Options Probability Calculator
Estimate the probability that an option expires in or out of the money, based on underlying price, strike, days to expiration, and implied volatility.
Calendar days until expiration
Enter option details above and click Calculate probabilities to see the probability of expiring in or out of the money.
For educational purposes only. Not financial advice. Read full disclaimer
Probability Formula (Black-Scholes d2)
d2 = (ln(S/K) - 0.5 × σ² × T) / (σ × √T)
Call P(ITM) = N(d2) | Put P(ITM) = N(-d2)
Where: S = price, K = strike, σ = IV, T = time in years
Worked Examples
Example 1: Probability of a call reaching its strike
A stock trades at $100.00. You are considering buying a $105 call with 30 days to expiration. Implied volatility is 25%.
- T = 30/365 = 0.0822 years
- σ√T = 0.25 × √0.0822 = 0.0717
- d2 = (ln(100/105) − 0.5 × 0.0625 × 0.0822) / 0.0717
- d2 = (−0.04879 − 0.00257) / 0.0717 = −0.7166
- P(ITM) = N(−0.7166) = 23.7%
- P(OTM) = 1 − 0.237 = 76.3%
This call has about a 24% chance of finishing in the money. The option seller retains premium roughly 76% of the time.
Example 2: Probability of a put expiring worthless
A stock trades at $50.00. You sold a $45 put with 45 days to expiration. Implied volatility is 35%.
- T = 45/365 = 0.1233 years
- σ√T = 0.35 × √0.1233 = 0.1229
- d2 = (ln(50/45) − 0.5 × 0.1225 × 0.1233) / 0.1229
- d2 = (0.10536 − 0.00756) / 0.1229 = 0.7960
- Put P(ITM) = N(−0.7960) = 21.3%
- P(OTM) = 1 − 0.213 = 78.7%
This put has roughly a 79% chance of expiring worthless, meaning the seller keeps the full premium about 4 out of 5 times in similar setups.
How to Use This Calculator
- Select option type — choose Call if you want to know the probability of the stock finishing above the strike, or Put for finishing below.
- Enter the underlying price — the current market price of the stock or ETF.
- Enter the strike price — the strike of the option you are evaluating.
- Enter days to expiration — calendar days until the option expires. Find this on your broker's option chain.
- Enter implied volatility — the IV percentage shown on the option chain. This drives the probability estimate.
- Click Calculate probabilities — the calculator returns the probability of expiring ITM and OTM, plus the 1σ price range at expiration.
Frequently Asked Questions
- What does "probability of expiring ITM" mean?
- It is the estimated chance that the option finishes in the money at expiration — meaning the stock is above the strike for a call, or below the strike for a put. This probability is derived from the Black-Scholes model using current implied volatility and time to expiration.
- How accurate are these probability estimates?
- These estimates are based on the assumption that stock returns follow a log-normal distribution with constant volatility. In practice, volatility changes, and real markets exhibit "fat tails" (extreme moves happen more often than the model predicts). Use these as a starting point, not a guarantee.
- Why is delta similar to probability of ITM?
- An option's delta is mathematically close to the probability of expiring ITM (technically, delta uses N(d1) while probability uses N(d2), but they are similar for most practical purposes). Many traders use delta as a quick proxy for ITM probability when selecting strikes.
- How does IV affect the probability?
- Higher IV means a wider expected price range, which increases the probability of deep OTM options finishing ITM and decreases the probability of ATM options finishing ITM. When IV rises, the market is pricing in larger potential moves, spreading probability across a wider range of strikes.
- Can I use this for American-style options?
- This calculator uses the Black-Scholes model, which is designed for European-style options. For American-style options (most stock options), the probability of expiring ITM is similar, but the actual option value may differ because American options can be exercised early. For probability estimation purposes, it is a reasonable approximation.