GPU-Accelerated American Option Pricing

📄 Papers Overview

This repository contains the implementation of GPU-accelerated American option pricing models based on two research papers:

1. Using the Graphics Processing Unit to Evaluate American-Style Derivatives
   • Published in The Journal of Financial Data Science (JFDS)
   • Authors: Leon Xing Li, Ren-Raw Chen
   • This paper explores the use of GPU computing for American option pricing, leveraging Monte Carlo simulations (MCS) and Particle Swarm Optimization (PSO) to efficiently solve free-boundary PDEs. The approach achieves significant performance gains over CPU-based methods, making it ideal for exotic derivatives and large financial portfolios.
2. GPU-Accelerated American Option Pricing: The Case of the Longstaff-Schwartz Monte Carlo Model
   • Published in The Journal of Derivatives (JOD)
   • Authors: Leon Xing Li, Ren-Raw Chen, Frank J. Fabozzi
   • This paper implements the Longstaff-Schwartz Monte Carlo (LSMC) model on GPUs, addressing computational challenges such as instability in basis function selection. It optimizes regression calculations for high-performance Single Instruction Multiple Data (SIMD) processing, enabling fast and accurate American option pricing.

The repository provides code implementations for evaluating American-style derivatives using GPU computing, with a focus on Monte Carlo simulation (MCS), Particle Swarm Optimization (PSO), and the Longstaff-Schwartz Monte Carlo (LSMC) method.

🚀 Features

• Parallelized Monte Carlo Simulations: Efficiently handles large-scale option pricing using GPU acceleration.
• Particle Swarm Optimization (PSO): Computes the early exercise boundary for American options.
• LSMC Model with Stability Enhancements: Implements regression adjustments to prevent numerical instability.
• Cross-Platform Compatibility: Built with OpenCL for portability across different GPU architectures (NVIDIA, AMD, Apple M Series).
• Python + PyOpenCL: Integrates GPU computation within Python for easy experimentation.

📊 Key Contributions

• Monte Carlo Simulation & PSO on GPU: Utilization of PyOpenCL to accelerate American option pricing via Monte Carlo simulations and PSO.
• Longstaff-Schwartz Monte Carlo on GPU: Implementation of the LSMC approach using OpenCL, with optimizations for numerical stability and parallel efficiency.
• Performance Benchmarks: Comparison between CPU and GPU implementations, demonstrating significant speed improvements using GPU computing.
• Hardware-Agnostic Design: Adoption of OpenCL for cross-platform GPU acceleration, supporting both Nvidia and non-Nvidia GPUs.

⚙️ Implementation Details

1. American Option Pricing using Monte Carlo Simulation & PSO

• Objective: Solve the free-boundary PDE problem for American options.
• Methodology:
  • Monte Carlo simulation for stock price paths.
  • Particle Swarm Optimization (PSO) to identify early exercise boundaries.
  • OpenCL-based parallelization for GPU acceleration.
• Performance: Achieves up to 300x speed improvement over CPU-based approaches.

2. GPU-Accelerated Longstaff-Schwartz Monte Carlo (LSMC) Method

• Objective: Enhance LSMC efficiency using GPU computing.
• Methodology:
  • Regression-based continuation value estimation.
  • Basis function optimization for numerical stability.
  • Matrix operations (transpose, inversion, multiplication) implemented in OpenCL.
• Performance: GPU-optimized regression computations reduce instability while maintaining speed improvements.

🛠 Installation

To run the implementations, install the required dependencies:

pip install numpy scipy pyopencl matplotlib

🧩 Usage

Run the model for American option pricing:

cd src

python3 American_option.py

📜 Citations

If you use this code, please cite the following papers:

Li, L. X., & Chen, R. R. (2023). Using the Graphics Processing Unit to Evaluate American-Style Derivatives. Journal of Financial Data Science.

Li, L. X., Chen, R. R., & Fabozzi, F. J. (2024). GPU-Accelerated American Option Pricing: The Case of the Longstaff-Schwartz Monte Carlo Model. Journal of Derivatives.

📧 Contact

For questions or collaborations, please contact Leon Xing Li at leonchao@yeah.net.

📝 License

MIT License - See LICENSE for details.