What the option probability analyzer calculates
This calculator combines a piecewise-linear expiration payoff with a lognormal price distribution. For each price interval with positive P&L, it adds the difference between the model cumulative probabilities at the interval endpoints. The integration covers all positive prices, including the upper tail. The finite chart window does not rescale the result.
The distribution is risk-neutral: log(S at expiry) has mean log(S today) + (r − σ²/2)T and standard deviation σ√T. This is a pricing assumption, not an estimate of the stock's real-world drift. The tool fixes the annual continuously compounded rate at 5% and dividend yield at zero. These assumptions can be unsuitable for a particular underlying or date.
Load, inspect, and build a scenario
- Load a ticker and check the underlying reference price. The page requests at most 250 snapshot contracts and does not follow subsequent pages. An unavailable contract is not evidence that it does not exist.
- Choose a template. Each template selects nearby strikes from the returned contracts; inspect those selections before using the result. If the page cannot find distinct legs for a template, add individual legs instead.
- Use one future expiration for every leg. Only contracts explicitly reporting 100 shares per contract are offered. The date is interpreted as 00:00 UTC, which is not the exchange settlement time; expiration-day contracts are excluded.
- Review each premium and IV. The initial premium is the last daily close, not a live bid or ask. Enter your own scenario values when needed. Missing data remains blank and stops calculation; it is not a zero-price option.
- Set whole contract quantities and adjust IV in percentage points. The model uses the unweighted mean of the leg IVs as one common volatility, then adds this adjustment. It does not fit a volatility smile or separate distributions for different strikes.
Read the outputs with their units
- Probability of profit: model probability of strictly positive expiration P&L after the entered premiums, before fees. A flat zero-payoff interval is not a profit.
- Model expected P&L: the undiscounted expected expiration intrinsic payoff minus the entered premiums. Equivalently, each model option value is multiplied by exp(rT), then its premium is subtracted. Premium financing is omitted; a positive value alone does not establish an edge.
- Maximum profit and loss: evaluated at price zero, every strike, and the upper tail. A long put has bounded profit because the underlying cannot fall below zero. An uncovered short call can have unlimited loss. Stock positions are not part of this calculator.
- Breakevens: zero-payoff points and endpoints of flat zero-payoff intervals. Consult the expiration payoff line when a strategy is flat at zero over a range.
- Position Greeks: European model Greeks multiplied by signed quantities and 100 shares per contract. Delta is share-equivalent exposure; gamma is delta change per $1 underlying move; theta is dollars per day; vega is dollars per one percentage-point change in IV. They are not the raw provider Greeks.
Why a high probability is not enough
Consider a deliberately simplified hypothetical: nine outcomes earn $10 each and one loses $100. With equal probability for these ten outcomes, the win rate is 90% but expected P&L is −$1. This is arithmetic, not a backtest or a claim about credit spreads. Strike selection, premiums, the loss distribution, and costs all matter.
The chart shows expiration P&L, a theoretical value curve at today's modeled remaining time, and another at half that time. Price and common IV assumptions are held as specified. The lines are scenarios, not a forecast of an actual path. They omit jumps, changing volatility, discrete dividends, early exercise, assignment, liquidity, spread costs, commissions, and margin requirements.
Data and model references
The Massive option-chain snapshot specification distinguishes daily bars, quotes, trades, optional IV, and pagination. This page uses daily close and IV; it does not substitute unavailable fields with zero. Its API response can be cached for one hour, in addition to provider delays.
The Options Industry Council explanation of Black–Scholes describes model inputs and the limitation of using a European formula for American exercise. The calculated probabilities and prices are educational model outputs, not a recommendation or a guarantee of future returns.