Probability Touch Calculator
Calculate the probability that the underlying price touches a barrier level at least once before option expiry. Based on Black-Scholes; essential for managing out-of-the-money and barrier option risk.
Upper barrier (above spot)
Chance that price reaches $110.00 at least once before expiry
Formula uses the Black-Scholes (GBM) framework and the reflection principle for a single barrier. Higher volatility and longer time to expiry increase touch probability.
What is Probability of Touch?
Probability of touch is the chance that the underlying asset's price reaches (or crosses) a specific barrier level at least once before option expiration. For out-of-the-money (OTM) options, this tells you how likely the price is to reach your strike or a target level before expiry—critical for managing risk on naked options, barrier options, and touch binaries.
How to Use This Calculator
- Spot Price: Current price of the underlying (e.g. stock or index).
- Barrier Price: The level you want to know "touch" probability for. Above spot = upper barrier; below spot = lower barrier.
- Time to Expiration: Days, months, or years until expiry.
- Volatility: Annualized volatility (e.g. from implied volatility or historical).
- Risk-Free Rate & Dividend Yield:Optional; improve accuracy for equities.
Why Use Our Probability Touch Calculator?
Our tool uses the same Black-Scholes (geometric Brownian motion) assumptions as standard option pricing, with a closed-form formula derived from the reflection principle for a single barrier. All calculations run in your browser—no server round-trip—so you get instant results. Use it to gauge OTM option risk, barrier option likelihood, or the chance a target price is hit before expiry.
Frequently Asked Questions
What model is used?
The calculator uses the Black-Scholes (GBM) framework and the reflection principle for a single barrier. The formula is a standard closed-form result for "probability of touching H (or B) before time T" under risk-neutral drift.
Does it work for American options?
The result is the probability that the price path touches the barrier at least once before expiry. It does not assume early exercise; it is path-based and applies to European-style barrier logic and OTM risk assessment.
Why is volatility important?
Higher volatility increases the chance that price reaches the barrier before expiry. Volatility is the main driver of touch probability after time to expiration.
Disclaimer: This calculator is for educational and informational purposes only. Results are based on the Black-Scholes model and may not reflect real-world prices or probabilities. Options and derivatives involve risk; consult a qualified advisor before trading.
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