Options Probability Calculator

Estimate the probability of finishing in the money, of touching a strike before expiry and of a position profiting.

Three figures around an option are routinely treated as though they were one: delta, the chance of finishing in the money, and the chance the position makes money. They are three different quantities, they can differ by tens of percentage points on the same contract, and holding them apart is the entire reason this options probability calculator exists. As a probability of profit calculator it answers the third question rather than the first, and for a written contract that is also the option assignment probability — the chance of being assigned is the chance of finishing in the money.

Formula: P(ITM) = N(d2) for a call, N(-d2) for a put; P(touch) is approximately 2 x P(ITM)

Your figures

Currency

Option type

Position

Days to expiry

Calendar days. The model converts to years internally.

Underlying price

Strike price

Implied volatility

Annualised, as a percentage. Every probability here comes from this figure.

Risk-free rate

Annualised. Roughly the yield on a short government bond.

Premium per share

Optional — what the option is bought or written for, per unit of the underlying. Adds the break-even and the probability of profit.

Results

Probability of profit

17.57%

buying this call, measured at a break-even of US$105.75

Probability of finishing in the moneyN(d2) — the chance of any intrinsic value at all, however small. For a writer it is the probability of assignment.: 20.96%
Probability of expiring worthlessThe complement of the figure above.: 79.04%
Probability of touching the strike before expiryRoughly twice the chance of finishing beyond it: for every path that ends past the strike there is a mirrored one that reached it and came back.: 41.91%
Delta, as a percentageWidely used as a shortcut for the probability of finishing in the money, and not the same number: d1 exceeds d2 by volatility x the square root of time, so a call's delta reads higher and a put's magnitude lower.: 22.65%
Break-even at expiryStrike plus the premium for a call, strike less the premium for a put. Profit is measured here, not at the strike.: US$105.75
Model value of the optionBlack-Scholes at the volatility entered, for comparison with the premium.: US$0.7308
Forward priceThe underlying carried at the risk-free rate. The model's distribution is centred here, not on today's price.: US$100.41
d1The exponent behind delta.: -0.7506
d2d1 less volatility x the square root of time. That gap is the whole difference between delta and the probability of finishing in the money.: -0.8079

What this means

At 20.00% annualised volatility over 30 days, the model puts the chance of finishing beyond the US$105.00 strike at 20.96%, and the chance of trading through that level at some point first at 41.91%. Delta reads 22.65%, which is the number most often quoted in place of the first — the gap between them is the volatility x square root of time separating d1 from d2, not a rounding difference. The premium moves the threshold from the strike to a break-even of US$105.75, and measured there the model puts the chance of this position finishing profitable at 17.57% — a different question from finishing in the money, which is why the two percentages differ. These are risk-neutral model probabilities derived from the volatility entered, and they are only as good as that figure.

Every probability here is a model output under a lognormal assumption, not a forecast. Real returns have fatter tails than the model allows, so extremes happen more often than it implies.
Finishing in the money counts any intrinsic value at all. An option a penny in the money is in the money, which is why a bought option's probability of profit sits below it.
The probability of touching uses the reflection approximation — twice the chance of finishing beyond the level, capped at 100%. It ignores drift, and treats a strike the price already sits on as touched.
For a writer, the probability of finishing in the money is the probability of assignment at expiry. American options can be assigned before it.
The break-even counts the premium only. Commission, fees and any financing on a short position move it further.

The link reopens this calculator with the same numbers. Nothing you enter is sent to a server.

Continue with these figures

About the Options Probability calculation

Under the pricing model the underlying's price at expiry is lognormally distributed, which means the probability of finishing beyond any level has a closed form. Set that level to the strike and you get the probability of finishing in the money — the probability ITM that most options platforms quote — which is N(d2) for a call and N(−d2) for a put. Set it to the break-even instead and you get the probability of profit, which is a different question with a different answer.

Delta is the third figure, and it is the one most often substituted for the first. It is close, and the closeness is not a coincidence — delta is N(d1), the probability is N(d2), and d1 exceeds d2 by exactly volatility times the square root of time. The gap is small on a short-dated, low-volatility contract and wide on a long-dated or highly volatile one, but it is always there, because delta is a hedge ratio that happens to resemble a probability.

Every probability on the page is a model output derived from the volatility typed in. Nothing is fetched, no historical distribution is fitted, and the answer is only ever as good as that one volatility figure — which is an assumption about the future, not an observation of it.

Options Probability formula

the terminal price is lognormal, so for any level L:

  P(S_T > L) = N(d2(L))
  d2(L) = [ln(S ÷ L) + (r − σ²/2) × T] ÷ (σ × √T)

measured at the strike:
  P(ITM, call) = N(d2)      P(ITM, put) = N(−d2)
  delta(call)  = N(d1),  where d1 = d2 + σ × √T

measured at the break-even, where the premium changes hands:
  break-even(call) = K + premium
  break-even(put)  = K − premium
  P(profit) = P(S_T beyond the break-even, profitable side)

touching before expiry, by reflection:
  P(touch) ≈ 2 × P(finishing beyond the strike), capped at 100%

S: The underlying's price now.
S_T: The underlying's price at expiry — the random quantity all of this is about.
L: Any level being measured against: the strike for P(ITM), the break-even for P(profit).
K: The strike of the contract.
T: Time to expiry in years, so 30 days is 30 ÷ 365.
σ (sigma): Annualised implied volatility as a decimal. Every probability here is derived from it.
r: Annualised risk-free rate, which sets the drift the model applies to the price.
N(x): Cumulative standard normal distribution — the area to the left of x.

The −σ²/2 term in the drift is the piece that looks like a typo and is not. A lognormal variable's median sits below its mean, and by exactly that amount: the model grows the price at r on average, but the typical path grows at r − σ²/2, because compounding an unchanged average return through volatility drags the middle of the distribution down. Since a probability is a statement about where the middle of the distribution lies, the median drift is the one that belongs in d2.

That single correction is the whole difference between d1 and d2, and therefore between delta and the probability of finishing in the money. d1 carries an extra σ√T, which is why a call's delta always reads above its P(ITM) and a put's delta magnitude always reads below it. At 30 days and 25% volatility the gap is about 0.07 in the exponent and roughly two percentage points in the answer; stretch the same contract to a year and it widens to something no one should be rounding away.

Profit is measured at the break-even rather than at the strike, because the break-even is where money actually changes hands. The premium moves the threshold by its own size — up for a call, down for a put — and shifts the probability by however much of the distribution sits between the strike and that new level. This is why a written option is profitable across a wider range of outcomes than it is out of the money, and a bought option across a narrower one.

The asymmetry that follows is the reason the two numbers are worth separating. A writer can hold a position with a high probability of profit and a modest probability of assignment at once, because assignment is measured at the strike and profit at a level further away. Neither figure says anything about the size of what happens in the remaining cases, and for a written option those cases are the large ones — a high probability of a small gain is not the same claim as a favourable position.

P(touch) comes from the reflection principle. For every path that ends beyond a level there is a mirror-image path that reached the level and came back, so the chance of trading through it at some point is roughly twice the chance of finishing past it. The doubling is applied to the far side of the strike from the current price, which is why a deep in-the-money strike shows a low probability of being touched again: the price has already moved away from it, and getting back is the unlikely event.

All of these are risk-neutral probabilities. They are computed under an artificial measure in which every asset drifts at the risk-free rate, chosen because it makes the pricing mathematics consistent, not because anyone believes it describes real returns. They are a reasonable way to read what a volatility figure implies, and they are not a forecast of what will happen.

Options Probability: a worked example

Writing a 95-strike put with the underlying at 100, 30 days to expiry, 25% implied volatility, a 4% risk-free rate and 1.20 of premium per unit received.

σ√T0.25 × √(30 ÷ 365) = 0.25 × 0.2867 = 0.0717
d2[ln(100 ÷ 95) + (0.04 − 0.03125) × 0.0822] ÷ 0.0717 = 0.7257
d10.7257 + 0.0717 = 0.7974
P(finishing in the money)N(−0.7257) = 23.40%
Delta, as a percentage21.26% — below P(ITM), by the σ√T gap
P(touching 95 first)2 × 23.40% = 46.80%
Break-even95 − 1.20 = 93.80
d2 at the break-even[ln(100 ÷ 93.80) + 0.00072] ÷ 0.0717 = 0.9031
P(profit)N(0.9031) = 81.68%
Model value at 25% volatility0.8964, against the 1.20 premium entered

A 23.40% chance of assignment at expiry but an 81.68% chance the written put finishes profitable, because 1.20 of premium moves the threshold from 95 down to 93.80. Nearly half the time the underlying touches 95 before expiry even so. The 1.20 premium sits above the model's 0.8964, which says the market is pricing a higher volatility than the 25% entered.

How to use the Options Probability calculator

Choose call or put, and whether the option is being bought or written — the direction decides which side of the break-even counts as profit, and on a written contract it turns the in-the-money figure into an assignment probability.
Enter the underlying price, the strike and the days to expiry.
Enter the implied volatility for that strike and expiry. Every probability on the page comes from this figure, so it deserves more care than any other input.
Enter the risk-free rate, which sets the drift the model applies between now and expiry.
Add the premium per unit to get the break-even and the probability of profit. Without it the calculator reports the probability of finishing in the money and stops there.
Compare the probability of profit against the probability of finishing in the money, read the gap as the premium's worth of distribution, and read the probability of touching alongside both if the position will be managed before expiry.
Compare the model value against the premium entered. A large difference means the two inputs disagree about volatility, and the probabilities follow the volatility rather than the premium.

Limitations of the Options Probability calculator

Every calculation makes assumptions. These are the ones that matter here.

Assumes lognormal returns with one constant volatility. Real returns have fatter tails and gap around news, so outcomes far from the current price happen more often than these figures imply.
Finishing in the money counts any intrinsic value at all. A contract one penny in the money is in the money, which is why a bought option's probability of profit always sits below it.
The probability of touching uses the reflection approximation, doubling the chance of finishing beyond the level and capping at 100%. It ignores drift, and treats a strike the price already sits on as touched.
Risk-neutral probabilities are a construct of the pricing model, computed under a measure in which everything drifts at the risk-free rate. They are not real-world odds and not a forecast.
The break-even counts the premium only. Commission, fees, the bid-ask spread and any financing on a written position all move it, and always against the holder.
Every figure is measured at expiry. A position closed early settles against a market price carrying time value, not against the payoff these probabilities describe.
For a writer this is the probability of assignment at expiry. American options can be assigned at any point beforehand, most often over a dividend, which no European-exercise model prices.
A high probability of profit says nothing about the size of the loss in the remaining cases, and on a written option those are the large ones. The two halves of a distribution have to be read together.

Frequently asked questions about Options Probability

Why is the probability of profit higher than the probability of finishing out of the money?

Because they are measured at different levels. Finishing out of the money is measured at the strike; profit is measured at the break-even, which the premium moves further away. On the worked example the written put is out of the money 76.60% of the time and profitable 81.68% of the time — the difference is the slice of distribution between 95 and 93.80.

What does a probability of touching calculator tell me that the others do not?

Finishing in the money is measured once, at expiry. Touching asks whether the price reaches the strike at any point before then, which it can do and then retreat from — so the probability of touching is roughly twice the probability of finishing beyond the same level, and it is the figure that matters for a position you would close or adjust on the way rather than hold to the end.

Is delta the same as the probability of finishing in the money?

No, though it is used as a shortcut for it constantly. Delta is N(d1) and the probability is N(d2), and d1 exceeds d2 by volatility times the square root of time. That makes a call's delta read higher than its probability and a put's magnitude lower. The gap is a couple of points on a short-dated contract and much wider on a long-dated or volatile one.

What does the probability of touching tell me that the others do not?

It measures the journey rather than the destination. An option can end well away from the strike having traded through it twice on the way, and anything managed before expiry — a stop, a roll, an early close — is exposed to that path. On the worked example the strike is reached 46.80% of the time despite only 23.40% of paths ending beyond it.

Is the in-the-money figure the same as the assignment probability on a written option?

At expiry, yes — a written contract finishing in the money is assigned, so the 23.40% on the worked example is the assignment probability under European exercise. It is not the whole picture on an American contract, which can be assigned at any point beforehand and most often is over a dividend. Note also that assignment and profit are separate readings: the same written put is profitable in 81.68% of outcomes.

Why does the model value differ from the premium I entered?

Because the two are independent inputs. The model value is what the contract is worth at the volatility typed in; the premium is what it actually trades for. A premium above the model value means the market is pricing a higher volatility than you entered. The probabilities follow your volatility figure, so a large gap is a signal to revisit it.

Are these real-world probabilities?

They are risk-neutral model probabilities. The model works in a constructed measure where every asset drifts at the risk-free rate, which makes the pricing mathematics consistent but is not a description of how anything actually behaves. Treat the output as a careful reading of what the entered volatility implies, not as odds on a future event.

Does a high probability of profit make a position favourable?

Not on its own, and this calculator does not judge it. Probability describes how often, never how much. A written option can be profitable in most outcomes while the minority of outcomes are far larger than the premium collected. The probability figure and the size of the payoff in each case are two separate questions, and only both together describe a position.

How does the risk-free rate affect these figures?

It sets the drift. The model carries the price forward at the risk-free rate, so the distribution is centred on the forward price rather than on today's price — the forward line on the results shows where. A higher rate pushes that centre up, which raises the probability of finishing above any level and lowers the probability of finishing below it.

Last reviewed 29 August 2026. See our methodology and editorial policy.

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