options.wiki

A complete, machine-readable reference for listed equity and index options: explicit payoff, maximum profit, maximum loss and breakeven formulas for every standard structure, Greeks in closed form with verified worked values, volatility and probability arithmetic, exercise and assignment mechanics, contract conventions, and Regulation T margin treatment.

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.

Sections

• Strategies Every standard structure with exact maximum profit, maximum loss, and breakeven formulas. - 28 entries, 10 tables
• Pricing models Closed forms, lattices and numerical schemes, with measured convergence and stability arithmetic. - 16 entries, 4 tables
• Greeks First and second-order sensitivities, with closed-form Black-Scholes-Merton expressions. - 22 entries, 8 tables
• Volatility Implied, realised and historical volatility, and the arithmetic that converts between them. - 20 entries, 7 tables
• Exotics Barriers, digitals, Asians, lookbacks and the rest: the payoff, the closed form where one exists, and the hedging problem. - 14 entries, 3 tables
• Exercise and assignment What actually happens at and before expiration, and who decides. - 17 entries, 5 tables
• Contract conventions Symbology, multipliers, expiration schedules, and quoting rules. - 2 entries, 3 tables
• Market microstructure How a listed option is quoted, ticked, cleared and filled, and the arithmetic of each. - 11 entries, 3 tables
• Margin treatment Baseline Regulation T and FINRA requirements by structure. - 13 entries, 5 tables
• Probability and expectancy Probability of touch, probability in the money, probability of profit, and the expectancy algebra that connects them. - 7 entries, 3 tables

For machine readers

Every section has a parallel JSON endpoint at /{section}.json containing the same facts without markup. A manifest of the full corpus is at /llms.txt. Structured data is emitted as schema.org DefinedTermSet on every page.

Related references

This site is one of 9 topical references built from the same open generator, indexed at wallstreet.wiki. Each one owns a single subject. Where two subjects touch, the arithmetic lives on one site and the other links to it rather than restating it. The whole network is machine-readable at /network.json.