Optimal Execution Model with Stochastic Control

A Python implementation of stochastic control for optimal execution models, incorporating real financial data from yfinance. This project calculates the optimal trade execution path for any given equity, taking into account market impact, liquidity, and stochastic price movements.

Table of Contents

• Introduction
• Features
• Theory and Background
• Installation
• Usage
• Example
• Project Structure
• Dependencies
• Contributing
• License
• Acknowledgments

Introduction

This project implements an optimal execution strategy for trading large orders in financial markets. It uses stochastic control techniques, specifically within the Almgren-Chriss framework, to minimize the expected cost and risk associated with executing a large order over a finite time horizon.

The model accounts for:

• Market Impact Costs: Temporary and permanent impacts due to trading.
• Timing Risk: The risk of adverse price movements while executing the order.
• Liquidity Profiles: Adjusting trading strategies based on intraday volume patterns.
• Real Market Data: Incorporating historical and real-time data fetched via yfinance.

Features

• Fetch historical and intraday market data for any equity using yfinance.
• Estimate model parameters dynamically based on fetched data.
• Calculate optimal trading trajectories using stochastic control.
• Simulate price paths and execution costs with enhanced market impact modeling.
• Adjust trading strategies based on intraday liquidity profiles.
• Modular codebase for easy extension and maintenance.
• Visualization of execution costs and trading trajectories.
• Placeholder for integration with broker APIs for real-market execution.

Theory and Background

The project is based on the Almgren-Chriss model for optimal execution, which balances the trade-off between market impact costs and timing risk. The model formulates a stochastic control problem, aiming to minimize the expected execution cost plus a risk penalty.

Key components include:

• Optimal Trading Trajectory: Determined by solving the Hamilton-Jacobi-Bellman (HJB) equation.
• Market Impact Modeling: Incorporates both temporary and permanent impacts, potentially using nonlinear functions.
• Stochastic Price Dynamics: Asset prices modeled as stochastic processes (e.g., geometric Brownian motion).
• Liquidity and Volume Profiling: Adjusting strategies based on historical intraday volume patterns.

For detailed mathematical formulations and derivations, please refer to the Almgren-Chriss framework.

Installation

1. Clone the repository from GitHub.

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

3. Install the required packages using pip and the requirements.txt file.

   • Note: If requirements.txt is not available, manually install dependencies.

Usage

Run the main script optimal_execution.py.

The program will prompt you for input:

• Ticker Symbol: The stock symbol (e.g., AAPL).
• Start Date: The start date for fetching historical data (format YYYY-MM-DD).
• End Date: The end date for fetching historical data (press Enter for today's date).
• Total Shares to Trade: The total number of shares you wish to buy or sell.
• Trading Horizon: The time horizon over which you want to execute the order (in days).
• Number of Time Steps: The number of intervals within the trading horizon (e.g., 390 for minute-by-minute trading).
• Risk Aversion Parameter: A parameter that balances cost vs. risk (e.g., 1e-6).
• Temporary Impact Coefficient (( \eta )): Press Enter to estimate or provide a value.
• Market Impact Exponent (( \gamma )): Press Enter for linear impact or provide a value (e.g., 0.5).
• Number of Simulation Paths: The number of simulations to run (e.g., 1000).

After entering the required information, the program will:

• Fetch market data and estimate model parameters.
• Calculate the optimal trading trajectory.
• Simulate price paths and calculate execution costs.
• Display the average execution cost and its standard deviation.
• Plot the distribution of execution costs and the optimal trading trajectory.

Example

Here's an example interaction:

• Enter the ticker symbol: AAPL
• Enter the start date for historical data: 2020-01-01
• Enter the end date for historical data: (press Enter)
• Enter the total shares to trade: 500000
• Enter the trading horizon in days: 1.0
• Enter the number of time steps: 390
• Enter the risk aversion parameter: 1e-6
• Enter the temporary impact coefficient eta: (press Enter)
• Enter the market impact exponent gamma: 0.7
• Enter the number of simulation paths: 1000

After processing, the program will output results and display plots.

Project Structure

• optimal_execution.py: Main script to run the program.
• market_data.py: Module for data fetching and processing.
• parameter_estimator.py: Module for parameter estimation.
• optimal_execution_model.py: Module for calculating optimal trajectories.
• simulation_engine.py: Module for simulations.
• execution_engine.py: Placeholder module for real-market execution.
• requirements.txt: List of dependencies.
• README.md: Project documentation.

Dependencies

• Python 3.7 or higher
• numpy
• pandas
• yfinance
• matplotlib
• scipy

Install dependencies using the requirements.txt file.

Contributing

Contributions are welcome! Please follow these steps:

1. Fork the repository.

2. Create a new branch for your feature or bug fix.

3. Commit your changes.

4. Push to the branch.

5. Create a new Pull Request.

Please ensure that your code follows best practices and includes appropriate tests.

License

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

Acknowledgments

• Almgren, R., & Chriss, N. (2000). Optimal execution of portfolio transactions. Journal of Risk, 3(2), 5-39.
• The open-source community and contributors to the libraries used in this project.

---