Free Option Probability of Profit Calculator
This tool provides estimates for educational purposes only. Probability outputs are not guarantees of future results. Actual market outcomes may differ due to volatility changes, early assignment, dividends, and other factors.
How This Calculator Works
We’re using the Black-Scholes model in this calculator. The Black-Scholes model is best suited for European-style options because they cannot be exercised early, and they do not account for dividends. ETF and equity options in the U.S. are American-style, which technically makes the binomial model a better fit.
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However, for most practical purposes, Black-Scholes still gives a solid ballpark estimate for both. It’s widely used, fast, and excellent for obtaining probability ranges.
To determine the Probability of Profit (POP), we calculated the breakeven price. We then used the Black-Scholes framework to estimate the probability that the stock ends above that breakeven level at expiration. All probability estimates are based on the option’s intrinsic value at expiration.
From there, everything else in the calculator relies on the core assumptions built into Black-Scholes, starting with how the model treats future stock prices.
1. Lognormal Price Distribution
The model our calculator uses assumes the underlying stock follows a lognormal distribution. In plain terms, this means:
- Prices can’t go below zero
- Large moves become less likely the farther you look from the current price
- Volatility grows with time
This is why the probability curve is skewed and not symmetrical.
2. Constant Implied Volatility
The calculator assumes IV stays the same from today until expiration.
3. Uses Black–Scholes d1/d2 for Key Estimates
We use Black–Scholes inputs to calculate:
- Probabilities of finishing ITM/OTM (via option delta as a proxy)
- Probability of profit based on the breakeven price
- Price-target probabilities (5%, 10%, 20% moves)
- Long-option payoff odds (2×, 3×, 5× projections)
- Short-option buyback odds (100% profit, 50% profit, 25% profit)
4. Interest Rate Adjustments
The strike price is discounted using the risk-free rate to calculate d1 and d2 correctly.
5. No Early Assignment / No Dividends
As we mentioned, this model uses Black-Scholes. This means:
- Early exercise risk is not modeled
- Dividends are assumed to be zero
6. Estimates Are Approximations, Not Certainties
These outputs are probability estimates, not market forecasts.
Real-world outcomes depend on:
- Changing volatility
- Option Liquidity
- Early assignment
- Dividend effects
- Volatility skew
To learn more about the Black-Scholes option premium pricing model, check out our video below!
This calculator is for educational and illustrative purposes only. It uses a simplified version of the Black-Scholes framework along with approximations commonly used in options analysis. Real-world option prices and probabilities can differ due to factors not captured here (volatility changes, early exercise, dividends, liquidity, market conditions, etc.). Nothing here should be taken as trading advice or a guarantee of any outcome.
FAQ
A long call option gives the buyer the right to purchase a stock at a set price before expiration, typically used when expecting the stock price to rise. A short call option involves selling a call, obligating the seller to sell the stock if exercised, often used to generate income but with unlimited risk if the stock price rises significantly.
Black-Scholes works best for European options because it doesn’t account for early exercise or dividends, while the binomial model does. For most quick estimates though, Black-Scholes is fast, simple, and usually close enough for stock and ETF options.
To determine option profitability, calculate your breakeven point (strike + premium for calls, strike - premium for puts) and compare it to the underlying asset's price at expiration.
This version is built for single legs. Spread pricing is doable, but it requires multiple legs, correlation between strikes, and more advanced modeling.
