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Probability of touch vs expiring ITM vs profit: three different events
Learn why touching a strike, expiring in the money, and finishing a trade profitably require different events, barriers, assumptions, and probability calculations
Prepared by Mark · Primary sources below
Direct answer
Touch asks whether price reaches a level before a deadline. Expiring ITM asks where the settlement ends versus the strike. Profit is a separate event because it also applies the position's premium, payoff, costs, and exit time
Define the event before calculating it
For a 100 call, “touch 100 by Friday,” “close above 100 on Friday,” and “finish the call trade with positive P&L” are separate events. One price path can satisfy the first and fail the other two
Specify whether the level counts on an intraday trade, closing print, official settlement, bid, ask, or midpoint. Also state the timezone, deadline, and whether touching exactly the level counts
Expiring ITM only looks at the endpoint
A call is in the money at expiration when the settlement value exceeds its strike; a put is ITM when settlement is below the strike. This ignores every earlier path
ITM status does not prove profit. A call bought for 5 can expire at 103 and be worth 3, producing an intrinsic gain relative to zero but a loss relative to the 5 premium before fees
Exercise-by-exception and broker cutoffs are operational rules, not probability formulas. Expiration settlement, after-hours movement, contrary instructions, and product style can affect the actual result
Touch probability is path-dependent
A level is touched if the monitored price reaches it at any qualifying time before the deadline, even if price later reverses and expires far away. The calculation therefore depends on the entire path, not just the terminal distribution
Continuous-path models, discrete daily monitoring, overnight gaps, trading halts, and jump models produce different touch probabilities. A barrier observed continuously is not the same contract as one checked only at the close
Probability of profit belongs to the whole position
At expiration, a long call's upper break-even is strike plus premium and costs, not the strike. A credit spread, iron condor, ratio spread, or position closed early has different profitable regions
Before expiration, P&L also depends on IV, time, skew, rates, dividends, quotes, and exit execution. There is no single stock-price threshold that represents profit for every date and volatility state
The “touch is twice delta” shortcut is not a law
For a simplified driftless continuous process and a one-sided barrier, reflection arguments can make a touch probability resemble twice a terminal tail probability. Traders sometimes turn this into “twice delta”
Delta is not the exact terminal tail probability, and real assets have drift, skew, jumps, dividends, discrete monitoring, and changing volatility. The shortcut can exceed 100% or misstate near, far, or event-driven barriers
Use a barrier model or path simulation aligned with the monitoring rule. Never present a capped two-times-delta number as an observed frequency without calibration
Assignment probability is a fourth event
American-style short options can be assigned before expiration. Assignment depends on holder exercise decisions, remaining extrinsic value, dividends, rates, borrow conditions, and broker allocation
Touching or becoming ITM does not force immediate assignment. Conversely, holders may exercise under special circumstances. Do not replace assignment analysis with touch or terminal ITM probability
Compare models with the same inputs
Record spot, barrier, strike, expiration, volatility surface, rates, dividends, drift or pricing measure, monitoring frequency, and timestamp. A calculator's percentage is inseparable from these inputs
To evaluate a real-world probability claim, group forecasts into probability buckets and compare predicted with observed rates out of sample. Include all eligible observations and preserve the original event definition
Use a three-row scenario table
Write separate rows for touch, expiration ITM, and position profit. Add the event definition, model measure, time, threshold, and decision each number changes
This prevents a high touch probability from being sold as a high win rate. It also reveals when a trade can be right about direction or barrier contact and still lose after premium and repricing
Common questions
Is probability of touch always twice probability of expiring ITM?
No. A doubling relationship can arise in simplified continuous models for certain barriers. Drift, skew, jumps, discrete monitoring, and the difference between delta and terminal probability break the shortcut
Can an option touch the strike and still expire worthless?
Yes. Price can reach the strike or move beyond it, reverse, and settle out of the money. Touch records any qualifying visit, while expiration status uses only final settlement
Does expiring ITM mean my option trade made money?
No. Profit includes the premium and costs. A long call can expire above its strike but below strike plus purchase cost, leaving a net loss
Is assignment probability the same as probability of expiring ITM?
No. American-style options can be exercised early, and assignment depends on holder behavior and contract economics. Expiration ITM status is only one input to operational exercise handling
Sources and further reading
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