Probability of Profit in Options - A Model Estimate, Not a Forecast
Reviewed by Leon Moyer - Published October 9, 2026 - Last reviewed October 9, 2026
In this lesson
Calculate a position's probability of profit from its break-even, state the assumptions behind the number, and explain how changing the volatility input changes it.
Probability of profit (POP) is a pricing model's estimate of the chance that an options position is profitable at expiration, which means the stock finishes beyond the position's break-even price. It is calculated from the stock price, the break-even, the time left, a volatility input and an interest rate. It is a model output under stated assumptions, not a forecast of what the stock will do.
How is probability of profit calculated?
There are two steps:
- Find the break-even at expiration, as in the three numbers for any position.
- Ask the model how likely the stock is to finish on the profitable side of it. For a position that profits above its break-even, POP is the model's chance that the stock finishes above that price; for one that profits below, it is the chance of finishing below.
The free OptionsPro profit calculator, and the figures in this lesson, use the Black-Scholes model's risk-neutral probability, the quantity written N(d2). Every figure here uses the same inputs: XYZ at $50, 30 days to expiration, 30% implied volatility and a 4.5% rate. The last three are the calculator's defaults.
Worked example
Probability of profit for a 48/45 bull put spread, 30 days
Sell the XYZ 48 put for $0.81 and buy the 45 put for $0.20, a net credit of $0.61 ($61 per spread).
- Break-even: the short strike minus the credit, $48 - $0.61 = $47.39.
- Probability of profit: the model's chance that XYZ finishes above $47.39 in 30 days is about 73%.
The position has three zones at expiration, and the model gives each its own probability:
The 73% is the 68% full-profit zone plus the slice of the middle zone between $47.39 and $48, where the spread still makes a little.
Illustrative and hypothetical. The ticker and prices are invented for teaching, and the figures exclude commissions, fees, margin interest and taxes, which reduce real results. Past or hypothetical outcomes do not indicate future results.
Where the XYZ 48/45 bull put spread makes money, at expiration
Hover or tap the chart, or focus it and use the arrow keys, to read any price.
Open this trade in the free calculatorShow as table
The bull put spread's three outcome zones, as the model sees them
Modeled chance at expiration
Is the chance of finishing in the money the same as the chance of profit?
No, and the gap matters most for bought options. With the same inputs, the model gives the XYZ 50 call about a 50% chance of finishing above its $50 strike. But you paid $1.81 for it, so it only profits above $51.81, and the model's chance of that is about 34%. The extra $1.81 the stock has to climb is the premium.
Call Options Explained put the break-even of a bought call at the strike plus the premium. Probability of profit is the chance of getting past that price, which is why it is lower than the chance of finishing in the money.
In the calculator, the per-leg "ITM chance" badge is approximated from each leg's delta, while the Probability of Profit panel uses the model's own probability for the whole position. The two answer different questions and can differ by a few points.
What does probability of profit assume?
Every POP figure rests on assumptions that real markets break. The main ones:
- Prices follow a smooth lognormal distribution. The Options Industry Council notes that most pricing models assume this, but "the normal distribution underestimates the probability of extremely large moves" (OIC technical FAQ). Earnings gaps and market shocks happen more often than the model expects.
- Volatility is known and fixed. The model uses one number you choose for the whole period. Real volatility changes from day to day.
- One volatility for every strike. The calculator's POP uses the position's base implied volatility, even though real chains usually show different implied volatilities at different strikes.
- Risk-neutral drift. The model grows the stock at the interest rate, not at anyone's forecast of its return. It is the probability that makes the option prices fair, not a prediction.
- You hold to expiration. POP ignores closing early, early assignment and the path the stock takes along the way.
- No costs. Commissions, fees and the bid-ask spread are left out.
The OIC's own summary of pricing models applies here too: "market forces determine actual premiums, not formulas" (OIC on the Black-Scholes formula).
How does volatility change the probability of profit?
Volatility is the input with the biggest effect, and it pulls different trades in opposite directions. Hold the two trades from this lesson fixed, with their premiums already paid or collected, and change only the volatility you give the model:
Higher volatility means a wider spread of possible prices. That helps a position that needs a big move and hurts one that needs the stock to stay put. The same trade can therefore show a POP anywhere from the low 60s to the low 80s depending on one assumption, which is why a POP figure should always be quoted with its inputs.
The same two trades, with different volatility assumptions
48/45 bull put spread (break-even $47.39)
Long 50 call (break-even $51.81)
How should you use probability of profit?
- Compare trades under the same assumptions. POP is most useful for ranking alternatives on the same stock with the same inputs.
- Never read it without the payoffs. A high POP usually buys a small maximum profit and a larger maximum loss, as the risk-to-reward ratio lesson showed.
- Combine both with expected value. Expected value weighs every outcome by its probability, which is the step POP alone leaves out.
Check your understanding
A long call profits above $55.33 at expiration. In words, what is its probability of profit?
Show answer
It is the model's estimated chance that the stock finishes above $55.33 at expiration, given the volatility, time and rate you put in. It is not the real-world chance and it says nothing about how much the position makes.
The model gives a call a 50% chance of finishing in the money but a 34% chance of profit. Why the gap?
Show answer
To profit, the stock has to rise past the strike by at least the premium paid. The break-even sits above the strike, and the chance of finishing above a higher price is lower.
You raise the volatility input from 30% to 40%. Does a credit spread's POP usually rise or fall?
Show answer
It usually falls. Higher volatility spreads out the possible prices, which makes it more likely the stock moves through the credit spread's break-even.
Key takeaways
- Probability of profit is the model's chance that the stock finishes beyond the break-even at expiration.
- It differs from the chance of finishing in the money, because the premium moves the break-even.
- It assumes lognormal prices, a fixed volatility, risk-neutral drift, holding to expiration and no costs. Real markets break each of those.
- Volatility is the biggest input. Quote POP with its inputs and use it alongside the payoffs and the expected value, never alone.
Common questions
What does probability of profit mean in options?
It is a model's estimate of the chance that a position is profitable at expiration, meaning the stock finishes beyond its break-even. It depends on the volatility and other inputs you give the model, and it does not say how much you would make or lose.
Is probability of profit the same as delta?
No. Delta is a measure of price sensitivity that traders sometimes use as a rough stand-in for the chance an option finishes in the money. Probability of profit asks a different question: the chance of finishing beyond the break-even, which includes the premium.
Is a high probability of profit good?
Not by itself. High probability usually comes with a small maximum profit and a larger maximum loss. A 73% chance of profit (about 68% of making the full $61) against an 11% chance of losing the full $239 is not automatically better than a 37% chance of making up to $352.
How accurate is probability of profit?
It is only as accurate as its inputs and assumptions. It assumes a smooth, lognormal distribution of prices with a fixed volatility, while real stocks can gap and their volatility changes. Treat it as a way to compare trades under the same assumptions, not as real-world odds.