profitable-expert-advisor/paper/simulations/README.md

Trading Strategy Simulations

This directory contains Python scripts for simulating and analyzing advanced trading techniques.

Scripts

1. martingale_simulation.py

Analyzes the statistical properties and risk of martingale strategies.

Key Analyses:

• Ruin probability calculations
• Position size growth
• Required capital analysis
• Monte Carlo simulations

Usage:

python martingale_simulation.py

Output:

• martingale_analysis.png: Comprehensive analysis plots
• Console output with statistics

2. trailing_stop_analysis.py

Compares fixed stop loss vs trailing stop loss performance.

Key Analyses:

• Return distribution comparison
• Sharpe ratio improvement
• Exit timing analysis
• Sample price path visualization

Usage:

python trailing_stop_analysis.py

Output:

• trailing_stop_analysis.png: Comparison plots
• Console output with performance metrics

3. partial_exit_analysis.py

Analyzes the statistical benefits of partial exits.

Key Analyses:

• Variance reduction calculation
• Sharpe ratio optimization
• Optimal exit percentage
• Return distribution comparison

Usage:

python partial_exit_analysis.py

Output:

• partial_exit_analysis.png: Analysis plots
• Console output with optimization results

4. grid_trading_analysis.py

Analyzes grid trading performance in different market conditions.

Key Analyses:

• Mean-reverting vs trending market performance
• Optimal grid spacing
• Trade frequency analysis
• Profit distribution

Usage:

python grid_trading_analysis.py

Output:

• grid_trading_analysis.png: Market condition comparison
• Console output with performance metrics

Installation

pip install -r requirements.txt

Running All Simulations

# Run all simulations
python martingale_simulation.py
python trailing_stop_analysis.py
python partial_exit_analysis.py
python grid_trading_analysis.py

Output Location

All figures are saved to ../figures/ directory:

• martingale_analysis.png
• trailing_stop_analysis.png
• partial_exit_analysis.png
• grid_trading_analysis.png

Mathematical Foundations

These simulations implement:

• Geometric Brownian Motion for price simulation
• Ornstein-Uhlenbeck process for mean-reverting prices
• Monte Carlo methods for statistical analysis
• Kelly Criterion for position sizing
• Sharpe ratio and other risk-adjusted metrics

Notes

• Simulations use random number generation - results may vary slightly between runs
• For reproducible results, set random seeds in scripts
• Adjust parameters in each script to match your trading conditions
• Results are illustrative - actual trading results will vary