GBMSimulator

GBMSimulator is a Python class designed to simulate Geometric Brownian Motion (GBM), a stochastic process widely used in mathematical finance for modeling stock prices and other financial instruments.

Features

• Simulates GBM paths given user-defined parameters.
• Supports customizable drift, volatility, initial value, number of paths, and time steps.
• Returns an array of simulated paths, which can be easily visualized or analyzed.

Installation

Ensure you have Python 3.12 or higher. You can install the package and its dependencies from source with:

pip install -e .

or from PyPi with:

pip install GBMSimulator==0.0.2

Usage

Please also refer to Examples/GBMnotebook.ipynb

1. Import the GBMSimulator class and matplotlib for plotting

from GBMSimulator.GBMSimulator import  GBMSimulator
import matplotlib.pyplot as plt

2. Set the parameters for the GBMsimulator

'''
Args:
    mu (int): drift coefficient
    n (int): number of steps
    T (int): time in years
    M (int): number of sims
    y0 (int): initial value
    sigma (int): volatility
'''
mu = 0.1
n = 100
T =  1
M = 1000
y0 = 0.01
sigma = 0.5

3. Create an instance of GMBSimulator

simulator = GBMSimulator()

4. Create an array of simulated paths

simulated_paths = simulator.simulate(mu, n, T, M, y0, sigma)

5. Plot the data

# template
plt.style.use('ggplot') 
# changing size of chart
plt.figure(figsize=(12, 5))

# Loop to do a line plot for each simulation
for num, sim in enumerate(simulated_paths.T):
    # length of each simulation
    t_values = list(range(len(sim)))
    # simulated values
    y_values = sim

    # line plot for each sim
    plt.plot(t_values, y_values, label=f"GBM path {num+1}")


# labelling chart
plt.xlabel("Time")
plt.ylabel("Y(t)")
plt.title("Simulated Geometric Brownian Motion Path")
if M <= 10:
    plt.legend()
else:
    plt.show()

Documentation

Visit our documentation page.

Contributing

Contributions are welcome! Fork our repository and submit a pull request.