Simulate the extrema of a geometric Brownian motion
Simulation parameters:
Paths: 1000000
Steps per path: 252
Log-return mean: 0.000000
Log-return std: 0.010000
Initial price: 100.0000
RNG seed: None
Batch size: 100000
Simulated 1000000 paths with 252 steps per path.
Summary statistics (Pandas dataframe):
mean median std min q1 q3 max
Maximum 113.3867 110.6745 11.3968 100.0000 104.5747 119.3459 221.3492
Minimum 89.0076 90.3753 8.1339 43.8623 83.7922 95.6354 100.0000
Terminal 101.2707 100.0191 16.1679 46.5662 89.8431 111.2831 219.0190
Probability initial price is path maximum: 3.5688%
Probability initial price is path minimum: 3.5363%
Zero-drift probability that initial price is path minimum: 3.5541%
Probability terminal price exceeds thresholds:
> 100.00: 50.0509%
> 104.00: 40.2749%