Options Probability Calculator: POP, ITM and Price Targets

Modeled probability at expiration

Options Probability Calculator

Estimate probability of profit, probability of finishing in the money and the chance of ending above or below a target price.

Probability of profit uses the premium-adjusted break-even.
Formatting only; no currency conversion.
Current price of the modeled stock or underlying.
Call ITM is above strike; put ITM is below strike.
Amount paid for long or received for short.
From 1 to 36,500 days.
Annualized standard deviation, often estimated from implied volatility.
Continuous model drift before subtracting dividend yield.
Continuous yield; enter 0 when not applicable.
Used for premium and fee totals, not probability.
Usually 100 for standard US equity options.
Fees shift the modeled break-even.
Shows probability above and below this price.

This is a single-path lognormal model with constant volatility and return assumptions. It is not a guarantee, live quote or recommendation.

Options probability formula

ln(ST) is modeled as a normal variable with mean ln(S0) + (μ − q − σ² ÷ 2)T and standard deviation σ√T.

P(ST > H) = N([ln(S0 ÷ H) + (μ − q − σ² ÷ 2)T] ÷ [σ√T]).

S0 is current price, H is a threshold, μ is expected annual total return, q is continuous dividend yield, σ is annual volatility, T is years and N is the standard normal cumulative distribution.

The calculator applies that distribution to the strike, option break-even and optional price target. It uses a physical or subjective drift supplied by you. Setting μ to a risk-free rate creates a risk-neutral style assumption, but it still does not reproduce a broker probability model exactly.

Break-even and probability of profit

  • Long call: break-even = strike + premium + fees per share; profit probability is P(ST > break-even).
  • Long put: break-even = strike − premium − fees per share; profit probability is P(ST < break-even).
  • Short call: break-even = strike + premium − fees per share; profit probability is P(ST < break-even).
  • Short put: break-even = strike − premium + fees per share; profit probability is P(ST > break-even).

Because the modeled terminal distribution is continuous, using strictly above or below gives the same probability as including the exact threshold. Early exercise, assignment before expiration and closing the trade early are excluded.

Verified example

Long call with a 45-day horizon

For current price US$100, strike US$105, premium US$3, one 100-share contract, US$1 fee, 45 days, 30% volatility, 8% expected total return and 0% dividend yield, break-even is US$108.01. The lognormal model gives approximately 24.49% probability of profit, 33.64% probability of finishing in the money and 19.38% probability of finishing above US$110.

How the price ranges work

The central 68.27% range uses one standard deviation around the median log price. The central 95% range uses 1.959964 standard deviations. These ranges are model quantiles, not guaranteed trading ranges or confidence intervals for the model itself.

Limits and assumptions

  • The underlying follows a lognormal distribution with constant annual volatility, expected return and dividend yield.
  • Probabilities refer only to the terminal price at expiration, not the probability of touching a level before expiration.
  • Probability of profit ignores bid-ask spread, taxes, slippage, changing volatility and closing costs beyond entered fees.
  • Long and short American-style options can be exercised or assigned early; that behavior is not modeled.
  • Current price, strike, premium and target support six decimals up to 100,000,000. Time is limited to 100 years and volatility to 1,000%.
  • A modeled probability is not the same as certainty, expected profit, option value or investment suitability.

Risk note: Small changes in volatility and expected return can materially change every result. Short options can have substantial or unlimited losses even when their modeled profit probability is high. This calculator is educational and is not investment advice.

Related calculators

Black-Scholes CalculatorImplied Volatility CalculatorOptions Profit CalculatorKelly Criterion Calculator