Simulated Stock Prices With Live Update

This script simulates stock prices over time using a GBM model with dynamically updating drift (mu) and volatility (sigma). The simulation inmates live stock price movements with Matplotlib, updating the x-axis and y-axis as the simulation progresses.

Features

• Dynamic Drift and Volatility:

  • The drift(mu) and volatility(sigma) evolve over time, simulating real-world market conditions where both can change dynamically.

• Real-Time Plot Update

  • The plot of simulated stock prices updates in real-tme, extending the x-axis and adjusting the y-axis as new prices are generated.

Components

fMu()

Generates a time-evolving drift (mu) using a mean-reverting Ornstein-Uhlenbeck process, which is commonly used to model stock returns reverting to a long-term mean.

Parameters:

• n_steps: Number of time steps in the simulation.
• mu_long_term: The long-term average value for the drift.
• mean_reversion_speed: The speed at which the drift reverts to the long-term mean.
• volatility_mu: Controls the volatility of the drift.

fSigma()

Generates a time-evolving volatility (sigma) using a random-walk process. The volatility fluctuates, and a lower bound is enforced to prevent it from becoming negative.

Parameters

• n_steps: Number of time steps in the simulation.
• sigma_base: The starting value of volatility.
• volatility_vol: The magnitude of fluctuations in volatility.

simulate_prices()

Simulates stock prices over time using GBM. The function updates stock prices based on dynamic my and sigma values generated by fMu() and fSigma().

Parameters:

• n: Number of simulation steps per call.
• k: Number of stock price realizations.
• mu: The drift values for each step.
• sigma: The volatility values for each step.
• delta_t: The time step size.

update()

Updates the plot with new stock prices for each frame in the animation.

Usage

Prerequisites

• Python 3.x
• Matplotlib for plotting and animation
• NumPy for numerical computations.

Run the script.

1. Run the script: python3 exec.py

The simulation will start, and you will see the stock prices being plotted live. The drift and volatility of the stock prices will change dynamically over time, creating a more realistic market simulation.

Customization

You can customize the parameters for drift and volatility fMu() and fSigma() functions to match different market conditions. For example: - Adjust mu_long_term for more bullish or bearish trends. - Changes volatility_mu or volatility_vol to simulate periods of high or low volatility.

License

This project is licensed under the MIT License - see the LICENSE file for details.