Distribution graphs reflect the probability of an event occurring.1 This is depicted in the sample graph as the green curve, whose height at any given underlying price is proportional to the probability that the underlying price ends up within a narrow range of that price at expiration. The accepted standard model of underlying price used in options pricing theory—like the Black-Scholes model—is the log-normal distribution.2 This distribution is characterized by two parameters: mean and width.
- The mean reflects the expected future price of the underlying security at expiration. In the distribution graph, the mean shifts the peak of the distribution graph to the left if the expected price of the underlying security is to fall, and to the right if the expected price is to rise.
- The width of the line reflects the market’s expectation of how volatile the underlying security will be until the option expires. In the distribution graph, the width of the distribution graph widens if the market expects the future price of the underlying security to rise and fall within a wide band and narrows if it expects the future price to rise and fall within a narrow band.
Alternatively, the Options Wizard allows the user to enter data that reflects her outlook on the future price, volatility, and time horizon of the price movement of the underlying security. Using this data, the wizard presents a set of standard strategies that you can filter by aggressiveness, Probability of Profit, Max Gain and more. Additionally, these user-defined values are used to create an alternative Probability of Profit and drive the data in the Distribution Graph:
- If the user’s forecast is that the future price of the underlying security is greater (or less) than what the market expects, the distribution graph used in the calculation will be shifted farther to the right (or left), relative to the market-implied distribution.
- If the user’s forecast is that the future price volatility of the underlying security will increase (or decrease), then the distribution graph used in the calculation of probability of profit will be wider (or narrower) relative to the market-implied distribution.
The area under the distribution curve is the likelihood of the event occurring. If the entire area is filled in, that means there is a 100% probability the event occurs, while a 30% slice of the graph indicates a 30% probability. In the sample chart, the area under the curve depicted with the orange stripes is the probability of the option price being equal to or higher than the breakeven point at expiration.
Choose between Market Implied Probability of Profit and User-Defined Probability of Profit (based on your forecasts) in the Filters section of the Options Wizard.
1Visit Investopedia to find out more about probability distribution.
2Visit Investopedia to find out more about log-normal distribution.
This article may contain links to third party websites and information, which are provided for educational purposes only. The broker does not warrant or in any way guarantee any third-party information that is provided. All links and information therein are subject to change. Probability of Profit is a mathematical expression based on accepted industry options pricing and statistical distribution models. Probability of Profit is for informational purposes only and is not a recommendation. Probability of Profit does not consider any individual investor’s financial profile, investment objectives, or other factors that would typically be used when making recommendations. The Probability of Profit calculation does not include fees or commissions.
Options involve risk and are not suitable for all investors. For more information read the “Characteristics and Risks of Standardized Options” that you can find on the OCC website.