Price Range Probability Estimator
Assuming a random walk (normal-approximation log returns, zero drift), estimate the probability the price stays inside or leaves a range from spot, annual volatility and days.
Results
Fill in the inputs and click Calculate.
- Below Lower Bound
- –
- Inside Range
- –
- Above Upper Bound
- –
- Horizon Volatility
- –
Risk disclaimer
The normal random-walk assumption understates extreme moves; nothing here promises returns or direction.
How should I read this?
For a given volatility, longer horizons widen the distribution — prices are more likely to leave a nearby band.
This is a statistical approximation, not a price forecast, and it says nothing about direction.
How to use
- Enter the current price and annualized volatility (%).
- Enter the horizon in days.
- Enter the lower and upper bounds of the range.
- Click Calculate for the probabilities below, inside and above the range.
Estimation formula
- Horizon volatility = annual vol × √(days ÷ 365)
- Convert prices to log returns and use the standard normal distribution
- Probability inside = Φ(upper) − Φ(lower), where Φ is the normal CDF
Example
Assume spot 100, 60% annual vol, 30 days, range 90–110 → inside ≈ 44.0%, below ≈ 27.0%, above ≈ 29.0%.
Higher volatility or longer horizons shrink the inside probability.
FAQ
Why might the probabilities not sum to 100%?
Below/inside/above should sum to 100% (rounding may differ by 0.1); use the three to cross-check.
Is this a forecast?
No. It assumes log-normal random-walk returns; real prices jump and have fat tails. Use it for risk intuition only.