condor 90/95/105/110 for 2.35 credit. Max profit 235.00, max loss 265.00, breakevens 92.65 and 107.35
- [Payoff calculator](https://options.wiki/calc/?legs=+1s@0,-1c110@1.10&spot=100): covered call on stock entered at 100 with the 110 written for 1.10. Max profit 1,110.00, max loss 9,890.00, breakeven 98.90
- [Decay viewer](https://options.wiki/decay/?legs=+1c100@0&iv=25&dte=90&spot=100): a long at-the-money 100 call over 90 days at 25 percent volatility. Theta accelerates from -3.31 to -12.88 per day and gamma rises from 3.18 to 14.36 into expiration
- [Decay viewer](https://options.wiki/decay/?legs=+1c100@0,-1c110@0&iv=30&dte=45&spot=100): a 100/110 call spread over 45 days at 30 percent volatility, showing how a spread decays more slowly than the long leg alone
- [Multi-leg strategy payoff builder](https://options.wiki/calc/payoff/?legs=+1c95@6.40,-2c100@3.40,+1c105@1.60): long 95/100/105 call butterfly for a 1.20 debit. Max profit 380.00 at 100, max loss 120.00, breakevens 96.20 and 103.80
- [Multi-leg strategy payoff builder](https://options.wiki/calc/payoff/?legs=+1p90@0.55,-1p95@1.30,-1c105@1.45,+1c110@0.60): iron condor 90/95/105/110 for a 1.60 credit. Max profit 160.00 from 95 to 105, max loss 340.00, breakevens 93.40 and 106.60
- [Multi-leg strategy payoff builder](https://options.wiki/calc/payoff/?legs=+1c100@3.20,-2c105@1.90): 1x2 call ratio spread for a 0.60 credit. Max profit 560.00 at 105, loss unbounded above the 110.60 breakeven
- [Multi-leg strategy payoff builder](https://options.wiki/calc/payoff/?legs=-1p90@2.20,-1c105@1.90,+1c107.5@1.10): jade lizard for a 3.00 credit against a 2.50-wide call spread, so no upside risk. Max profit 300.00 from 90 to 105, 50.00 above 107.50, max loss 8,700.00 at zero, single breakeven 87.00
- [Multi-leg strategy payoff builder](https://options.wiki/calc/payoff/?legs=+1c100@3.20,-1c110@1.10,+1p110@10.50,-1p100@2.80): 100/110 box spread for a 9.80 debit. Payoff is a constant 20.00 at every underlying price, so there is no breakeven

## Network

- [wallstreet.wiki](https://wallstreet.wiki): the parent index for this network of references
- [Network registry](https://options.wiki/network.json): every sibling site, its subject, and its corpus endpoint, spec wiki-network/1
- [hedgefund.wiki](https://hedgefund.wiki/llms.txt): Hedge funds. Institutional hedge fund knowledge graph: terms, strategies, regulations, calculators.
- [venture-capital.wiki](https://venture-capital.wiki/llms.txt): Venture capital. Venture financing arithmetic: liquidation waterfalls, convertible conversion, dilution, term sheet mechanics.
- [privatecredit.wiki](https://privatecredit.wiki/llms.txt): Private credit. Private credit structure: instruments and the waterfall, SOFR pricing, return metrics, covenants, vehicles.
- [m-a.wiki](https://m-a.wiki/llms.txt): Mergers and acquisitions. Deal arithmetic: LBO returns and value attribution, accretion and dilution, the value bridge, valuation cross-checks.
- [pe-finance.wiki](https://pe-finance.wiki/llms.txt): Private equity funds. Fund economics: the distribution waterfall, carried interest, performance measurement and what inflates it.
- [fixed-income.wiki](https://fixed-income.wiki/llms.txt): Fixed income. Bond mathematics and market convention: day counts, accrual, price and yield, duration, curves and spreads.
- [quants.wiki](https://quants.wiki/llms.txt): Quantitative finance. Estimators and their failure modes: performance statistics, covariance estimation, portfolio construction, backtest validity.
- [aicrawl.dev](https://aicrawl.dev/llms.txt): AI crawler control. Verified AI crawler registry, robots.txt matching rules, the standards, and what enforcement actually works.

This site owns one subject. A formula or convention appears on exactly one site in the network and the others link to it, so fetching all of them yields no duplicated entries. The membership list is published rather than implied.

## Access and licensing

- [Access terms](https://options.wiki/access/): the corpus is free under CC BY 4.0; embed licences and hosted API access are the paid products
- [Pricing, JSON](https://options.wiki/pricing.json): machine-readable price list, what is free, and how to request a quote
- [MCP descriptor](https://options.wiki/.well-known/mcp.json): every resource and calculator as a tool definition

Nothing on this site is metered. There is no per-crawl charge, no key, and no rate limit; fetch the corpus in one request from llms-full.txt or index.json. The paid products are an embed licence for the calculators and a delivery guarantee on the data, neither of which restricts the free corpus.

## Optional

- [Deep link schema](https://options.wiki/.well-known/deeplinks.json): machine-readable parameter definitions for the calculators
- [Pricing plan](https://options.wiki/.well-known/pay-per-crawl.json): which paths are free and what the charged ones cost

Entries carry a source field naming the primary authority where one exists. Entries without one state conventions in general use rather than the rule of any single venue.

Reference information only. Not investment advice, not a recommendation, and not a solicitation. Options involve substantial risk of loss. Contract terms, margin requirements, and exchange rules change; confirm against the current OCC and exchange rulebooks and your broker's house requirements before trading.