Probabilities explained: In the Money vs. Out of the Money

Probability OTM is the probability the underlying expires above a put’s strike price or below a call’s strike price.

Probability ITM is the probability the underlying expires below a put’s strike price or above a call’s strike price. We can derive an options probability of ITM by subtracting its probability of OTM from 100%. If the option is not out of the money, it must be in the money or at the money.

Prob.OTM = 100% - Prob.ITM

How do I calculate probability ITM and OTM?

We assume that the distribution of stock prices in the future is subject to a log-normal distribution. As long as the distribution function are known, the probability of the stock price closing within the ITM range at expiration can be calculated. This probability is Probability of ITM.

Stock prices follow a log-normal distribution, and the density distribution function is described as follows:

A well known model for financial option pricing is a GBM with constant volatility, it has a log-normal price distribution with density,

At any T：option expiration, where ST is the stock price at time t, r is the riskless interest rate, τ = T − t is time to maturity, and σ is the volatility. The model also has the characteristic that all options on the underlying must have the same BS implied volatility.

Therefore:

For buying a call, Probability of ITM =

For buying a put, Probability of ITM =

For selling a cash secured put, Probability of ITM =

For selling a covered call, Probability of ITM =

Remember, the calculation of OTM probability is based on the probability distribution of stock prices. It only represents a theoretical value, not a probability that it will actually happen.

The probability of ITM display is not guaranteed and only an calculation using a set of assumptions. This tool is not designed to produce definite returns for your investments and will not guarantee profits or returns. The information supplied by this tool is subject to error and only gives investors a general estimate of possible outcomes. Details rendered by this tool may not be exact or act as an accurate representation of the potential gains or losses made from your investments. Webull Financial is not liable for miscalculations or inaccuracies, including computational or human-made oversights and errors, contrived as a result of using the probability of ITM display. Additionally, Webull and its affiliates are not responsible for measures taken based upon these calculations. The ITM probability display does not constitute investment advice; it is heavily encouraged that all financial objectives and risks are carefully considered before investing in options.