The three probabilities
Same option, three questions. ITM asks where spot lands on expiry day. POP asks whether that landing spot pays back the premium. Touch asks whether the market ever reaches the strike on the way — roughly double the ITM chance, and the reason a "safe" short strike still hurts.
| Question | Level | Probability |
|---|
Strike by strike
The same expiry and implied volatility across a range of strikes. Use it to see what you are really buying when you reach for a further strike: the fair premium collapses much faster than the probability does.
| Strike | Prob. ITM | Prob. touch | Fair premium |
|---|
Probability is not edge
A high probability of profit is not the same as a good trade — selling a far strike wins nine times out of ten and can still lose money over a year if the tenth loss is big enough. What decides expected value is the premium versus the model value at the volatility you entered, which is why this page shows both. Check whether the implied volatility you are being quoted is historically rich or cheap on the IV rank calculator, see how the position's exposure moves with the greeks calculator, price a full position on the crypto options calculator, and if you are structuring a spread instead of a single leg, run it through the vertical spread calculator.
The math
Under Black-Scholes with zero rates, log spot at expiry is normal with mean ln S − σ²T⁄2 and standard deviation σ√T. The risk-neutral chance of finishing above a level L is therefore N(d₂) with d₂ = [ln(S⁄L) − σ²T⁄2] ⁄ (σ√T). Probability ITM uses L = strike; probability of profit uses L = break-even — strike plus premium for a call, strike minus premium for a put — which is why POP is always below the ITM chance for a buyer and above it for a seller.
Probability of touch comes from the reflection principle for driftless Brownian motion: the chance of ever reaching a barrier B before T is 2·N(−|ln(B⁄S)|⁄(σ√T)), which is close to twice the terminal probability and hits 100% once the barrier is at spot. Fair value is the standard Black-Scholes price, S·N(d₁) − K·N(d₂) for a call, and the edge is that value minus what you pay (or what you collect minus that value, if you are short).
These are risk-neutral probabilities, so they carry the model's assumptions: constant volatility, lognormal returns, no jumps, no funding on the underlying. Crypto violates all four to some degree — real distributions have fatter tails, so far strikes are more likely to be reached than the numbers here suggest. Treat the output as a well-calibrated baseline for comparing strikes, not as a forecast.