Options Probability Calculator

Every option has an implied probability of expiring in the money (ITM) or out of the money (OTM). These probabilities are derived directly from the Black-Scholes model and the option’s implied volatility. Understanding them is essential for selecting strikes and managing risk in any options income strategy, including the wheel.

Probability of Expiring ITM vs OTM

The probability of an option expiring ITM tells you the market-implied likelihood that the stock will finish beyond the strike price at expiration. For a call option, this is the chance the stock closes above the strike. For a put option, it is the chance the stock closes below the strike. These probabilities are closely related to an option’s delta — a 0.30 delta call has roughly a 30% chance of finishing ITM.

Wheel traders selling cash-secured puts typically target strikes with a 70–80% probability of expiring OTM (i.e., delta around 0.20–0.30). This ensures a high likelihood of keeping the premium without being assigned shares.

Probability of Touching

The probability of touching the strike is different from the probability of expiring ITM. An option can touch the strike price at any point during the contract’s life, even if it later reverses and expires OTM. A common approximation is that the probability of touching is roughly 2x the probability of expiring ITM. This matters for risk management: even if you expect a put to expire OTM, there is a significant chance the stock will dip to your strike at some point, which can trigger margin stress or early assignment anxiety.

Standard Deviations & Expected Move

Implied volatility prices in the market’s expected range of movement over a given period. The expected move is calculated as:

Expected Move = Stock Price × IV × √(DTE / 365)

This gives you the 1 standard deviation (1 SD) range. Statistically, the stock has approximately a 68% chance of staying within this range by expiration. The 2 SD range (approximately 95% probability) is simply double the expected move. These ranges are symmetric around the current stock price and assume a lognormal distribution of returns.

Using Probability for Strike Selection

Understanding probability helps you make disciplined strike selection decisions rather than guessing. Here is how to apply it:

• Conservative approach: Sell puts at or below the 1 SD move (around 0.15–0.20 delta). This gives roughly an 85% probability of expiring OTM, but yields smaller premiums.
• Balanced approach: Target the 0.25–0.30 delta range (70–75% OTM probability). This is the sweet spot for most wheel traders, balancing premium income with a reasonable safety margin.
• Aggressive approach: Sell closer to the money (0.35–0.45 delta). Higher premiums, but assignment probability rises sharply. Only appropriate if you genuinely want to own the shares.

The expected move range can serve as a sanity check: if your strike is inside the 1 SD range, you are taking on more risk than the “normal” implied range of movement. If it is outside the 2 SD range, the premium may be too small to justify the trade.