Grizzly Bulls

Options Probability Calculator

Estimate risk-neutral model probabilities that an underlying finishes below, between, or above price targets you enter.

Distribution assumptions

The calculator reports the probability of finishing below this price and at or above it.
Must be above the lower target. The calculator also reports the probability of finishing between the two targets.
Enter 1 to 3,650 whole calendar days. The model converts this to years using days ÷ 365.
Enter your own annualized volatility assumption. You can use the separate implied-volatility calculator to solve a model IV from an option premium.
Enter the continuously compounded annual rate used for the risk-neutral model distribution.
Enter a continuous annual dividend-yield assumption. Discrete dividend dates and amounts are not modeled.

Risk-neutral target probabilities

24.93%Finish below $90.00
37.87%Finish between both targets
37.20%Finish above $110.00
75.07%Finish at or above lower target
62.80%Finish at or below upper target
$105.13Risk-neutral expected terminal price
$103.05Model median terminal price

Build a strategy with these assumptions Carries only stock price, time, volatility, risk-free rate, and dividend yield. Target prices and probability results stay here; strategy legs, strikes, premiums, and quantities remain separate.

Outcome partition

The three mutually exclusive rows below cover the full terminal-price distribution and sum to 100% subject only to displayed rounding.

Terminal-price outcomeModel probability
Below $90.0024.93%
$90.00 to $110.0037.87%
Above $110.0037.20%

How the probability model works

The calculator uses the same standard-normal distribution convention as the Options Pricing & Greeks Calculator. Under the Black-Scholes-Merton risk-neutral lognormal model, the terminal stock price follows:

ln(ST) ~ Normal[ln(S) + (r − q − σ²/2)T, σ²T]
z(H) = [ln(H/S) − (r − q − σ²/2)T] ÷ (σ√T)
P(ST ≤ H) = N(z(H))

S is the current stock price, H is a target price, T is calendar days divided by 365, σ is annual volatility, r is the continuously compounded annual risk-free rate, q is the continuous annual dividend yield, and N is the standard normal cumulative distribution function. The between-target probability is the upper-target cumulative probability minus the lower-target cumulative probability.

Because the modeled distribution is continuous, the probability of landing on one exact price is effectively zero. That is why “above” versus “at or above,” and “below” versus “at or below,” do not differ numerically here.

Risk-neutral probability is not a forecast

These are Black-Scholes-Merton risk-neutralprobabilities. The model uses the entered risk-free rate minus dividend yield as its pricing-measure drift. It does not estimate the stock's real-world expected return, so the percentages should not be read as forecasts of what will actually happen.

This also is not a probability-of-profit calculator. The model does not know an option premium, strategy payoff, breakeven, transaction cost, tax treatment, assignment decision, or portfolio objective. A trade can make or lose money even when the underlying finishes inside a high-probability price region.

The tool assumes constant volatility, rates, and continuous dividend yield and a lognormal terminal-price distribution. It does not model volatility skew or term structure, jumps, discrete dividends, early exercise, borrow constraints, or changing market conditions. It does not fetch stock prices, option chains, implied volatility, rates, or dividend data, and it does not recommend a target, strike, expiration, strategy, or trade.

Use the Implied Volatility Calculator to solve model volatility from an entered option premium, or the Options Profit/Loss Calculatorfor single-leg expiration P&L.

Probability-model references