Brownian Motion Simulator

> PARAMETERS

[CONFIG]

Process_Type

Geometric (log-normal prices) or Standard (additive random walk).

Initial_Value (S₀)

Starting value of the process at t=0.

100.00

Drift (μ)

Expected return or trend component of the process.

0.0500

Volatility (σ)

Standard deviation of returns (diffusion coefficient).

0.2000

Time_Horizon (T)

Total duration to simulate.

1.00

Time_Steps (N)

Number of discrete intervals in the simulation.

252

Sim_Paths

Number of independent Monte Carlo paths to generate.

2000

Barrier_Conditions

Optional price levels that trigger events (knock-in/out placeholders).

Upper Barrier

Lower Barrier

/ COMPUTING_PATHS...

Model Definition: Geometric Brownian Motion (GBM) is defined by the SDE: dS_t = μS_t dt + σS_t dW_t. It assumes log-normally distributed prices and is the foundation for the Black-Scholes option pricing framework.

Awaiting Input

> Adjust parameters on left sidebar
> Click RUN_SIMULATION to generate paths

> PARAMETERS

Barrier_Conditions Optional price levels that trigger events (knock-in/out placeholders).

Awaiting Input

Barrier_Conditions

Optional price levels that trigger events (knock-in/out placeholders).