financial-asset-dynamics

Financial Asset Dynamics Modeling

A Python project for exploring, implementing, and applying Stochastic Differential Equations (SDEs) for modeling financial asset dynamics.

Features

• Implementation of Geometric Brownian Motion (GBM)
• Implementation of Ornstein-Uhlenbeck (OU) process
• Advanced simulation methods (Euler-Maruyama, Milstein)
• Parameter calibration from historical data
• Correlated asset simulation
• Jump diffusion modeling (optional)

Installation

1. Clone this repository:

   git clone <repository-url>
   cd sde_asset_modeling
   

2. Create a virtual environment (optional but recommended):

   python -m venv venv
   source venv/bin/activate  # On Windows: venv\Scripts\activate
   

3. Install dependencies:

   pip install -r requirements.txt
   

4. Install the package in development mode:

   pip install -e .
   

Project Structure

• data/: Directory for storing raw or processed data
• notebooks/: Jupyter notebooks for exploration and presentation
• src/sde_asset_modeling/: Main source code
  • models/: SDE model definitions
  • simulation/: Simulation schemes
  • calibration/: Parameter estimation methods
  • utils/: Utility functions
• tests/: Unit tests

Usage

The project is organized as a series of Jupyter notebooks that demonstrate each aspect of SDE modeling:

1. 01_GBM_Simulation.ipynb: Basic simulation of GBM
2. 02_OU_Simulation.ipynb: Basic simulation of OU process
3. 03_Milstein_Comparison.ipynb: Comparison of simulation methods
4. 04_Calibration.ipynb: Parameter estimation from real data
5. 05_Correlated_Simulation.ipynb: Simulation of correlated assets
6. 06_Jump_Diffusion.ipynb: Optional extension for jump diffusion modeling

License

MIT License

SDE Asset Modeling - Directory Structure

This project is organized into the following structure to keep simulations, dashboards, and plots separate and well-organized.

Directory Structure

sde_asset_modeling/
├── simulations/           # Simulation scripts for each model
│   ├── gbm_simulation.py  # Geometric Brownian Motion
│   ├── ou_simulation.py   # Ornstein-Uhlenbeck process
│   ├── jump_diffusion_simulation.py
│   ├── heston_simulation.py
│   ├── sabr_simulation.py
│   └── correlated_simulation.py
│
├── dashboards/            # Dashboard creation scripts
│   ├── gbm_dashboard.py
│   ├── ou_dashboard.py
│   ├── jump_diffusion_dashboard.py
│   ├── heston_dashboard.py
│   ├── sabr_dashboard.py
│   └── correlated_dashboard.py
│
├── plots/                 # Generated plots organized by model
│   ├── gbm/               # GBM simulation plots
│   ├── ou/                # OU process plots
│   ├── jump_diffusion/    # Jump Diffusion model plots
│   ├── heston/            # Heston model plots
│   ├── sabr/              # SABR model plots
│   └── correlated/        # Correlated assets plots
│
├── src/                   # Core implementation code
│   └── sde_asset_modeling/
│       ├── models/        # SDE model implementations
│       ├── simulation/    # Simulation engines and numerical methods
│       └── utils/         # Utility functions
│
├── notebooks/             # Jupyter notebooks for analysis
├── tests/                 # Unit tests
└── data/                  # Data files

Running Simulations

To run a simulation for a specific model, use the corresponding script in the simulations/ directory:

python simulations/gbm_simulation.py  # Run GBM simulation

Creating Dashboards

To create a dashboard for a specific model, use the corresponding script in the dashboards/ directory:

python dashboards/gbm_dashboard.py  # Create GBM dashboard

Each dashboard script will check if the required plots exist and run the simulation if needed.

Model Overview

1. Geometric Brownian Motion (GBM)
   • Standard model for stock price movements
   • Constant drift and volatility
2. Ornstein-Uhlenbeck (OU) Process
   • Mean-reverting stochastic process
   • Used for interest rates, volatility, and spread modeling
3. Jump Diffusion (Merton) Model
   • GBM with added discrete jumps
   • Captures market shocks and sudden price changes
4. Heston Stochastic Volatility Model
   • Extends GBM with stochastic volatility
   • Captures volatility clustering and smile effects
5. SABR Model
   • Stochastic Alpha Beta Rho model
   • Used for interest rate derivatives and volatility smile
6. Correlated Assets Model
   • Multi-asset simulation with correlation structure
   • Used for portfolio analysis and diversification studies