Probability Distribution Chart

A probability distribution chart visualizes the likelihood of an underlying asset reaching different price levels at a specific expiration date. It uses options market data and mathematical models to show where the stock is most likely to trade, helping traders assess risk and make informed decisions.

Lognormal distribution is a theoretical model based on the Black-Scholes equation, assuming stock prices follow a lognormal pattern. Implied probability distribution is derived from actual market options prices, reflecting what traders collectively believe about future price movements. Comparing both can reveal market sentiment versus theoretical expectations.

The PDF shows the relative likelihood of the stock price landing at each specific price point. The peak of the curve indicates the most probable price at expiration. A wider, flatter curve suggests higher uncertainty, while a narrow, tall curve indicates more confidence in a specific price range.

The CDF shows the probability that the stock price will be below a certain level at expiration. For example, if the CDF shows 70% at $150, there is a 70% probability the stock will be below $150 at expiration. This is useful for calculating probability of profit and assignment risk.

Use probability distributions to: (1) Assess the likelihood of your options reaching profitability, (2) Select optimal strike prices based on probability zones, (3) Choose strategies that match the expected price distribution, (4) Identify market sentiment by comparing theoretical vs. implied distributions, and (5) Plan earnings trades by understanding expected move ranges.

Standard deviation (σ) measures price volatility. ±1σ covers approximately 68% of probable outcomes, ±2σ covers 95%, and ±3σ covers 99.7%. Filtering by standard deviation helps you focus on the most likely price ranges and ignore extreme outliers.

Longer expiration dates allow more time for price movement, resulting in wider probability distributions. Shorter expirations have tighter distributions because there is less time for significant price changes. This is why longer-dated options have higher premiums due to increased uncertainty.

Implied volatility (IV) is a key input for calculating the lognormal distribution. Higher IV results in wider probability distributions, indicating greater expected price movement. IV is derived from options prices and reflects market expectations of future volatility.

Yes! Before earnings, analyze the probability distribution to understand the expected move range. The width of the distribution reflects market expectations for volatility. You can use this to plan straddles, strangles, iron condors, or directional plays based on whether you expect the actual move to exceed or fall short of market expectations.

You can analyze any optionable stock symbol that has liquid options markets. Popular symbols include SPY, QQQ, AAPL, TSLA, NVDA, and other major stocks and ETFs. The tool requires sufficient options data to generate accurate probability distributions.

The probability distributions are calculated in real-time based on current stock prices and options data. Each time you load a symbol or refresh, the tool fetches the latest market data to ensure accurate probability calculations.

The probability summary shows three key metrics: (1) Probability of the price being below the current price, (2) Probability of staying within ±5% of the current price, and (3) Probability of the price being above the current price. These help you quickly assess directional bias and range-bound probability.