Probability of Touch
Estimates the probability that an asset's price touches a given level (a barrier) before expiry, using the reflection-principle approximation: roughly twice the probability of finishing beyond the barrier, 2·N(−|d|), with d = ln(H/S)/(σ√T). It's the back-of-the-envelope calculation traders use for barrier options and for judging the chance of a stop being hit. It assumes zero drift; with high interest rates the real probability is a little higher. Enter the spot price, the barrier level, the volatility and the term.
Result
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Probability of Touch
Estimates the probability that an asset's price touches a given level (a barrier) before expiry, using the reflection-principle approximation: roughly twice the probability of finishing beyond the barrier, 2·N(−|d|), with d = ln(H/S)/(σ√T). It's the back-of-the-envelope calculation traders use for barrier options and for judging the chance of a stop being hit. It assumes zero drift; with high interest rates the real probability is a little higher. Enter the spot price, the barrier level, the volatility and the term.
What are the odds the price reaches it?
Will the stop get hit? Will the barrier option be triggered? These questions share the same root: what's the probability that the price touches a certain level before a date. There's an elegant approximation for it, borrowed from physics' reflection principle: the chance of touching the barrier is roughly twice the chance of the price finishing on the other side of it.
In formula terms it's 2·N(−|d|), with d measuring the distance to the barrier in standard deviations. The factor of two is the key insight: the price can touch the barrier and come back, so the probability of touch is much higher than that of simply closing beyond it. It's a rule traders run in their heads to calibrate barriers and stops without opening a full model.
Enter the spot price, the barrier level, the volatility and the term. A word of warning: this is an approximation that assumes zero drift in the log price. With high interest rates or long terms, the real touch probability tends to be a little higher than the estimate. Treat the number as a good quick guide, not as the model's exact truth.
Related Tools
One-Touch Option
Computes the price of a one-touch option: it pays a fixed amount if the asset touches a barrier above the current price at any time before expiry, and nothing if it never touches. It's one of the most traded American binary options in the FX market, and its price is the risk-neutral probability of the price reaching the barrier, brought to present value. Enter the spot price, the barrier, the rate, the volatility, the term and the payout.
No-Touch Option
Computes the price of a no-touch option: it pays a fixed amount if the asset does NOT touch a barrier before expiry, and nothing if it touches. It's the opposite bet to the one-touch — you win as long as the price behaves and stays away from the barrier. The two are complementary: the sum of a one-touch and a no-touch with the same barrier is always the discounted payout. Enter the spot price, the barrier, the rate, the volatility, the term and the payout.
Down-and-Out Barrier Call
Computes the price of a down-and-out barrier call: an option that ceases to exist if the asset touches a barrier below the current price before expiry. Because of that knockout risk, it costs less than a plain call, and the difference is exactly the value of the down-and-in version. The Reiner-Rubinstein closed form holds for a barrier at or below the strike. Enter the spot price, the strike, the barrier, the interest rate, the term and the volatility.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.