Parameters
$62,000
$30k
$120k
65.0%
20%
130%
-15.0%
-60%
+80%
140 Days
30 Days
365 Days
$35,000
$100,000
Asymmetric Barrier Dynamics:
First-passage time (FPT) under Geometric Brownian Motion accounts for path dependency. The probability of touching a price level before expiry is strictly higher than ending at that level.
Log-Normal Price Probability Density (PDF)
Drag visual lines to adjust barriers
Touch < $35k Floor Probability
52.4%
Terminal Expiry < $35k: 18.2%
Touch > $100k Ceiling Probability
28.7%
Terminal Expiry > $100k: 12.1%
Asymmetric Barrier Skew Ratio
1.83x
Downside crash 1.83x more likely
Mode / Expected Price
$54,200
Expected Mean: $58,800
Export Probability Surface Artifacts
Download validated PDF/CDF grid calculations and barrier hit probabilities.