Options Probability of Profit Calculator
This calculator estimates the chance the stock finishes above or below a target price at expiration, using implied volatility. It also shows the one-standard-deviation expected move.
Estimated probability the price ends above $100 at expiration is 51.1%. The 1-standard-deviation expected move is ±$5.73.
Educational estimate, not advice.
How it works
It uses the Black-Scholes lognormal model: the risk-neutral probability of finishing above a price is N(d2).
- T = days ÷ 365
- d2 = [ln(S/B) + (r − σ²/2)·T] ÷ (σ·√T)
- P(above B) = N(d2); P(below B) = 1 − N(d2)
- Expected move = S × σ × √T
Worked example
Stock $100, target $100, 30 days, IV 20%, rate 0%: P(above) ≈ 49%. The expected move is about ±$5.73.
Limitations
Assumes lognormal prices and constant volatility; ignores early management, fees and skew. It is a model estimate, not a forecast.
Questions
What is probability of profit in options?
The modelled chance a position makes at least $0.01 at expiration.
Is delta the same as probability?
Delta is a rough proxy for the chance of finishing in the money, but not identical to N(d2).
Why is ATM probability below 50%?
The lognormal model's drift term (−σ²/2) tilts the median slightly below the current price.
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