SPDE Monte Carlo Simulator

A Python package for simulating various stochastic partial differential equations commonly used in financial modeling. https://huggingface.co/time-series-foundation-models/Lag-Llama

Features

• Geometric Brownian Motion (GBM)
• Heston Model
• Cox-Ingersoll-Ross (CIR) Model
• Ornstein-Uhlenbeck (OU) Process
• Merton Jump Diffusion (MJD) Model

Installation

poetry install

Usage

from spde_mc_simulator import SPDEMCSimulator

# Initialize simulator
simulator = SPDEMCSimulator(
    symbol='AAPL',
    start_date='2022-01-01',
    end_date='2022-03-01',
    dt=1,
    num_paths=1000,
    eq='gbm'
)

# Run simulation
simulator.download_data()
simulator.set_parameters()
simulator.simulate()
simulator.plot_simulation()

Models

Geometric Brownian Motion (GBM)

Standard model for stock price movements assuming log-normal distribution.

Heston Model

Stochastic volatility model that captures volatility clustering.

Cox-Ingersoll-Ross (CIR)

Mean-reverting square-root process, commonly used for interest rates.

Ornstein-Uhlenbeck (OU)

Mean-reverting process useful for modeling mean-reverting financial quantities.

Merton Jump Diffusion (MJD)

Extends GBM with jump components to capture sudden price movements.

License

MIT