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POP vs POT vs P50: Options Probabilities Explained
Probability of profit, probability of touch and probability of 50% profit answer three different questions about the same trade. Here is what each one means, how we calculate it, and how to use them together.
The three questions
POP: will it make money at expiration?
The chance the price finishes past your breakeven on expiration day. For a short put: above the strike minus the credit. For a put credit spread: above the short strike minus the net credit. For calls, the mirror image.
POT: will the price reach my strike?
The chance the price touches your short strike at any moment before expiration. A touch is not a loss, but it is when you may face a decision to hold, roll or close.
P50: will I get to take 50% profit?
The chance the trade can be bought back for half the credit at some point before expiration. It is the number that fits a “close at 50%” rule.
Worked example: IBIT 15-delta cash-secured put (Oct 23, 2026 close)
IBIT closed at $45.96. The 40 put expiring Dec 4, 2026 (42 days) was about 0.14 delta and paid $0.525 a share at the mid, so the breakeven is $39.48. Using its implied volatility of 42.7%:
Notice the pattern: POT (35%) is about double the chance of finishing below the strike, and P50 (92%) is higher than POP (84%). See the live idea card.
How we calculate them
- POP: the price at expiration is lognormal (the Black-Scholes assumption) with the option’s implied volatility and the risk-free rate as drift. POP = the probability of the ranges where profit at expiration is above zero, using the trade’s breakeven(s).
- POT: the exact first-passage (reflection) formula for a lognormal random walk with drift, not just 2 × delta. For a strike below the price: N((ln(K/S) − νT)/σ√T) + (K/S)2ν/σ² N((ln(K/S) + νT)/σ√T), with ν = r − σ²/2.
- P50: a Monte Carlo simulation of 40,000 daily price paths at the same implied volatility (fixed random seed, so the number only changes when the data does). Each day every option in the trade is repriced with Black-Scholes at its own entry implied volatility; a path counts if the cost to close falls to 50% of the credit or less at any daily close.
- Inputs: price, strikes, days to expiration, implied volatility and credit come from Cboe’s delayed option quotes after each close; the rate is the 13-week T-bill yield. No dividends (IBIT pays none).
POP vs POT vs P50 at a glance
| Number | Question it answers | Looks at | Typical size for a 15-delta put |
|---|---|---|---|
| POP | Profit if held to expiration? | Expiration day only | Mid 80s % |
| POT | Will the price reach the strike? | Whole path | About 30–40% |
| P50 | Can I close at 50% profit? | Whole path | About 90% |
Limits of these numbers
- A high POP does not mean low risk. An 85% POP short put can still lose many times the credit on the other 15%.
- Real markets jump, especially bitcoin. Gaps make touches and big losses more likely than a smooth model suggests.
- Implied volatility changes. A selloff usually raises it, which makes a short put cost more to close even before the strike is touched.
- Credits use mid prices. Real fills, fees and early assignment can change the result.
See them in use: IBIT options trade ideas with POP, POT and P50IBIT buy the dip calculatorHow much bitcoin is in one IBIT shareAll tools
FAQ
What is POP (probability of profit) in options?
POP is the chance a trade makes at least $0.01 if you hold it to expiration. For a short put it is the chance the stock finishes above the strike minus the credit (the breakeven). We calculate it from a lognormal price distribution using the option’s implied volatility.
What is POT (probability of touch)?
POT is the chance the stock trades at your short strike at least once before expiration, even if it later recovers. It is always higher than the chance of finishing past the strike, roughly double it. A common rule of thumb is POT ≈ 2 × delta; we use the exact barrier (reflection) formula instead.
What is P50 (probability of 50% profit)?
P50 is the chance that, at some point before expiration, you can buy the trade back for half of what you collected, so you keep 50% of the credit. It fits a “take profit at 50%” rule. We estimate it by simulating tens of thousands of daily price paths and repricing the option each day.
How are POP, POT and P50 different, and why is P50 often higher than POP?
POP looks only at the price on expiration day. POT asks whether the price ever reaches the strike. P50 asks whether the trade ever reaches half its maximum profit. Because time decay usually brings a short option to half its value long before expiration, and many paths reach 50% profit and only later turn against you, P50 is usually a bit higher than POP. For example, the IBIT 15-delta cash-secured put on Oct 23, 2026 had a POP of 84%, a POT of 35% and a P50 of 92%.
Is a 2 × delta probability of touch accurate?
It is a decent shortcut. Delta is close to the chance of finishing in the money, and for a random walk the chance of touching a level is about twice the chance of ending past it. The exact number moves with drift, volatility and time, so the shortcut can be off by a few points. For a 15-delta put it gives about 30%, while the full formula is usually a bit higher.
Which number matters most for a 50% profit-taking strategy?
P50, because the plan is to close at 50% of the credit. POP tells you how often holding to expiration works, and POT tells you how often you will be tested. Look at all three, and at the size of the loss when you are wrong.
Do these probabilities predict where the stock will go?
No. They come from implied volatility, which is the option market’s price for movement, plus a lognormal model. Real prices jump and trend, and implied volatility usually runs a bit above realized volatility. Treat them as model odds, not forecasts.