Continuous-Time Stochastic Processes Library (CTSL)

This is a submission for the GitHub Copilot CLI Challenge

What I Built

Continuous-Time Stochastic Processes Library (CTSL) is a comprehensive Python library for simulating and analyzing continuous-time stochastic processes, with a focus on Geometric Brownian Motion (GBM) and Ornstein-Uhlenbeck (OU) processes.

The library provides:

• Exact Solutions: Closed-form analytical simulation of GBM
• Numerical Methods: Euler-Maruyama discretization
• Theoretical Analysis: Statistical moments and properties
• Convergence Validation: Law of Large Numbers testing
• Error Analysis: Discretization error comparison
• Statistical Metrics: Comprehensive analysis tools

Demo

GitHub Repository: https://github.com/CrazyLoveMachine/ctsl

Quick Start:

from exact_solutions import simulate_gbm_exact
from metrics import calculate_statistics

prices = simulate_gbm_exact(S0=100, mu=0.1, sigma=0.2, T=1.0, n_paths=10000)
stats = calculate_statistics(prices)
print(f"Mean: {stats['mean']:.2f}, Std Dev: {stats['stddev']:.2f}")

My Experience with GitHub Copilot CLI
GitHub Copilot CLI significantly accelerated my development:

Code Generation - Rapidly scaffolded statistical functions and numerical methods
Algorithm Implementation - Generated accurate stochastic differential equation solvers
Documentation - Wrote clear mathematical docstrings
Error Handling - Suggested robust validation patterns
Testing - Generated comprehensive examples and test cases
Performance - Optimized with vectorized NumPy operations
Impact: Reduced development time by 40-50%, allowing focus on mathematical correctness rather than syntax.
Project: https://github.com/CrazyLoveMachine/ctsl Submitted by: CrazyLoveMachine